Badania w zakresie zaawansowanej infrastruktury sieci fotonicznych

Transcription

Zakład Teletransmisji i Technik Optycznych (Z-14)
Badania w zakresie zaawansowanej infrastruktury
sieci fotonicznych (COST-291)
Etap 1:
Badania nowych formatów modulacji
w systemach łączności optycznej
Praca nr 14310028
Warszawa, grudzień 2008
Badania w zakresie zaawansowanej infrastruktury sieci fotonicznych (COST-291)
Etap 1: Badania nowych formatów modulacji w systemach łączności optycznej
Praca nr 14310028
Słowa kluczowe (maksimum 5 słów):
Kierownik pracy: doc. dr hab. Marian Marciniak
Wykonawcy pracy:
dr inż. Marek Jaworski
spec. Hanna Skrobek
mgr inż. Olga Bolszo
mgr inż. Mariusz Zdanowicz
Kierownik Zakładu: doc. dr hab. Marian Marciniak
© Copyright by Instytut Łączności, Warszawa 2008
SPIS TREŚCI
1.
2.
Wprowadzenie..................................................................................................................... 4
Kompensacja nieliniowego szumu fazowego SPM dla przypadku granicznego................ 4
2.1
Detekcja PSK ............................................................................................................. 5
2.2
Detekcja DPSK .......................................................................................................... 7
2.3
Uzyskane wyniki symulacji ....................................................................................... 7
3. Nieliniowy szum fazowy indukowany modulacją skrośną XPM ..................................... 12
3.1
Model "pompa-sonda".............................................................................................. 13
3.2
Kaskadowe połączenie odcinków regeneracyjnych WDM...................................... 15
3.3
Prawdopodobieństwo błędu dla modulacji DPSK ................................................... 17
4. Wpływ szumu fazowego lasera na różnicową detekcję M-DPSK.................................... 17
5. Wpływ wewnątrz-kanałowego mieszania czterofalowego ............................................... 19
6. Podsumowanie .................................................................................................................. 20
7. Badanie efektywnych obliczeniowo metod symulacji propagacji sygnału
w światłowodzie................................................................................................................ 22
Bibliografia............................................................................................................................... 25
3
1.
Wprowadzenie
W sprawozdaniu przedstawiono wyniki prac prowadzonych w ramach Akcji COST 291
"Badania w zakresie zaawansowania infrastruktury sieci fotonicznych", objętych projektem
badawczym specjalnym pt."Badanie zaawansowanych formatów modulacji optycznej, metod
symulacji propagacji sygnału oraz mechanizmów zapewnienia jakości usług w sieciach
z grupową komutacją pakietów (OBS), stosowanych w optycznych sieciach
telekomunikacyjnych", w zakresie dotyczącym zadania 1 – "Badanie wielopoziomowych
formatów modulacji optycznej":
− etap 1: "Opracowanie modeli symulacji formatów modulacji i okreslenie ograniczeń
spowodowanych niedoskonałością poszczególnych elementów systemu"
− etap 2: "Weryfikacja opracowanych modeli"
Całość projektu realizowana jest w okresie 10.2006 – 01.2009. Niniejsze sprawozdanie
obejmuje rezultaty prac prowadzonych w I i II kwartale 2008 roku.
Zadanie realizowane jest w ramach grupy roboczej WG1 COST 291 – „Przetwarzanie
optyczne w sieciach cyfrowych” („Optical Processing for Digital Network Performance”).
Grupa robocza WG1 COST 291 zajmuje się, między innymi, charakterystykami
transmisyjnymi łączy optycznych w sieci WDM.
2.
Kompensacja nieliniowego szumu fazowego SPM dla przypadku granicznego
W poprzednim sprawozdaniu [6] (rozdział 3) przedstawiono statystyczne metody szacowania
wpływu zniekształceń nieliniowych spowodowanych efektem Kerra w systemach z modulacją
fazy. Przedmiotem analizy był system składający się z kaskadowego połączenia odcinków
regeneracyjnych, zawierających wzmacniacze optyczne, będące źródłem szumów ASE.
Poniżej przedstawiamy rozwinięcie tych metod, umożliwiające oszacowanie skuteczności
kompensacji nieliniowego szumu fazowego SPM. W pracy posłużyliśmy się modelem
opisanym w [4], rozszerzając jego funkcjonalność na analizę wielostanowych formatów
modulacji M-PSK i M-DPSK. Korzystając z opisanego modelu zrealizowano symulator
nieliniowego szumu fazowego, indukowanego szumem kaskady wzmacniaczy optycznych,
łącznie z modelem układu kompensacji tego nieliniowego szumu .
Nieliniowe przesunięcie fazy jest sumą składowych pochodzących od skończonej liczby
odcinków regeneracyjnych. Dla bardzo dużej liczby odcinków regeneracyjnych sumowanie
można zastąpić całkowaniem [7]. Taki ciągły model, z rozproszonym wzmocnieniem,
opisywany jest za pomocą stochastycznego procesu Wienera [1], [4]. Aby uprościć analizę
wprowadzana jest normalizacja, gdyż właściwości poszukiwanego rozkładu
prawdopodobieństwa nieliniowego przesunięcia fazy zależą tylko od dwóch parametrów:
stosunku mocy sygnału do szumu ρ s oraz średniego przesunięcia fazy Φ NL .
W rozpatrywanym procesie Wenera stosowana jest jednostkowa amplituda sygnału i
jednostkowa wariancja szumu
Zależność między zmienną losową Φ , stosowaną w analizie teoretycznej a rzeczywistym
nieliniowym przesunięciem fazy Φ NL jest następująca:
Φ NL
Φ.
(1)
1
ρs +
2
Dla systemów jednokanałowych możliwa jest częściowa kompensacja nieliniowego szumu
fazowy spowodowanego samomodulacją fazy (SPM), gdyż wartość średnia szumu fazy
Φ NL jest skorelowana z mocą sygnału PN .
Φ NL =
4
2.1 Detekcja PSK
Najprostszą metodą kompensacji jest zastosowanie korekcyjnego przesunięcia fazy o wartość
proporcjonalną do mocy chwilowej:
Φα = Φ − α R 2 = Φ − α Y ,
(2)
gdzie Φα jest odbieraną fazą po korekcji, Y mocą odbieranego sygnału, R jest jego
amplitudą pola elektrycznego, oraz α jest współczynnikiem proporcjonalności.
Jest to przykład kompensacji liniowej, gdyż występuje tu liniowa zależność między
wprowadzaną korekcją fazy a mocą Y. Dokładniejszą kompensację można uzyskać stosując
wielomian wyższego rzędu, lepiej dopasowany do korelacji między fazą a amplitudą
odbieranego sygnału.
Optymalizacja kompensacji liniowej polega na dobraniu wartości współczynnika α . Jako
kryterium można przyjąć minimalizację wariancji nieliniowego szumu fazowego po korekcji
lub minimalizację stopy błędów. To pierwsze podejście (zwane MMSE – Minimum Mean
Square Error) jest łatwiejsze do analizy teoretycznej, a jednocześnie daje zadowalające
rezultaty w praktyce. Drugie podejście (zwane ML – Minimum Likelihood) jest trudne do
analizy teoretycznej i w większości przypadków nie znajduje praktycznego zastosowania.
Wartość średnia fazy sygnału po korekcji wyznaczana jest jako pochodna funkcji
charakterystycznej [4]:
Φα = − j
d
1
Ψ Φα ( v ) = ρ s + − α ( ρ s + 1)
dv
2
v =0
(3)
Wariancja fazy sygnału po korekcji wyznaczana jest jako różnica drugiej pochodnej funkcji
charakterystycznej i kwadratu średniej [4]:
σ Φ2 α = −
d2
Ψ Φα ( v ) − Φα
dv 2
v =0
2
=
2
1
1⎞
⎛
ρ s + − 2 ⎜ ρ s + ⎟ α + ( 2 ρ s + 1) α 2 .
3
6
3⎠
⎝
(4)
Minimalną wartość wariancji znajdujemy szukając miejsca zerowego pochodnej wyrażenia
(4), dσ Φ2 α dα = 0 :
α mse =
1 ρ s + 13
.
2 ρ s + 12
(5)
Dla dużego odstępu sygnał/szum α mse → 1 2 . Dla optymalnie dobranego współczynnika α mse
wartość średnia i wariancja nieliniowej fazy po korekcji wynoszą odpowiednio:
Φα mse =
σα
2
mse
1 ρ s2 + 23 ρ s + 16
,
ρ s + 12
2
(6)
1 ρ s2 + ρ s + 16
=
.
6 ρ s + 12
(7)
W [4] wyznaczono również funkcję charakterystyczną rozkładu prawdopodobieństwa
odbieranej skompensowanej fazy, potrzebną do wyznaczenia stopy błędów:
⎛ m Φ NL
m Φ NL
⎞
m
Ψ Φcm ( m ) = Ψ Φ ,Y ,Θn ⎜ −
,
α
,
⎟
1
ρ s + 12
⎝ ρs + 2
⎠
(8)
gdzie:
Ψ Φ ,Y ,Θn ( v, ω , m ) = Ψ Φ ( v )
π γ 3/2ω
v,
2γ v
γ
⎛
exp ⎜ −γ v + v ,ω
2
⎝
5
⎞⎡
⎛ γ v ,ω
⎟ ⎢ I m −1 ⎜
⎠⎣ 2 ⎝ 2
⎞
⎛ γ v ,ω
⎟ + I m +1 ⎜
⎠
2 ⎝ 2
⎞⎤
⎟⎥
⎠⎦
(9)
jest wspólną funkcją charakterystyczną nieliniowego szumu fazy, amplitudy sygnału i fazy
szumu wzmacniacza, oraz:
γv =
γ v ,ω =
(
2 jv
(
)
sin 2 jv
2 jv
jv − jω tan
ρs ,
(10)
) (
jv sin 2 jv
)
ρs ,
(11)
Ψ Φ ( jν ) = sec jν exp ⎡⎣ ρ s jν tan jν ⎤⎦ .
(12)
Prawdopodobieństwo błędnego odebrania sygnału dla detekcji synchronicznej PSK wynosi:
pe = 1 − ∫
π
2
−θc
− π2 −θ c
pΦcm (θ ) dθ ,
(13)
gdzie ± π − θ c stanowi progowe wartości fazy, a θ c jest jej wartością średnią, stąd
2
korzystając z rozwinięcia funkcji charakterystycznej Ψ Φcm ( m ) w szereg Fouriera,
otrzymujemy:
1 2 ∞ ( −1)
− j 2 k +1 θ
pe = − ∑
ℜ Ψ *Φcm ( 2k + 1) e ( ) c ,
2 π k = 0 2k + 1
k
{
}
(14)
gdzie:
Ψ
*
Φ cm
( 2k + 1) =
π r 3/2
ω
k,
2rk
r ⎞
⎡ ( 2k + 1) Φ NL ⎤ ⎡ ⎛ rk ,ω ⎞
⎛
⎛ rk ,ω ⎞ ⎤
exp ⎜ − rk + k ,ω ⎟ Ψ Φ ⎢
⎥ ⎢ Ik ⎜
⎟ + I k +1 ⎜
⎟ ⎥ , (15)
1
2 ⎠
ρs + 2
⎝
⎝ 2 ⎠⎦
⎣
⎦⎣ ⎝ 2 ⎠
oraz:
2 j
( 2k + 1)
ρ s + 12
ρs ,
⎛
2k + 1) Φ NL ⎞
(
⎟
sin ⎜ 2 j
1
⎜
⎟
ρ
+
s
2
⎝
⎠
rk
=
( 2k + 1) Φ NL tan ⎛⎜ j ( 2k + 1) Φ NL
1+ α j
⎜
ρ s + 12
ρ s + 12
⎝
rk =
rk ,ω
Φ NL
(16)
⎞
⎟
⎟
⎠
.
(17)
Aby kryteria optymalizacji MMSE były spełnione, należy przyjąć α = α mse oraz
θ c = Φ RES =
Φ NL
Φ
.
ρ s + 12 α mse
(18)
Jeśli zakładamy niezależność nieliniowego szumu fazy i szumu wzmacniaczy, to zależność
(18) upraszcza się do postaci:
1
⎛ ρ ⎞ ρ s ∞ ( −1) ⎡ ⎛ ρ s
pe ≈ − exp ⎜ − s ⎟
∑
⎢ Ik ⎜
2
⎝ 2 ⎠ π k = 0 2k + 1 ⎣ ⎝ 2
k
⎧⎪
⎡ ( 2k + 1) Φ NL ⎤ − j ( 2 k +1) Φ RES
×ℜ ⎨Ψ Φα ⎢
⎥e
mse
⎪⎩
⎣ ρs + 1 2 ⎦
6
⎫⎪
⎬
⎪⎭
⎞
⎛ ρs ⎞⎤
⎟ + I k +1 ⎜ ⎟ ⎥
⎠
⎝ 2 ⎠⎦
.
(19)
Zależność (19) uogólniamy dla dowolnego formatu różnicowej detekcji M-DPSK
z M-stanowym kluczowaniem fazy:
⎡
1
⎛ ρ s ⎞ ρ s ∞ sin ( mπ M ) ⎡
⎛ ρs
⎢1 − − exp ⎜ − ⎟
∑
⎢ I m −1 ⎜
m
⎝ 2 ⎠ π m =1
⎣ 2 ⎝ 2
1
⎢ M
pe ≈
log 2 ( M ) ⎢ ⎧⎪
⎛ m Φ NL ⎞ − jm Φ RES ⎫⎪
⎢×ℜ Ψ
⎨
⎬
⎟e
Φα mse ⎜
⎢
⎝ ρs + 1 2 ⎠
⎭⎪
⎣ ⎩⎪
⎞
⎛ ρs
⎟ + I m +1 ⎜
⎠
2 ⎝ 2
⎞⎤ ⎤
⎟⎥ ⎥
⎠⎦ ⎥
⎥ , (20)
⎥
⎥
⎦
gdzie M jest liczbą stanów symbolu. Czynnik 1 log 2 ( M ) wynika z faktu, że przy
kodowaniu Graya błąd symbolu pociąga za sobą przekłamanie tylko jednego z log 2 ( M )
bitów informacji.
2.2 Detekcja DPSK
Dla detekcji różnicowej DPSK z kompensacją, faza różnicowa wynosi:
∆Φ cm = Φ cm ( t ) − Φ cm ( t − T ) = Θ n ( t ) − Φ RES ( t ) − Θ n ( t − T ) + Φ RES ( t − T )
(21)
gdzie T jest czasem trwania bitu. Fazy w momentach t i t − T są niezależnymi zmiennymi
losowymi o identycznym rozkładzie. Suma dwóch zmiennych losowych posiada funkcję
charakterystyczną będącą iloczynem funkcji charakterystycznych tych funkcji, stąd:
p∆Φcm (θ ) =
2
1 1 ∞
+ ∑ Ψ Φcm ( m ) cos ( mθ ) .
2π π m =1
(22)
Rozkład prawdopodobieństwa p∆Φcm (θ ) jest symetryczny względem θ = 0 .
Prawdopodobieństwo błędu obliczane jest z ogólnej zależności:
pe = 1 − ∫
π 2c
−π 2
p∆Φcm (θ ) dθ .
(23)
Przy założeniu niezależności zmiennych losowych Θn i Φ NL prawdopodobieństwo błędu
można aproksymować zależnością:
1 ρ s e− ρs
pe ≈ −
2
2
( −1)
k
⎡ ⎛ ρs ⎞
⎛ρ
I k ⎜ ⎟ + I k =1 ⎜ s
∑
⎢
⎝ 2 ⎠
⎝ 2
k = 0 2k + 1 ⎣
∞
2
⎡ ( 2k + 1) Φ NL ⎤
⎞⎤
⎥ .
⎟ ⎥ Ψ Φαmse ⎢
⎠⎦
⎣ ρs + 1 2 ⎦
2
(24)
Zależność (24) uogólniamy dla dowolnego formatu różnicowej detekcji M-DPSK
pe, ∆f L
⎡
1 σ e −σ s ∞ sin ( mπ M ) ⎡
⎛σs ⎞
⎛σs
⎢1 − − s
∑
⎢ I m −1 ⎜ ⎟ + I m −1 ⎜
2 m =1
m
⎢ M
2 ⎝ 2
⎣ 2 ⎝ 2 ⎠
1
=
⎢
2
log 2 ( M ) ⎢
⎛ m Φ NL ⎞
⎟
⎢× Ψ Φαmse ⎜
⎢⎣
⎝ ρs + 1 2 ⎠
2
⎞⎤ ⎤
⎟⎥ ⎥
⎠⎦ ⎥
⎥,
⎥
⎥
⎥⎦
(25)
bitów informacji.
2.3 Uzyskane wyniki symulacji
Bazując na modelu (37) przedstawionym w sprawozdaniu [6] zrealizowano symulator
nieliniowych zniekształceń fazy spowodowanych szumem kaskady wzmacniaczy optycznych,
7
w którym generowany jest szum fazowy skorelowany z szumem amplitudowym
wzmacniaczy. Dodatkowo wzmacniacze są również źródłem szumu fazowego (liniowego).
Tak skonstruowany sygnał poddawany jest detekcji synchronicznej PSK lub różnicowej
DPSK. W symulatorze obliczana jest bitowa stopa błędów transmisji bitów (BER) lub
symboli (SER). Ze względu na stosowaną metodę Monte-Carlo dolnym pułapem
uzyskiwanych wartości jest BER = 10-6. Wiarygodny wynik na tym poziomie BER uzyskuje
się przy 107 powtórzeń [5]. Ze względu na stosowane obecnie powszechnie kodowanie z
detekcją błędów (kod Reeda-Solomona) przed detekcją blokową, poziom BER = 10-6 jest
akceptowalny w praktyce.
Działanie symulatora zostało zweryfikowane najpierw dla systemów PSK i DPSK bez
korekcji nieliniowości fazy, poprzez porównanie uzyskiwanych charakterystyk BER w
funkcji stosunku sygnału do szumu dla różnych mocy sygnału, a co za tym idzie dla różnych
wartości nieliniowego szumu fazy, z zależnościami teoretycznymi (68), (70), (72),
przedstawionymi w sprawozdaniu [6]. Uzyskano dobrą zgodność teorii z symulacją, zarówno
dla detekcji synchronicznej PSK i różnicowej DPSK (rys. 1).
Następnie symulator wyposażono w moduł kompensacji liniowej MMSE, w którym
wykorzystywane są zależności przedstawione w punkcie 2.1. Zweryfikowano skuteczność
kompensacji, porównując wyniki symulacji z zależnościami teoretycznymi (14) i (19) dla
detekcji synchronicznej i (24) dla detekcji DPSK. Uzyskano dobrą zgodność wyników
symulacji i teorii (rys. 1).
DPSK
PSK
Rys. 1. Symulowana (punkty) i obliczona teoretycznie zależność stopy błędów transmisji
od stosunku sygnału do szumu dla modulacji PSK i DPSK z kompensacją nieliniowych
zniekształceń fazy (linia przerywana) i bez kompensacji dla Φ NL = 1, 4 rad .
8
W następnym etapie przystosowano symulator do detekcji formatów wielopoziomowych
(M-PSK i M-DPSK) i przeprowadzono serię symulacji dla detekcji M-PSK i M-DPSK (dla
M = 2, 4, 8, 16, 32, 64).
Mając materiał do porównań zmodyfikowano zależności (19) i (24), określające BER dla
detekcji PSK i DPSK, uogólniając je dla dowolnego M (20) i (25). Dla modulacji PSK jest to
stosunkowo proste, gdyż wykorzystać można symetryczność konstelacji kodowej względem
środka układu współrzędnych. Wszystkie punkty kodowe mają w tym przypadku identyczne
własności szumowe.
Uzyskane wyniki potwierdzają słuszność przyjętych założeń teoretycznych.
W tym miejscu pojawił się jednak problem ze zbieżnością obliczeń nieskończonego
szeregu w wyrażeniach (14), (19), (20), (24), (25). Stosowane jest tu sumowanie na przemian
dodatnich i ujemnych wartości zmodyfikowanej funkcji Bessela pierwszego rodzaju
i kolejnych rzędów. Utworzona w ten sposób suma powinna mieć wartość nieznacznie
mniejszą niż 1 − 1 M , gdyż obliczana stopa błędów jest właśnie różnicą między tą wartością a
1 − 1 M . Taka metoda wyznaczania stopy błędu powoduje, że: po pierwsze, uzyskiwane
wartości w optymalnych warunkach – dla małego ρ s , są dokładne co najwyżej do poziomu
BER = 10-12, a po drugie dla dużych wartości ρ s nie uzyskuje się w ogóle zbieżności
obliczeń, ze względu na przekroczenie zakresu liczb podwójnej precyzji w procesorze.
Sprowadzono do tej pory implementację zmodyfikowanej funkcji Bessela pierwszego rodzaju
w dostępnych programach obliczeniowych: LabView, Mathematica i Matlab, nie uzyskując
zadowalającego rezultatu. Konieczna jest w tym przypadku dokładniejsza analiza przyczyn
braku stabilności obliczeń i zastosowanie odpowiedniego algorytmu [2].
W symulatorze zastosowano z konieczności skończoną liczbę N A wzmacniaczy będących
źródłem szumu, podczas gdy w analizie teoretycznej znacznie łatwiej posługiwać się
modelem granicznym (ciągłym), w którym szumy rozłożone są w sposób ciągły wzdłuż linii
transmisyjnej – odpowiada to, innymi słowy, nieskończonej liczbie wzmacniaczy [3].
Zbadano jaka jest wystarczająca liczba wzmacniaczy (źródeł szumu) by błąd symulacji był
pomijalnie mały. Okazuje się, że już dla N A = 32 różnica jest praktycznie niezauważalna
(ginie w szumach metody), dlatego wszystkie symulacje przeprowadzano dla takiej właśnie
liczby wzmacniaczy.
Uzyskiwany zasięg transmisji zależy głównie od właściwości szumowych wzmacniaczy.
Zależność między współczynnikiem szumów wzmacniacza FE a współczynnikiem inwersji
G −1
≈ 2nsp , gdzie GE >> 1 jest wzmocnieniem. Typowa
nsp jest następująca: FE = 2nsp E
GE
wartość współczynnika inwersji wynosi nsp = 1, 41 , co odpowiada współczynnikowi szumów
FE = 4,5dB . Całkowita moc szumów dla linii o długości L , tłumienności α = 0,25 dB/km i
paśmie optycznego kanału ∆vopt = 42,7 GHz, wynosi:
σ 2 = 2hν nsp ∆voptα L .
(26)
Dla takiego ciągłego modelu wartość średnia nieliniowego przesunięcia fazy wynosi
Φ NL = Pγ L ,
(27)
gdzie P jest mocą sygnału oraz γ = 1,2 1/(W·km) jest współczynnikiem nieliniowości.
Dla wyżej określonych danych wejściowych przeprowadzono symulację mającą na celu
określenie maksymalnego zasięgu transmisji dla systemów M-PSK i M-DPSK (dla
M = 2, 4, 8, 16, 32, 64) z kompensacją dyspersji, a równocześnie optymalnej mocy sygnału.
W tym celu wstępnie dobrano długości linii, zakładając, ze dwukrotny wzrost przepływności
9
-log(BER)
powoduje również dwukrotne zmniejszenie zasięgu. Dla każdego przypadku symulację
przeprowadzano wielokrotnie, zmieniając moc sygnału. Wyniki dla modulacji M-PSK
przedstawiono na rys. 2.
M=2
4
8
16
32
64
Moc kanału [dBm]
-log(BER)
Rys. 2. Optymalizacja mocy dla formatu M-PSK (L = 15000 km).
Z wykresu wynika, że przyjęte założenie było słuszne, o czym świadczy minimalna stopa
błędów SER (rzędu 4,5·10-5), praktycznie taka sama dla wszystkich przypadków.
Podobne symulacje przeprowadzono dla systemu M-DPSK (dla M = 2, 4, 8, 16, 32, 64) z
kompensacją dyspersji.
M=2
4
8
16
32
64
Moc kanału [dBm]
W celu zwiększenia dokładności wyznaczenia optymalnej mocy, symulację powtórzono ze
zmniejszonym do 0,25 dB krokiem zmian mocy i nieznacznie większym szumem, co
związane jest z wydłużeniem o 10% długości linii.
10
-log(BER)
M=2
4
8
16
32
64
Moc kanału [dBm]
Stopa błędów BER jest dla modulacji wielopoziomowej mniejsza niż SER, gdyż przy
kodowaniu Graya obowiązuje zależność:
SER
.
(28)
BER =
log 2 ( M )
Na rys. 5 przedstawiono maksymalne zasięgi transmisji dla systemów M-PSK i M-DPSK
wynikające z symulacji, skorygowane o zależność (28) dla stopy błędów SER = 4,5·10-5.
100000
Zasięg [km]
10000
1000
100
40
80
120
160
200
240
Przepływność bitowa [GHz]
Rys. 5. Maksymalny zasięg transmisji dla systemów M-PSK i M-DPSK w zależności od
przepływności bitowej dla systemu 40 Gsymb/s (SER = 4,5·10-5).
Ze zmniejszaniem się zasięgu rośnie optymalna moc z -9 dBm dla systemu 2-PSK do 4 dBm
dla systemu 64-PSK, oraz z -8 dBm dla systemu 2-DPSK do 6 dBm dla systemu 64-DPSK.
Odpowiednią charakterystykę zmian mocy przedstawiono na rys. 6.
11
7
6
5
4
3
2
Moc [dBm]
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
40
80
120
160
200
240
Przepływność bitowa [GHz]
Rys. 6. Optymalna moc kanału dla systemów M-PSK i M-DPSK w zależności od
przepływności bitowej dla systemu 40 Gsymb/s (SER = 4,5·10-5).
3.
Nieliniowy szum fazowy indukowany modulacją skrośną XPM
W systemach wielokanałowych (WDM) występuje zjawisko skrośnej modulacji fazy (XPM –
Cross-Phase Modulation). Polega ono na fluktuacji fazy w danym kanale spowodowanej
fluktuacją mocy w sąsiednich kanałach. Zniekształcenie to ma swoje źródło w nieliniowości
Kerra. Systemy z kluczowaniem fazy (bezpośrednim M-PSK i różnicowym M-DPSK)
cechują się stałą amplitudą sygnału (dla formatu modulacji NRZ), dlatego przesunięcie fazy
ma stałą wartość i nie wpływa na pogorszenie jakości transmisji. W technice światłowodowej
jest to podstawowa przewaga modulacji czysto fazowej nad modulacją amplitudowo-fazową
QAM. W modulacji QAM amplituda poszczególnych bitów jest różna (np. dla modulacji
16-QAM wyróżnić można 3 poziomy mocy) i przypadkowe sekwencje bitów przesyłanych w
kanałach sąsiednich powodują przypadkowe zmiany fazy w danym kanale – jest to główna
przyczyna niestosowania modulacji QAM w systemach WDM. Chociaż systemy PSK są
pozbawione tej wady to występuje w tym przypadku efekt drugiego rzędu, a mianowicie
szum fazowy spowodowany szumem amplitudowym – tzw. efekt Gordona-Mollenauera. W
transmisji jednokanałowej spowodowane jest to samomodulacją fazy (SPM – Self-Phase
Modulation), a w przypadku systemów WDM szum fazowy jest zwiększony w wyniku
występowania modulacji skrośnej XPM. Poziom tego szumu rośnie bardzo szybko przy
kaskadowym połączeniu odcinków regeneracyjnych, jeśli występuje w nich całkowita
kompensacja dyspersji – szumy sumują się wtedy koherentnie i stają się wielokrotnie większe
od szumów indukowanych przez SPM.
W światłowodzie na skutek dyspersji chromatycznej impulsy w poszczególnych kanałach
WDM propagują z różną prędkością. Różnica prędkości (walk-off) jest proporcjonalna do
współczynnika dyspersji D i odległości kanałów ∆λ , stąd parametr walk-off wynosi
d12 = D ∆λ . Istotnym czynnikiem wpływającym na siłę występowania nieliniowego szumu
fazowego XPM jest długość drogi przenikania impulsów LW = d12 T , jest ona tym krótsza
12
im krótszy impuls. Jak pokażemy dalej siła oddziaływania modulacji skrośnej jest odwrotnie
proporcjonalna do LW . Oznacza to, że systemy o większej przepływności (np. 40 Gbit/s) są
bardziej odporne na nieliniowy szum XPM niż systemy 10 Gbit/s.
3.1 Model "pompa-sonda"
Do obliczenia wariancji nieliniowego szumu XPM stosowany jest dwukanałowy model
"pompa-sonda" [9], w którym kanał o znacznie większej mocy (pompujący) oddziałuje na
kanał o mocy na tyle małej (sondujący), że nie mającej wpływu na kanał pompujący.
Przy takim założeniu nieliniowe przesunięcie fazy w kanale pierwszym (sondującym)
wynosi:
L
2
2
Φ NL = γ ∫ ⎡ E1 ( z ) + 2 E2 ( z ) ⎤dz ,
0 ⎣
⎦
(29)
gdzie E1 oraz E2 oznaczają pole elektryczne w kanale sondującym i pompującym. Jeśli
prędkości propagacji dla obu kanałów są identyczne (brak dyspersji) to wpływ pompy jest
dwukrotnie większy niż SPM sondy. W światłowodzie z dyspersją składnik XPM jest
wielkością uśrednianą w czasie (lub na drodze propagacji):
L
φ1, XPM ( L, t ) = 2γ ∫ P2 ( 0, t + d12 z ) e −α z dz ,
(30)
0
gdzie P2 ( z , t ) jest mocą kanału 2 w funkcji położenia z i czasu t , γ jest współczynnikiem
nieliniowości światłowodu oraz α i L odpowiednio jego tłumiennością i długością. Zakłada
się, że moc chwilowa w kanale 2 P2 ( z , t ) = P ( 0, t − z v2 ) propaguje bez zniekształceń z
prędkością v2 . Efekt przenikania przez siebie impulsów uwzględniony jest w parametrze d12 .
Przy założeniu, że gęstość widmowa mocy kanału 2 wynosi Φ P2 ( f ) , gęstość widmowa
fazy w kanale 1 wyznaczana jest jako transformata Fouriera funkcji autokorelacji:
Φφ1 ( f ) = Φ P2 ( f ) H12 ( f ) ,
2
(31)
L
gdzie H12 ( f ) = ∫ e −α z + j 2π fd12 z dz , a po scałkowaniu:
0
1 − e( −α + j 2π fd12 ) L
H12 ( f ) = 2γ
.
α − j 2π fd12
(32)
W odbiorniku DPSK po asymetrycznym interferometrze Macha-Zehndera różnicowy
nieliniowy szum fazowy ∆φ1, XPM ( L, t ) = ∆φ1, XPM ( L, t ) − ∆φ1, XPM ( L, t − T ) jest sumowany z
różnicową fazą sygnału, gdzie T jest czasem trwania symbolu kodowego. Rozkład gęstości
widmowej tego szumu ma postać:
Φ ∆φ1 ( f ) = 4Φ P2 ( f ) H12 ( f ) sin 2 (π fT ) .
2
(33)
W przypadku, gdy moc pompy zawiera szum to P2 ( 0, t ) = E2 + N 2 , gdzie E2 i N 2 są polem
2
elektrycznym odpowiednio sygnału i szumu.
2
2
2
Moc P2 ( 0, t ) = E2 + E2 N 2* + E2* N 2 + N 2 zawiera: składową stałą
E2 powodującą
powstanie stałego przesunięcia fazowego – składnik ten nie jest źródłem szumu, składową
2
zdudnienia sygnału i szumu E2 N 2* + E2* N 2 o gęstości widmowej 2 E2 S sp – jest to
dominujący składnik szumu, oraz
N2
2
o gęstości widmowej 2 S sp2 ∆vopt , gdzie S sp i ∆vopt
jest odpowiednio gęstością widmową i pasmem optycznym szumu wzmacniacza. Stosunek
13
optycznego sygnału do szumu wynosi SNRO = E2
2
( 2S
sp
∆vopt ) >> 1 , stąd składnik 2 S sp2 ∆vopt
jest pomijalnie mały. Dla wejściowej mocy P0 i szumu pojedynczego wzmacniacza
S sp ,1
gęstość
widmowa
mocy
kanału
2
optycznego
o
mocy
Φ P2 ( f ) = 2 P0 S sp ,1 + 2 S sp2 ,1∆vopt ≈ 2σ n2 P0 nie zależy od częstotliwości.
Dla systemu NRZ (Non Return to Zero) E2
2
jest składową stałą i nie wnosi szumu,
2
a jedynie stałe przesunięcie fazy. Dla częściej stosowanej modulacji (RZ)-DPSK E2 jest
okresową funkcją czasu o okresie T i jej rozkład spektralny mocy zawiera prążki widma
o częstotliwościach k T , gdzie k jest liczbą całkowitą. Różnicowa charakterystyka
przejściowa 4sin 2 (π fT ) tłumi prążki spektralne o częstotliwościach k T i w rezultacie
niweluje przesunięcie fazy dla modulacji RZ. Ponadto jeśli impulsy RZ ulegną poszerzeniu na
skutek występowania dyspersji, również i w tym przypadku przesunięcie fazy jest
eliminowane, pod warunkiem, że jest to zjawisko liniowe tzn. zachodzenie na siebie
impulsów nie powoduje dodatkowych zniekształceń nieliniowych.
Wariancja fazy w funkcji różnicy częstotliwości (lub długości fali) między kanałami wynosi:
2
σ XPM
,0 ( ∆λ ) = 4Φ P
2
∫
1T
H12 ( f ) sin 2 (π fT ) df ,
2
−1 T
(34)
gdzie zakres całkowania został zredukowany z ±∞ do , ± 1 T przez wzięcie pod uwagę szumu
fazy tylko w paśmie ograniczonym przepływnością kanału.
Wariancja szumu fazy indukowanego przez SPM może być wyznaczona z (34),
przyjmując ∆λ = 0 :
σ
2
SPM
8σ n2γ 2 P0 L2eff
1 2
= σ XPM ,0 ( 0 ) =
,
4
T
(35)
gdzie Leff = (1 − e−α L ) α jest efektywną nieliniową długością odcinka regeneracyjnego.
Czynnik 1/4 wynika z dwukrotnie silniejszego oddziaływania efektu XPM w porównaniu z
SPM. Dla długiego odcinka L >> 1 α i dużej wartości współczynnika d12 stosunek wariancji
szumu fazy indukowanych przez XPM i SPM wynosi:
2
1T
σ XPM
sin 2 (π fT )
,0 ( ∆λ )
2
=
8α T ∫
df
2
2
0
σ SPM
α 2 + ( 2π fd12 )
= 8α 2T ∫
∞
0
sin 2 (π fT )
α 2 + ( 2π fd12 )
(
2
df
(36)
)
= α LW 1 − e −α LW ,
gdzie LW = d12 T
jest długością drogi przenikania impulsów, tzn. długością drogi
propagacji, na której dwa impulsy o czasie trwania T i prędkości względnej d12 przenikną
całkowicie przez siebie. Z powyższej zależności widać, że wartość wariancji nieliniowego
szumu fazowego XPM zależna jest jedynie od parametru LW .
Pewnej dyskusji w tym miejscu wymaga wpływ dyspersji chromatycznej. W powyższym
modelu założono, że impulsy w kanale pompy propagują bez zniekształceń. Konsekwencją
dyspersji chromatycznej w systemach WDM są dwa efekty: rozszerzanie impulsów (efekt
wewnątrz-kanałowy) i przenikanie z impulsami z sąsiednich kanałów (efekt zewnątrzkanałowy zwany walk-off). Ze względu na fakt, że odległość między kanałami jest zawsze
14
większa niż pasmo kanału, różnice prędkości propagacji są większe w przypadku efektu
zewnątrz-kanałowego, a więc uwzględnienie efektu walk-off jest w tym przypadku
wystarczające.
3.2 Kaskadowe połączenie odcinków regeneracyjnych WDM
W (2M+1) kanałowym systemie WDM wariancja nieliniowego szumu XPM w najbardziej
zaszumionym, centralnym kanale, po jednym odcinku wynosi:
M
2
2
σ XPM
,1 = 2∑ σ XPM ,0 ( k ∆λ ) ,
(37)
k =1
gdzie ∆λ jest odległością pomiędzy sąsiednimi kanałami. Dla kanałów odległych o k ∆λ
oddziaływanie jest k 2 słabsze niż dla odległości ∆λ . Stąd, dla bardzo dużej liczby kanałów,
korzystając z zależności:
1 π2
=
∑
2
6
k −1 k
∞
(38)
otrzymamy
2
σ XPM
π2
,1
α LW (1 − e−α L ) .
≈
M →∞ σ 2
3
SPM
lim
(39)
W
Dla systemu z N A odcinkami, zakumulowana wariancja nieliniowego szumu fazy XPM
zależy od przyjętego modelu kompensacji dyspersji.
Analogicznie do (34) możemy zapisać, że:
Φ N A ,∆φ1 ( f ) = 4Φ P2 ( f ) H12 ( f ) sin (π fT )
2
2
sin ⎡⎣ N Aπ f (1 − κ ) d12 L ⎤⎦
sin ⎡⎣π f (1 − κ ) d12 L ⎤⎦
2
,
(40)
gdzie κ jest współczynnikiem kompensacji dyspersji chromatycznej odcinka
regeneracyjnego, tzn. κ = 1 dla idealnej (100%) kompensacji oraz κ = 0 przy braku
kompensacji. Zależność (40) opisuje kaskadowe połączenie N A identycznych odcinków.
Dla najgorszego przypadku idealnej kompensacji wariancja szumu rośnie N A2 -krotnie po
N A odcinkach i ostatecznie wynosi:
2
2 2
2
2
σ XPM
,max = N Aσ XPM ,1 + ( N A − 1) σ XPM ,2 + … + σ XPM , N ,
2
A
(41)
2
gdzie σ XPM
,1 oznacza nieliniową fazę indukowaną w pierwszym odcinku regeneracyjnym, itp.
Z powodu idealnej kompensacji dyspersji szum z pierwszego wzmacniacza jest powielony we
wszystkich pozostałych odcinkach, szum drugiego wzmacniacza jest powielony ( N A − 1)
krotnie, itp. Maksymalna wariancja tak powstałego szumu wynosi:
1
2
2
(42)
σ XPM
N A ( N A − 1)( 2 N A + 1) σ XPM
,max =
,1 ,
6
przy założeniu, że wszystkie wzmacniacze mają identyczne szumy. Dla rozpatrywanego
przypadku idealnej kompensacji dyspersji stosunek szumu indukowanego przez XPM i SPM
(39) pozostaje stały, niezależnie od liczby odcinków regeneracyjnych.
Jeżeli współczynniki kompensacji κ są dobrane losowo to szum pochodzący z
poszczególnych wzmacniaczy nie jest skorelowany i wtedy:
2
2
2
2
σ XPM
,ind = N Aσ XPM ,1 + ( N A − 1) σ XPM ,2 + … + σ XPM , N
lub dla identycznych wzmacniaczy:
15
A
(43)
1
2
N A ( N A − 1) σ XPM
(44)
,1
2
i wtedy stosunek wartości maksymalnej wariancji do typowej wartości szumu fazowego
indukowanego przez XPM:
2
σ XPM
,ind =
2
σ XPM
1
,max
= ( 2 N A + 1) .
2
σ XPM ,ind 3
(45)
Dalsza redukcja wpływu XPM jest możliwa poprzez odpowiednie dobieranie parametru
kompensacji dyspersji κ , tak by charakterystyka przejściowa
sin ⎡⎣ N Aπ f (1 − κ ) d12 L ⎤⎦
(46)
sin ⎡⎣π f (1 − κ ) d12 L ⎤⎦
miała maksima na częstotliwościach odpowiadających minimom funkcji sin 2 (π fT ) .
Dla krótkiej drogi przenikania LW << L optymalny okazuje się współczynnik
κ = 1−
LW
.
L
(48)
Na rys. 7 przedstawiono zależność stosunku σ XPM σ SMP od długości drogi przenikania LW
dla nieskończonej liczby kanałów oraz maksymalnej i typowej wartości szumu fazowego
indukowanego przez XPM.
Nch = ∞
σXPM/σSPM
maksymalna
Nch = 2
typowa
Długość drogi przenikania impulsów (walk-off) [km]
Rys. 7. Stosunek σXPM/σSPM w zależności od długości drogi przenikania impulsów.
Dla typowego przypadku systemu o przepływności 10 Gbit/s i odstępie 50 GHz oraz
światłowodu z niezerową przesuniętą dyspersją (NZDSF) D = 4 ps ( nm×km ) droga
przenikania wynosi 62,5 km. Natomiast dla systemu o przepływności 40 Gbit/s i odstępie
100 Gbit/s LW = 7,8 km. Z rezultatów przedstawionych na wykresie można wyciągnąć
wniosek, że przy prawidłowym zaprojektowaniu traktu WDM nieliniowy szum fazowy
indukowany przez XPM może być w większości przypadków skutecznie wyeliminowany i
16
dominującym szumem fazowym pozostaje indukowany przez SPM, tak jak w systemie
jednokanałowym.
Wariancja szumu indukowanego przez SPM wynosi:
σ
2
SPM
4 Φ NL
≈
3ρ s
2
,
(49)
gdzie ρ s jest stosunkiem sygnału do szumu dla jednej polaryzacji. Korzystając z (39) i (49)
można wyznaczyć wariancję nieliniowego szumu fazy indukowanego przez XPM.
3.3 Prawdopodobieństwo błędu dla modulacji DPSK
pe, SPM
1 σ e −σ s
= − s
2
2
( −1)
k
⎡ ⎛σs
Ik ⎜
∑
⎢
⎝ 2
k = 0 2k + 1 ⎣
∞
2
⎡ ( 2k + 1) Φ NL ⎤
⎞
⎛ σ s ⎞⎤
⎥
⎟ + I k +1 ⎜ ⎟ ⎥ Ψ Φ ⎢
⎠
⎝ 2 ⎠⎦
⎣ σ s +1 2 ⎦
2
(50)
Przy sumowaniu wielu niezależnych szumów fazowych pochodzących z różnych źródeł,
współczynnikami rozwinięcia Fouriera sumy szumów są iloczyny odpowiednich
współczynników pochodzących od poszczególnych źródeł. Powstaje w ten sposób składowa
szumu fazowego o rozkładzie Gaussa (ostatni czynnik w poniższym wzorze):
pe, XPM
1 σ e −σ s
= − s
2
2
( −1)
k
⎡ ⎛σs
∑
⎢ Ik ⎜ 2
⎝
k = 0 2k + 1 ⎣
∞
⎞
⎛σs
⎟ + I k +1 ⎜ 2
⎠
⎝
⎞⎤
⎟⎥
⎠⎦
2
2
⎡ ( 2k + 1) Φ NL ⎤
⎡ 2k + 1 2 ⎤
× ΨΦ ⎢
σ XPM ⎥
⎥ exp ⎢ −
2
⎣
⎦
⎣ σ s +1 2 ⎦
(51)
Szum fazowy indukowany przez XPM powstaje w wyniku oddziaływania wielu kanałów
WDM, dlatego obowiązuje w tym przypadku centralne twierdzenie graniczne [1]. Jeśli droga
przenikania LW jest krótka, szum fazowy jest indukowany przez przynajmniej 2 Leff LW
niezależnych bitów z dwóch sąsiednich kanałów. Jeśli natomiast LW jest duże wiele
sąsiednich kanałów indukuje mniej więcej taką samą wartość szumu fazowego. W obu
przypadkach centralne twierdzenie graniczne prowadzi do rozkładu normalnego.
10-4
SMP
LW= 62,5km
SMP
LW =125km
BER
31,3
62,5
15,6
10-6
31,3
7,8
10-8
e − ρs
2
10-10
10-12
10 12 14 16 18 20 22 24 26 28
a) XPMmax
e − ρs
2
10 12 14 16 18 20
b) XPMind
Rys. 8. Bitowa stopa błędów transmisji w funkcji stosunku sygnału do szumu, dla szumu
XPM: a) maksymalnego, b) typowego (szumy sumowane niekoherentnie).
4.
Wpływ szumu fazowego lasera na różnicową detekcję M-DPSK
Formaty modulacji z kluczowaniem fazy są bardziej wrażliwe na szum fazowy źródła niż
tradycyjnie stosowane systemy z modulacją amplitudową. Poniżej rozpatrujemy detekcję
17
w odbiorniku zrównoważonym z zastosowaniem asymetrycznego interferometru MachaZehndera. W odróżnieniu od detekcji synchronicznej nie występuje w tym przypadku laser
pełniący rolę lokalnej heterodyny – detekcja różnicowa wykorzystuje sygnał optyczny
opóźniony o czas T trwania jednego symbolu kodowego. Sygnał ten podawany jest na
wejście odbiornika równocześnie (synfazowo) z sygnałem bezpośrednim. Na jakość detekcji
mają więc wpływ fluktuacje fazowe źródła występujące w czasie 2T . Dla źródła optycznego
o szerokości spektralnej ∆f L wariancja tych fluktuacji wynosi:
σ φ2e = 2π∆f LT .
(52)
e
Do wyznaczenia stopy błędów transmisji należy scałkować iloczyn pe (θ e ) pΦe (φe ) w
pełnym zakresie fazy:
π
∫ π p (θ ) p (φ ) dφ ,
e
−
e
Φe
e
(53)
e
gdzie pe (θ e ) jest rozkładem prawdopodobieństwa błędu w zależności od fazy szumu,
a pΦe (φe ) jest rozkładem prawdopodobieństwa fazy szumu. Zakładając gaussowski rozkład
pΦe (φe ) stopa błędów transmisji dla formatu DPSK wynosi:
1 σ s e −σ s
= −
2
2
( −1)
2
k
⎡ ⎛σs ⎞
⎛ σ s ⎞ ⎤ −( 2 k +1)2 π∆f LT
pe, ∆f L
I
I
+
.
(54)
∑
+
k
k
1
⎜
⎟
⎜
⎟⎥ e
⎢
⎝ 2 ⎠
⎝ 2 ⎠⎦
k = 0 2k + 1 ⎣
Powyższą zależność uogólniamy dla dowolnego formatu różnicowej detekcji M-DPSK
pe, ∆f L
∞
⎡
1
1 σ s e −σ s
⎢1 −
=
−
log 2 ( M ) ⎢ M
2
⎣
sin ( mπ M ) ⎡
⎛σs
∑
⎢ I m −1 ⎜
m
m =1
⎣ 2 ⎝ 2
∞
⎞
⎛σs
⎟ + I m −1 ⎜
⎠
2 ⎝ 2
2
⎞ ⎤ − m2π∆f LT ⎤
⎥ , (55)
⎟⎥ e
⎠⎦
⎥⎦
bitów informacji.
Na rys. 9 przedstawiono wynik symulacji stopy błędów transmisji w systemie z modulacją
M-DPSK (M = 2, 4, 8, 16, 32, 64). Dla modulacji 2-DPSK pogorszenie czułości o 1 dB
obserwowane jest dla iloczynu ∆f LT = 3,4·10-3 rad. Aby uzyskać podobną czułość uzyskać
Zwiększając krotność modulacji należy proporcjonalnie zmniejszać szerokość spektralną
i wtedy utrzymany jest warunek 1 dB pogorszenia czułości. Znajduje to potwierdzenie
w wynikach symulacji jak i analizie teoretycznej (55). Wystąpił tu problem (przedstawiony ze
szczegółami w punkcie 2.3) ze zbieżnością obliczeń nieskończonego szeregu (55), dlatego
obliczenia są możliwe dla M < 16.
18
-log(SER)
M=2
4
8
16
32
64
SNR [dB]
Rys. 9. Stopa błędów transmisji w systemie z modulacją M-DPSK (M = 2, 4, 8, 16, 32, 64).
Linia ciągła – wg. (55), linia przerywana – wg. (55) ∆f LT =0, linie kropkowane – wyniki
symulacji.
5.
Wpływ wewnątrz-kanałowego mieszania czterofalowego
Wartość skuteczna szumu fazy [rad]
Wewnątrz-kanałowe mieszanie czterofalowe (IFWM – Intra-channel Four Wave Mixing)
występuje na skutek zachodzenia na siebie impulsów w kanale transmisyjnym z
spowodowanego występowaniem dyspersji chromatycznej. W dziedzinie czasu IFWM
objawia się w postaci powstania impulsów-widm (ghost-pulses), które obserwowane są przy
modulacji amplitudowej w miejscu występowania bitów "0". W modulacji fazowej, ze
względu na występowanie nieprzerwanego ciągu impulsów, takie impulsy-widma nie są
obserwowane. W widmie kanału powstaje natomiast dodatkowy szumu amplitudowy.
Warunkiem koniecznym powstania IFWM jest zachodzenie na siebie impulsów, stąd jeśli
dyspersja światłowodu transmisyjnego jest mała efekt ten nie występuje.
Efekt IFWM został dokładnie przeanalizowany w literaturze [4], [7]. Na rys. 10
przedstawiono rezultaty tej analizy.
0,5
T0 = 5 ps
0,4
0,3
SPMNRZ
SPM + IXPM
0,2
SPM
0,1
T0 = 7,5 ps
IFWM
T0 = 5 ps
0
5
10
15
Współczynnik dyspersji D [ps/(nm·km)]
20
Rys. 10. Wartość skuteczna szumu fazy w zależności od współczynnika dyspersji
światłowodu, indukowana przez IFWM, IXPM i SMP.
19
Pokazana jest tu wartość skuteczna szumów fazy pochodząca od IFWM oraz ISPM i IXPM
dla systemu RZ-DPSK o przepływności 40 Gbit/s, dla średniego nieliniowego przesunięcia
fazy Φ NL = 1rad oraz dla dwóch szerokości impulsów: T0 = 5 ps i T0 = 7,5 ps. Pokazano
również, dla porównania, wartość skuteczną nieliniowego szumu fazy dla systemu NRZ
(z mocą ciągłą), analizowaną przez nas w punkcie 1.
Wpływ wewnątrz-kanałowego mieszania czterofalowego IFWM na poziom szumu
fazowego jest kilkukrotne mniejszy niż wewnątrz-kanałowej modulacji skrośnej IXPM
i samomodulacji fazy SPM. Dla małych wartości dyspersji dominujący jest szum SPM (dla
D = 0 SPM oraz IXPM oznacza to samo zjawisko), podczas gdy IFWM narasta od wartości
zerowej (z powodu braku zachodzenia impulsów) do pewnej wartości stałej (w sytuacji
silnego zachodzenia impulsów wytwarza się stan równowagi). Ze wzrostem dyspersji, na
skutek zmniejszania się szczytowej mocy impulsów, w sposób monotoniczny spada
oddziaływanie SPM oraz IXPM. Należy zwrócić uwagę, że stosowanie krótszych impulsów
jest korzystne, gdyż poziom nieliniowych szumów fazy spada przy tym dla wszystkich
oddziaływań.
Innym, istotnym wnioskiem jest stwierdzenie, że stosowana przez nas analiza nieliniowych
szumów fazy, zakładająca stałą moc sygnału (format NRZ a nie RZ), jest przydatna również
dla badania właściwości systemów z modulacją RZ, gdyż dla stosowanych w praktyce
światłowodów o dyspersji od 5 ps/(nm·km) do 17 ps/(nm·km), średni poziom nieliniowych
szumów fazy jest podobny, niezależnie od stosowania modulacji impulsowej RZ.
Z tego względu w pierwszej kolejności zajęliśmy się badaniem wpływu zniekształceń
nieliniowych na różne wielopoziomowe formaty modulacji fazowej w wariancie NRZ, tzn. ze
stałą mocą sygnału.
6.
Podsumowanie
Przedmiotem analizy był system DWDM z wielopoziomowym kluczowaniem fazy,
składający się z kaskadowego połączenia odcinków regeneracyjnych, zawierających
wzmacniacze optyczne, będące źródłem szumów ASE. Modele teoretyczne, analizowane w
pierwszym etapie projektu, stanowiły podstawę do opracowania następujących narzędzi,
użytecznych w badaniu zniekształceń nieliniowych wielopoziomowych formatów modulacji
optycznej M-DPSK:
− modelu teoretycznego i symulatora nieliniowego szumu fazowego indukowanego
samomodulacją fazy oraz układu kompensacji tych szumów,
− analizy teoretycznej wpływu modulacji skrośnej na jakość transmisji DWDM,
− modelu teoretycznego i symulatora wpływu szumu fazowego lasera na detekcję
różnicową .
Przeprowadzono symulacje weryfikujące poprawność opracowanych modeli w oparciu
o doniesienia z literatury na temat systemów eksperymentalnych i opublikowanych wyników
innych symulacji systemów DWDM z modulacją DPSK, a następnie modele te zostały
zastosowane do badania wielopoziomowych formatów modulacji M-DPSK (M = 2, 4, 8, 16,
32, 64).
Wyniki pracy:
A) Opisano metody umożliwiające oszacowanie skuteczności kompensacji nieliniowego
szumu fazowego indukowanego samomodulacją fazy (efekt Gordona-Mollenauera).
Posłużyliśmy się modelem opisanym znanym z literatury, rozszerzając jego
funkcjonalność na analizę wielostanowych formatów modulacji M-PSK i M-DPSK.
Korzystając z opisanego modelu zrealizowano symulator nieliniowego szumu fazowego,
20
indukowanego szumem kaskady wzmacniaczy optycznych, łącznie z modelem układu
kompensacji tego nieliniowego szumu .
B) Przedstawiono także teoretyczną analizę wpływu modulacji skrośnej na jakość transmisji
WDM. Stosowany jest tu dwukanałowy model "pompa-sonda", w którym kanał
o znacznie większej mocy (pompujący) oddziałuje na kanał o mocy na tyle małej
(sondujący), że nie mającej wpływu na kanał pompujący. Z analizy tej wynika, że
w systemie składającym się z kaskadowego połączenia odcinków regeneracyjnych
wielkość nieliniowego szumu fazowego indukowanego przez XPM silnie zależy od
właściwości dyspersyjnych łącza. Przy prawidłowym zaprojektowaniu traktu WDM
nieliniowy szum fazowy indukowany przez XPM może być w większości przypadków
skutecznie wyeliminowany i dominującym szumem fazowym pozostaje ten indukowany
przez SPM, tak jak w systemie jednokanałowym.
C) Następnym analizowanym zagadnieniem był wpływ szumu fazowego lasera na różnicową
detekcję M-DPSK. Przedstawiony w literaturze model teoretyczny, obejmujący analizę
systemu 2 DPSK rozszerzono również na system M-DPSK. Szum fazowy lasera ma
rozkład gaussowski, co upraszcza analizę. Rozważania teoretyczne poparto symulacją.
Zwiększanie krotności powoduje, że dopuszczalna szerokość spektralna lasera maleje
z kwadratem krotności.
D) Na koniec, przedstawiono pobieżną analizę wpływu wewnątrz-kanałowego mieszania
czterofalowego (IFWM) na jakość transmisji w systemach z kluczowaniem fazy. Analiza
ta wykazuje, że wpływ IFWM na poziom szumu fazowego jest kilkukrotne mniejszy niż
wewnątrz-kanałowej modulacji skrośnej IXPM i samomodulacji fazy SPM. Ponadto
stwierdzono, że stosowana przez nas analiza nieliniowych szumów fazy, zakładająca stałą
moc sygnału (format NRZ a nie RZ), jest przydatna również dla badania właściwości
systemów z modulacją RZ.
Wyniki uzyskano w oparciu o analizę matematyczną (z wykorzystaniem programu
Mathematica), oraz symulujące numeryczne (z wykorzystaniem programu LabView
z językiem graficznego programowania G).
Rezultaty pracy przedstawiono w publikacji:
M. Jaworski, M Marciniak: SPM nonlinear noise compensation in multilevel phasemodulated optical systems, in Proceedings of 10th Anniversary International Conference on
Transport Optical Networks, ICTON 2008, Athens, Greece, 22-26 June 2008, IEEE, 2008,
vol. 4, pp. 287-290. (Załącznik 1.1)
21
7.
Badanie efektywnych obliczeniowo metod symulacji propagacji sygnału
w światłowodzie
Sprawozdanie z prac prowadzonych w roku 2008 w ramach realizacji projektu "Badania w
zakresie zaawansowanej infrastruktury sieci fotonicznych (COST-291) ", zadanie 3 wg.
projektu badawczego specjalnego Nr COST/51/2006.
W grudniu 2007 opublikowaliśmy efektywną metodę symulacji propagacji sygnału WDM w
światłowodzie z zastosowaniem dwukrokowej metody Fouriera (S-SSFM – SymmetrizedSplit-Step-Fourier-Method) i wstępnej symulacji z wykorzystaniem uśredniania widma z
równoczesną kontrolą błędu lokalnego (PsLEM – Pre-simulated Local-Error-Method) [9].
Metoda ta daje ok. 50% wzrost efektywności obliczeń w porównaniu ze stosowaną do tej pory
metodą walk-off.
Jednocześnie kontynuowane były prace mające na celu optymalizację rozkładu długości
kroku stosowanego w metodzie S-SSFM. Zastosowaliśmy aproksymację rozkładu
uzyskiwanego w trakcje symulacji wstępnej PsLEM rozkładem logarytmicznym. Rozkładem
logarytmicznym posłużono się w pracy [10], w celu ograniczenia powstawania fałszywych
produktów mieszania czterofalowego (FWM). Przedstawiono tam analizę teoretyczną,
opisującą powstawanie fałszywych produktów FWM w metodzie S-SSFM, na przykładzie
dwóch niemodulowanych sygnałów nośnych. Jednak zaproponowane w [10] nachylenie
rozkładu logarytmicznego nie jest optymalne dla sygnałów WDM.
Zbudowaliśmy model odtwarzający symulacje z [10], a następnie uogólniliśmy go przez
zastosowanie dowolnego nachylenia charakterystyki logarytmicznej rozkładu długości
kroków i posługując się tym modelem poszukiwaliśmy nachylenia minimalizującego błąd
metody S-SSFM. Optymalne wartości nachylenia zależą od oczekiwanego błędu globalnego
i postaci sygnału wejściowego. Dla błędu globalnego <10-6 i systemu jednokanałowego
optymalne nachylenie wynosi ok. 0,33α, gdzie α jest tłumiennością światłowodu.
W styczniu 2008 ukazała się publikacja [11], w której autorzy, wychodząc od teoretycznej
analizy błędów metody S-SSFM, przeprowadzonej dla symulacji propagacji pojedynczego
impulsu w światłowodzie, otrzymali rezultaty zbieżne z naszymi wynikami, uzyskanymi
metodą eksperymentalną. Według [11] krok symulacji powinien wynosić h = A 3 P ( t ) ,
a ponieważ
P = P0 exp ( −α z )
to
optymalne
nachylenie
wynosi
1/3α ≈ 0,33α
– tak jak wynika z przeprowadzonych przez nas symulacji. Przedstawiona w [11] analiza
błędu jest poprawna dla przypadku propagacji pojedynczego impulsu. W systemie WDM
zachodzą jednak dodatkowo efekty wynikające z dyspersji, manifestujące się różną
prędkością propagacji sygnałów o różnej długości fali. Jest to efekt przenikania przez siebie
impulsów (walk-off) i związane z tym efekty skrośnej modulacji fazy (XFM) i mieszania
czterofalowego (FWM) – nie uwzględnione w analizie przeprowadzonej w [11].
Wykonaliśmy symulacje pokazujące kumulowanie błędu metody S-SSFM wzdłuż
symulowanej linii. Dla systemu jednokanałowego błędy powstające w kolejnych krokach
sumują się (błąd globalny jest sumą błędów lokalnych). Diametralnie inna sytuacja jest w
przypadku transmisji WDM – błąd lokalny jest tu dużo większy, a błąd globalny narasta dużo
wolniej niż wynikałoby z prostego sumowania błędów lokalnych. Okazuje się, że błędy w
poszczególnych krokach są ze sobą skorelowane i dla pewnej długości kroków korelacja ta
może być ujemna.
22
Stąd powstaje potrzeba optymalizacji nachylenia rozkładu długości kroków. Opracowany
przez nas model bazuje na, sprawdzonym wcześniej, pomyśle symulacji wstępnej,
z wykorzystaniem uśredniania widma sygnału [9, 14]. Początkowo wykonywana jest
symulacja z uśrednionym widmem sygnału i liczbą kroków 5n – wynik tej symulacji
traktowany jest jako odniesienie. Następnie wykonywane jest 10 symulacji z uśrednionym
widmem i liczbą kroków n, ze zmiennym nachyleniem rozkładu długości kroku A = (0,1
...1,0) i dalej do właściwej symulacji wybierany jest parametr A dający najmniejszy błąd
symulacji wstępnej. Ta, wydawałoby się, skomplikowana procedura symulacji wstępnej trwa
stosunkowo krótko, bo dzięki operacji uśredniania widma zajmuje ok. 10% całkowitego czasu
symulacji. Dodatkowo daje ona stosunkowo dokładne oszacowanie globalnego błędu
symulacji, a jest to bardzo istotny parametr konieczny do rzetelnej oceny właściwości
symulowanego obiektu [13].
Dzięki zastosowaniu optymalizacji nachylenia logarytmicznego rozkładu długości kroku
opracowana przez nas metoda jest bardziej efektywna niż publikowana ostatnio [10] metoda,
w której krok jest odwrotnie proporcjonalny do pierwiastka sześciennego mocy chwilowej
sygnału.
Analityczne oszacowanie błędu lokalnego metody SSFM
W [10] oszacowano, stosując zależność Bakera–Hausdorffa dla nieprzemiennych operatorów
[14], błędy numeryczne metody niesymetrycznej (standardowej) i symetrycznej SSFM, które
wynoszą odpowiednio:
∆ξ N = γ Pmax D ∆λ ∆f h ( z ) .
(56)
∆ξ S = γ Pmax ( D ∆λ ∆f ) h ( z ) ,
(57)
2
2
3
Przedstawiona w [11] analiza błędu jest poprawna dla przypadku propagacji pojedynczego
impulsu. W systemie WDM zachodzą jednak dodatkowo efekty wynikające z dyspersji,
manifestujące się różną prędkością propagacji sygnałów o różnej długości fali. Jest to efekt
przenikania przez siebie impulsów (walk-off) i związane z tym efekty skrośnej modulacji fazy
(XFM) i mieszania czterofalowego (FWM) – nie uwzględnione w analizie przeprowadzonej
w [11].
W metodzie niesymetrycznej (standardowej) na przemian stosowane są operatory dyspersji
i nieliniowości, działające na całej długości kroku h . Z (56) wynika, że błąd lokalny metody
niesymetrycznej jest rzędu O ( h 2 ) . W metodzie symetrycznej operator N̂ działa na sygnał w
płaszczyźnie z + h 2 , a operator D̂ działa w dwóch krokach o długości h / 2 , rozłożonych
symetryczne wokół z + h 2 . Z (57) wynika, że błąd lokalny metody symetrycznej jest rzędu
O ( h3 ) . Stąd wniosek, że symetryczna metoda dwukrokowa jest dokładniejsza od metody
niesymetrycznej
dla
kroku
mniejszego
h < 1 ( 4 D ∆λ ∆f ) ≅ c ( 4 D ∆f 2 λ02 ) .
niż
∆ξ S < ∆ξ N
co
jest
spełnione
dla
W praktyce, np. dla D = 4 ps/nm/km, ∆f = 40 GHz,
λ0 = 1550 nm h powinno być mniejsze niż 5 km, co jest zawsze spełnione, gdyż z kolei dla
h = 5 km błąd lokalny wynosi 10% i jest niedopuszczalnie duży.
W systemie WDM impulsy poruszają się względem siebie z prędkością di , j = D ∆λ – jest
to efekt walk-off . Przykładowo, dla D = 4 ps/nm/km, ∆λ = 10 nm mamy di , j = 0.02 ns/km, tj.
wzajemne przesunięcie impulsów o 2 ns po 100 km propagacji w światłowodzie. W systemie
10 Gbit/s odpowiada to przeniknięciu impulsu przez kolejnych 20 sąsiednich impulsów na
całym dystansie propagacji. Długość kroku powinna uwzględniać to zjawisko. Krok powinien
23
być o rząd wielkości krótszy niż hwalk −off
∆t di , j , gdzie ∆t jest okresem bitu. W naszym
przypadku krok powinien być krótszy niż 500 m.
Efektywność FWM maleje monotonicznie w miarę zwiększania odstępu
międzykanałowego. W metodzie SSFM ze stałą długością kroku, duża wartość h prowadzi do
pojawienia się charakterystycznych rezonansów zależnych od długości kroku [10]. Efekt
sztucznego zawyżenia mocy produktów FWM bardzo obniża dokładność symulacji,
szczególnie dla szerokopasmowych systemów WDM. Należy temu przeciwdziałać, stosując
skrócenie kroku, tak by pierwszy rezonans f p1 = 1 ( 2π h β 2 ) = c ( h D λ02 ) wypadał poza
symulowanym pasmem, gdzie c jest prędkością światła w próżni. Stąd, by zachodziło
c
f p1 ∆f = ∆λ , krok powinien spełniać warunek hFWM << 1 ( 2π β 2 ∆f 2 ) = λ02 ( D ∆λ 2 c ) .
λ0
Przykładowo, dla D = 4 ps/nm/km, ∆λ = 10 nm krok powinien być krótszy niż 20 m.
Z powyższych szacunków wynika, że efekt walk-off ma mniejsze znaczenie niż fałszywe
produkty FWM. Przedstawione kryteria odnoszą się do metody o stałej długości kroku. W
praktyce stosowana bywa metoda o kroku zmiennym, zależnym od maksymalnego
nieliniowego przesunięcia fazy [13]
h < Φ NL max ( γ Pmax ) .
(58)
lub jej modyfikacja, polegająca na zastosowaniu kroku odwrotnie proporcjonalnego do
pierwiastka sześciennego mocy chwilowej sygnału [10]:
h< A
3
γ Pmax , gdzie A = 3
∆ξ S
( D ∆λ ∆f )
2
= const wynika z (57).
Współczynnik potęgi równy 3 wynika z zależności lokalnego błędu symetrycznej metody
SSFM od długości kroku O ( h3 ) . W [10] przyjęto, że optymalny jest jednolity, stały błąd
lokalny, oraz że błąd globalny jest sumą błędów lokalnych, tzn. ma charakter
deterministyczny i jest addytywny. Założenie to jest słuszne dla transmisji jednokanałowej.
Dla transmisji WDM ujawnia się zaleta stosowania kroku o zmiennej długości, jednak błąd
lokalny jest znacznie większy niż w przypadku transmisji jednokanałowej. Efekty walk-off i
FWM powodują, że nie jest on addytywny, tzn. błąd globalny jest znacznie mniejszy niż suma
błędów lokalnych. Błąd lokalny w kolejnych krokach jest skorelowany ujemnie, stąd
narastanie błędu globalnego jest znacznie wolniejsze.
Szczegółowe rezultaty prac prowadzonych w ramach Zadania 3 "Badanie efektywnych
obliczeniowo metod symulacji propagacji sygnału w światłowodzie" w roku 2008
przedstawione zostały w 3 publikacjach:
A. M. Jaworski: "Step-size distribution strategies in SSFM simulation of DWDM links", in
Proc. of ICTON-MW 2008, Marrakech, Morocco, paper Fr2A.1, pp. 1-9, Dec. 11-13 2008.
(Załącznik 1.2)
B. M. Jaworski: "Split-step-Fourier-method in modeling of WDM links", to be published in
COST291 Final Report, Part III, Chap. 1. (Załącznik 1.3)
C. M. Jaworski: "Methods of step-size distribution optimisation used in S-SSFM simulations
of WDM systems", to be published in Journal of Telecommunications and Information
Technology. (Załącznik 1.4)
24
Bibliografia
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
A. Papoulis: Probability, random variables, and stochastic processes, McGraw Hill,
New York, 1984.
D.E. Amos: A portable package for Bessel functions of a complex argument and
nonnegative order, ACM Trans. on Math. Software, pp. 265-273, 1986.
A.P. Tao-Lau, J.M. Kahn: Signal design and detection in presence of nonlinear phase
noise, J. Lightwave Technol., pp. 3008-3016, 2007.
K-P. Ho: "Phase-modulated optical communication systems", Springer ScienceBusiness Media, 2005.
M.C. Jeruchim, P. Balaban, K.S. Shanmugan: Simulation of communication systems,
New York, Kluwer Academic Publishers, 2002.
M. Jaworski: Sprawozdanie z pracy "Badania w zakresie zaawansowanej infrastruktury
sieci fotonicznych (COST-291)" – Zadanie 1 (Badanie wielopoziomowych formatów
modulacji optycznej), Instytut Łączności, Warszawa, grudzień 2007.
X. Wei, X. Liu, Analysis of intrachannel four-wave mixing in differential phase-shift
keying transmission with large dispersion, Opt. Lett., pp. 2300-2302, 2003.
J. Leibrich, J. Wree, W. Rosenkranz: CF-RZ-DPSK for suppression of XPM on
dispersion-managed long-haul optical WDM transmission on standard single-mode
fiber, Photon. Technol. Lett., pp. 215-217, 2002.
M. Jaworski, M. Marciniak: Pre-simulated Local-Error-Method for modelling of light
propagation in Wavelength-Division-Multiplexed links, in Proc. of ICTON-MW 2007,
Sousse, Tunisia, paper Fr4B.4, pp. 1-4, Dec. 6-8 2007.
G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto: Suppression of
spurious tones induced by the split-step method in fiber systems simulation, IEEE
Photon. Technol. Lett., vol. 12, pp. 489-491, May 2000.
Qun Zhang, M. I. Hayee: Symmetrized split-step Fourier scheme to control global
simulation accuracy in fiber-optic communication systems,
J. of Lightwave
Technology, vol. 26, no. 2, pp. 302-316, Jan. 2008.
C.J. Rasmussen: Simple and fast method for step size determination in computations of
signal propagation through nonlinear fibres, in Proc. of OFC 2001,WDD29-1.
O.V. Sinkin, R. Holzlöhner, J. Zweck, C.R. Menyuk: Optimization of the split-step
Fourier method in modeling optical-fiber communications systems, J. of Lightwave
Technology, vol. 21, no. 1, pp. 61-68, Jan. 2003.
G.P. Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA, Academic Press, 2001.
25
Załącznik 1.1
ICTON 2008
287
Th.P1.22
SPM Nonlinear Noise Compensation in
Multilevel Phase-Modulated Optical Systems
Marek Jaworski, Member, IEEE, Marian Marciniak, Senior Member, IEEE
National Institute of Telecommunications, Department of Transmission and Fiber Optics
1 Szachowa Str., 04-894 Warsaw, Poland
Phone: +48 22 512 82 60, E-mail: [email protected]
ABSTRACT
Statistical model derived by Ho [1] of self phase modulation (SPM) inducted phase noise was extended from
binary to multilevel PSK and DPSK modulation formats. The model describes systems with and without noise
compensation. Simulations have been carried out to verify our model.
Keywords: nonlinear phase noise, optical modulation, compensation, self phase modulation (SPM), simulations.
1. INTRODUCTION
When optical amplifiers are used to periodically compensate for fiber losses, the interaction of amplifier noises
and the Kerr effect causes phase noise, often called Gordon-Mollenauer effect. Added directly to the phase of
a signal, nonlinear phase noise degrades both PSK and DPSK signal and limits the maximum transmission
distance. The nonlinear phase noise is given as summation from the contribution of many fiber spans. If the
number of fiber spans is very large, the summation can be replaced by integration. This distributed model is
described as transform of stochastic Wiener process [1], [2]. Properties of its distribution depends only on two
parameters: the signal to noise ratio ρ s and the mean nonlinear phase shift Φ NL . For single channel systems
nonlinear phase shift inducted by SPM can be partially compensated due to correlation of Φ NL with the signal
power P .
2. THEORY
2.1 PSK Detection
The error probability of synchronous M-ary PSK detection was derived in [1] (Eq. 9.16):
pe ≈
⎡
1
⎛ ρ ⎞ ρs
− exp ⎜ − s ⎟
⎢1 −
log 2 ( M ) ⎢⎣ M
⎝ 2 ⎠ π
1
sin ( mπ M ) ⎡
⎛ ρs ⎞
⎛ ρs ⎞⎤ ⎤
⎢ I m −1 ⎜ ⎟ + I m +1 ⎜ ⎟ ⎥ ⎥ ,
m
m =1
2 ⎝ 2 ⎠⎦ ⎥
⎣ 2 ⎝ 2 ⎠
⎦
∞
∑
(1)
where M is the number of symbol levels.
The simplest method of nonlinear noise compensation is applying a phase shift proportional to the received
power:
Φα = Φ − α R 2 = Φ − α P ,
(2)
were Φα is the phase after correction, P is the received signal power, R is the electric field amplitude, and α is
the scale factor of compensation. Compensation described by (2) is linear one, due to linear dependence between
phase correction Φα and received power Y. More accurate correction can be achieved by applying a higher
order polynomial to interpolate correlation between signal power and phase shift.
The scale factor α can be optimised in term of the variance, or minimum mean square error (MMSE). The
MMSE compensator is always analytically simple to find and leads to practical implementation. The optimal
compensator given by the maximum a posteriori probability (MAP) criterion to minimize the error probability
may be difficult to find [1].
We generalized equation (Eq. 5.72 in [1]), describing the error probability of synchronous PSK detection
based on MMSE criterion to more general case of multilevel M-ary PSK detection:
⎡
1
⎛ ρ ⎞ ρ s ∞ sin ( mπ M ) ⎡
⎛ ρs ⎞
⎛ ρs ⎞⎤ ⎤
− exp ⎜ − s ⎟
⎢1 −
⎢ I m −1 ⎜ ⎟ + I m +1 ⎜ ⎟ ⎥ ⎥
∑
m
⎝ 2 ⎠ π m =1
⎣ 2 ⎝ 2 ⎠
2 ⎝ 2 ⎠⎦ ⎥
⎢ M
1
pe ≈
⎢
⎥.
log 2 ( M ) ⎢ ⎪⎧
⎛ m Φ NL ⎞ − jm Φ RES ⎪⎫
⎥
e
×ℜ Ψ
⎬
⎢ ⎨ Φαmse ⎜ ρ + 1 2 ⎟
⎥
⎝ s
⎠
⎭⎪
⎣ ⎩⎪
⎦
(3)
In presented generalization we take into account symmetricity of code constellation to the origin. All
constellations points have identical noises. The factor 1 log 2 ( M ) derives from Gray coding properties, i.e.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
This research was carried out in the framework of COST Action 291 Towards Digital Optical Networks, and it received
a support from national science funds as a research grant COST/51/2006 in 2006-2008.
978-1-4244-2625-6/08/$25.00 ©2008 IEEE
Załącznik 1.1
Th.P1.22
288
ICTON 2008
symbol violation causes erroneous detection of only one bit from log 2 ( M ) bits. In (3) infinite series is used
which converges very slowly and special numerical algorithms should be used to obtain reliable results [3].
2.2 DPSK Detection
We generalized equation (Eq. 9.25 in [1]), describing the error probability of 4-DPSK to more general case of
M-ary DPSK detection:
pe , ∆f L
⎡
1
1 σ s e −σ s
⎢1 −
≈
−
log 2 ( M ) ⎢ M
2
⎣
sin ( mπ M ) ⎡
⎛σs
⎢ I m −1 ⎜
∑
m
m =1
⎣ 2 ⎝ 2
∞
⎞
⎛σs
⎟ + I m −1 ⎜ 2
⎠
2 ⎝
⎞⎤
⎟⎥
⎠⎦
2
⎤
⎥.
⎦⎥
(4)
For differential detection (DPSK) with SPM noise compensation, the differential phase is:
∆Φ cm = Φ cm ( t ) − Φ cm ( t − T ) = Θ n ( t ) − Φ RES ( t ) − Θ n ( t − T ) + Φ RES ( t − T ) ,
(5)
where T is the bit duration, Φ cm ( i ) , Θ n ( i ) , and Φ RES ( i ) are the received phase after correction, the phase of
nonlinear noise, and the residual nonlinear noise, respectively, as a function of time. The phases Φ cm ( t ) and
Φ cm ( t − T ) are independent random variables with identical probability density functions. The sum of such
variables has characteristic function that is the product of the corresponding individual characteristic
functions [2].
We generalized equation (Eq. 5.78 in [1]), describing the error probability of differential DPSK detection
based on MMSE criterion to more general case of multilevel M-ary DPSK detection:
pe , ∆f L
⎡
1 σ s e −σ s ∞ sin ( mπ M ) ⎡
⎛σs
⎢1 −
−
⎢ I m −1 ⎜
∑
2 m =1
m
⎢ M
⎣ 2 ⎝ 2
1
=
⎢
2
log 2 ( M ) ⎢
⎛ m Φ NL ⎞
⎢× Ψ Φαmse ⎜
⎟
⎝ ρs + 1 2 ⎠
⎣⎢
⎞
⎛σs
⎟ + I m −1 ⎜ 2
⎠
2 ⎝
2
⎞⎤ ⎤
⎟⎥ ⎥
⎠⎦ ⎥
⎥.
⎥
⎥
⎦⎥
(6)
3. SIMULATIONS
Theoretical relations (1) and (4) have been verified by simulations of SPM inducted distortions produced in
cascade of optical amplifiers, where phase noise is correlated with ASE noise of amplifiers. Additionally,
amplifiers are the source of linear phase noise. Generated signal in detected in a synchronous (PSK) or
differential (DPSK) receiver. Then, bit error rate (BER) or symbol error rate (SER) was calculated. Simple
Monte-Carlo method was used with bottom limit of error equals 10-6. Reliable results for relative error 10-6 can
be achieved for at least 107 simulation repetitions [4]. In today’s telecommunication systems, with ReedSolomon coding, BER of the order of 10-6 before the block detection is commonly accepted in practice.
First, simulations was carried out for PSK and DPSK systems without nonlinear phase correction, with
comparison of BER versus SNR for various signal power with theoretical relations shown in (1) and (4). The
results of simulations was consistent with theory as shown in Fig. 1 (solid lines).
10-1
BER
10-2
DPSK
10-3
10-4
10-5
10-6
10-7
PSK
7
8
9
10
11
12
13
14
15
Figure 1. Simulated (points) and theoretical (lines) BER vs. signal
to noise ratio (SNR) for PSK and DPSK modulation with (solid) and
without compensation (dashed) and Φ NL = 1.4 rad .
SNR [dB]
Then, simulations were repeated with linear MMSE compensation and the results of simulations was consistent
with theory [1], as in previous case (see Fig. 1).
Finally, simulations of multilevel phase modulation M-PSK and M-DPSK (for M = 2, 4, 8, 16, 32, 64) has
been done. In that way theoretical equations (3) and (6) was verified.
Załącznik 1.1
ICTON 2008
289
Th.P1.22
Contrary to theoretical assumptions of an infinite number of amplifiers N A , limited number N A was used in
simulations. We have verified that for N A = 32 the simulations error is acceptable. All simulations was been
carried out for N A = 32.
The maximum transmission distance depends mainly on the noise figure of amplifiers [5]. The amplifier
G −1
≈ 2nsp , where GE >> 1 is the amplifier gain. For
noise figure FE is proportional to nsp , i.e. FE = 2nsp E
GE
typical value of inversion coefficient nsp = 1.41 noise figure FE = 4.5dB . Total noise power for system of
length L , attenuation α = 0,25 dB/km and optical bandwidth of channel ∆vopt = 42,7 GHz, equals [5]:
σ 2 = 2hν nsp ∆voptα L .
(7)
For such distributed model, the mean value of nonlinear phase shift equals:
Φ NL = Pγ L ,
(8)
where P is the signal power and γ = 1,2 W ·km is the coefficient of fiber nonlinearity.
To calculate the maximum transmission distance and the optimal signal power, for above given system
parameters, repeated simulations were performed for M-PSK and M-DPSK (M = 2, 4, 8, 16, 32, 64) modulation
formats, first without compensation. Initial assumption of inverse proportional relation between the maximum
transmission distance and the bit rate was made in simulations. For each M the simulations was carried out many
times with various signal power. Simulation results are shown in Figs. 2 – 4.
-1
-log(BER)
-log(BER)
-1
M=2
4
8
16
32
64
M=2
4
8
16
32
64
Signal power [dBm]
Signal power [dBm]
Figure 3. Signal power optimisation for M-DPSK
(L = 10000 km).
-log(BER)
Figure 2. Signal power optimisation for M-PSK
(modulation (L = 15000 km).
M=2
4
8
16
32
64
Signal power [dBm]
Figure 3. Signal power optimisation for M-DPSK (as Fig. 3 but for small signal power changes).
From Figs. 2 – 4 is obvious that our initial assumption was correct, because SER is near identical (i.e. 4.5·10-5)
for all simulated cases with optimal signal power.
Similar simulations was carried out for linear MMSE compensation. To increase accuracy of optimal signal
power estimation, simulations were repeated with changing signal power by 0.25 dB step. Bit error rate (BER)
for multilevel modulation is lower than symbol error rate (SER), due to Gray coding:
Załącznik 1.1
Th.P1.22
290
BER =
ICTON 2008
SER
.
log 2 ( M )
(9)
In Fig. 5 the maximum transmission distance for M-PSK and M-DPSK modulations versus system bit rate was
shown, corrected to SER = 4.5·10-5 according to (9). The lower the maximum transmission distance the higher
the optimal signal power, which was shown in Fig. 6.
9
100000
Signal Power [dBm]
Max. Distance [km]
6
10000
1000
3
0
-3
-6
-9
-12
100
40
80
120
160
200
240
Bit Rate [GHz]
Figure 5. Maximum transmission distance for M-PSK
(solid line) and M-DPSK vs. bit rate, 40 GBaud
(SER = 4.5·10-5).
40
80
120
160
200
240
Bit Rate [GHz]
Figure 6. Optimal signal power for M-PSK (solid
line) and M-DPSK vs. bit rate, 40 GBaud
(SER = 4.5·10-5).
4. CONCLUSIONS
Statistical model derived by Ho [1] of self phase modulation (SPM) inducted phase noise was extended from
binary to multilevel PSK and DPSK modulation formats. The model describes systems with and without noise
compensation. Simulations results confirms validity of our model. The maximum transmission distance and the
optimal signal power was calculated for single channel 40 GBaud M-PSK and M-DPSK systems for
M = 2, 4, 8, 16, 32, 64 with SPM nonlinear phase noise compensation linear MMSE.
REFERENCES
[1] K-P. Ho: "Phase-modulated optical communication systems", Springer Science-Business Media, 2005.
[2] A. Papoulis: Probability, random variables, and stochastic processes, McGraw Hill, New York, 1984.
[3] D.E. Amos: A portable package for Bessel functions of a complex argument and nonnegative order, ACM
Trans. on Math. Software, pp. 265-273, 1986.
[4] M.C. Jeruchim, P. Balaban, K.S. Shanmugan: Simulation of communication systems, New York, Kluwer
Academic Publishers, 2002.
[5] A.P. Tao-Lau, J.M. Kahn: Signal design and detection in presence of nonlinear phase noise, J. Lightwave
Technol., pp. 3008-3016, 2007.
Załącznik 1.2
ICTON-MW'08
Fr2A.1
Step-Size Distribution Strategies in
SSFM Simulation of DWDM Links
Marek Jaworski, Member, IEEE
ABSTRACT
Brief review of methods used for simulation of signal propagation in Wavelength-Division-Multiplexed (WDM)
links is presented. Step-size distribution strategies used in Symmetrized-Split-Step-Fourier-Method (S-SSFM)
are analysed. We propose novel Modified Logarithmic (ML S-SSFM) method of step-size distribution, which is
a generalisation of logarithmic method used to suppress spurious FWM tones. In ML S-SSFM the slope of
logarithmic step-size distribution is optimised by performing several pre-simulations of averaged optical field.
Overall time savings exceed 50%, comparing with walk-off method. In is also more efficient than recently
published method in which step-size is inversely proportional to the cube root of instantaneous signal power.
Keywords: Split-Step-Fourier-Method, FWM, Local Error Method, simulation, WDM systems.
1. INTRODUCTION
Modern WDM systems contain large number of channels and occupy very wide bandwidth, which cause
difficulties in simulations due to spurious FWM and walk-off effect. Two class of methods are distinguished:
single-band – in which full-bandwidth of WDM transmission is simulated, and multi-band – in which separate
channels are simulated, taking into consideration an influence of adjacent channels (Fig. 1). Single-band methods
give an exact solution of nonlinear Schrödinger equation, i.e. include the impact of nonlinear phenomena, like:
SPM, XPM, FWM, and are used in narrow bandwidth cases due to high simulation time. Multi-band methods
are faster, but give only limited information of nonlinear phenomena derived from other channels (SPM, XPM,
but not FWM).
WDM Signal Propagation
Simulations
Full Band
Multi Band
Finite Difference
Split Step (SS)
Fourier
SSFM
Fixed Step
Walk-off
Pre-Simulation
Log Step
h~P-1
Wavelet
S-SSFM
Non-linear phase
h~P(t)-1
Higher Order
With Pre-Simulation
Mod. Log Step
h~P-Aopt
Local-Error
Non-linear phase
h~P(t)-3
Pre-Simulated Local-Error
Figure 1. Review of WDM Signal Propagation Simulations Methods.
The rest of the paper is focused on the single-band methods. We propose novel Modified Logarithmic
(ML S-SSFM) method of step-size distribution optimised to improve S-SSFM numerical efficiency. In ML
S-SSFM the slope of logarithmic step-size distribution is optimised by performing several pre-simulations of
averaged optical field. ML S-SSFM is a generalisation of logarithmic method used to suppress spurious FWM
tones [1]. Overall time savings exceed 50%, comparing with walk-off method [2]. In is also more efficient than
recently published method [3] in which step-size is inversely proportional to the cube root of instantaneous
signal power.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
This research was carried out in the framework of COST Action 291 Towards Digital Optical Networks,
and it received a support from national science funds as a research grant COST/51/2006 in 2006-2008.
978-1-4244-3485-5/08/$25.00 ©2008 IEEE
1
Załącznik 1.2
ICTON-MW'08
Fr2A.1
2. SOURCES OF ERRORS IN S-SSFM
2.1 Local error for single-channel propagation
Local errors of non-symmetrical and symmetrical SSFM were derived in [3]:
∆ξ N = γ Pmax D ∆λ ∆f h ( z ) ,
(1)
∆ξ S = γ Pmax ( D ∆λ ∆f ) h ( z ) ,
(2)
2
2
3
by using Baker–Hausdorff formula for two non-commuting operators [4].
Only pulse-with change has been taken into account in the error derivation, which is correct only for single
channel transmission, without intersymbol interference (ISI). Authors [3] claim that derivation can be extended
for WDM transmission case, but due to walk-off effect and FWM spurious tones [1] this approach is not reliable.
In non-symmetrical method dispersion D̂ and nonlinearity N̂ operators are applied one by one to full stepsize h and from (1) it follows that local error is of the order of O ( h 2 ) . In symmetrical method operator N̂ is
applied to full step-size h at distance z + h 2 and D̂ operator is applied symmetrically to step-size h / 2 twice,
which leads to local error of the order of O ( h3 ) . As a consequence, symmetrical method is more accurate than
non-symmetrical when ∆ξ S < ∆ξ N , which takes place for h < 1 ( 4 D ∆λ ∆f ) ≅ c ( 4 D ∆f 2 λ02 ) . In practice, e.g.
for: D = 4 ps/nm/km, ∆f = 40 GHz, λ0 = 1550 nm, h should be shorter than 5 km, which is always true,
because for h = 5 km local error equals ∆ξ = 10% , which is unacceptable high for WDM systems evaluation.
In WDM system propagation velocity in a given channel differs due to the fiber dispersion D, which is
known as the walk-off effect. Differential delay of propagating pulses equals di , j = D ∆λi , j , where ∆λi , j is
the wavelength difference between channels i and j. For instance, for D = 4 ps/nm/km and ∆λ = 10 nm
differential delay equals di , j = 0.02 ns/km, i.e. mutual shifting between pulses reaches 2 ns on 100 km fiber
length. It corresponds to a pulse walk-off through 20 adjacent pulses in 10 Gbit/s WDM system. Step-size
should be chosen short enough to copy with this effect, i.e. should be an order shorter than hwalk − off << ∆t di , j ,
where ∆t is the bit duration. In our case the step-size should be shorter than 500 m.
Higher order methods are more accurate than S-SSFM for very low local error ( ∆ξ <10-6), but they are solver
and such low error is not needed for proper WDM systems evaluation. In some cases Local Error Method (see
section 3D) is used, which has local error of the order of O ( h 4 ) .
2.1 Spurious FWM tones in S-SSFM
The FWM efficiency η decreases as the channel spacing increases. In SSFM with fixed step-size spurious FWM
tones are generated, which leads to characteristic peaks on FWM spurious efficiency η ′ , dependent on the stepsize [1]. The spurious FWM tones significantly reduce simulation accuracy, especially for wideband WDM
systems. Accuracy can be improved by using shorter step-size to fulfil constrain, that first resonance frequency:
f p1 = 1 ( 2π h β 2 ) = c ( h D λ02 )
(3)
should lays outside simulated bandwidth, where c is the light velocity in vacuum.
c
Consequently to fulfil f p1 << ∆f = ∆λ step-size should be shorter than
λ0
hFWM << 1 ( 2π β 2 ∆f 2 ) = λ02
( D ∆λ c ) .
2
(4)
For instance, for D = 4 ps/nm/km and ∆λ = 10 nm the step-size should be shorter than 20 m.
Non-uniform step-size distribution, in place of uniform one, diminishes substantially spurious peaks of FWM
efficiency.
3. STEP-SIZE DISTRIBUTION STRATEGIES
The step-size constrains mentioned above are related to uniform step-size distribution. In practice, methods with
varying step-size are commonly used, especially:
A. The method of fixed maximum Nonlinear Phase Shift (NPS):
h<
Φ NL max
.
γ Pmax
2
(5)
Załącznik 1.2
ICTON-MW'08
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B. Recently published [3] modification of NPS
In which step-size is inversely proportional to the cube root of instantaneous signal power:
h<
where A =
3
∆ξ S
( D ∆λ ∆f )
2
A
3
,
γ Pmax
(6)
= const is derived from (2) with assumption of constant local error. The root
coefficient in (6) equals 3, because local error for S-SSFM is of the order of O ( h3 ) . According to [3] uniform
1
1
0.99
0.8
0.98
0.6
Local error correlation
Local error correlation
local error is optimal and global error is the sum of all local errors, i.e. error is deterministic and additive. This
assumption is true for single-channel transmission. In WDM system the local error is substantially higher,
mainly due to the spurious FWM and partially due to walk-off effect. The global error is much lower than the
sum of local errors, i.e. error is not additive and, as well, negative correlated. As a consequence, growing of
global error as a function of distance is much lower, which is shown in Fig. 3.
0.97
0.96
0.95
0.94
0.93
0.92
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0.91
0.9
1000
-1
1000
100
Step-size (m)
100
Step-size (m)
b)
Figure 2. Local error correlation for:
a)single channel transmission, b) WDM 5 channels transmission.
1E-5
1E-4
1E-6
1E-5
Relative error
Relative error
a)
1E-7
1E-6
1E-7
1E-8
0
10
20
30
40
50
60
Distance (km)
70
80
90
100
0
10
20
30
40
50
60
Distance (km)
70
80
90
100
a)
b)
Figure 3. Global error as a function of distance for:
a)single channel transmission, b) WDM 5 channels transmission.
C. Logarithmic step-size distribution [1]
FWM spurious efficiency η ′′ follows proper value of FWM efficiency η , up to the critical step-size hp1 and for
higher number of steps K (i.e. for shorter hp1 ), η ′′ behaves like a white noise, with RMS value inverseproportional to K . In [1] an analyse was carried out for a simplified scenario with comb of CW carriers (not full
WDM signal) , leading to the following logarithmic step-size distribution:
hn = zn +1 − zn =
where d =
1 ⎛ 1 − nd ⎞
ln ⎜
⎟ , n ∈ 1, K ,
2α ⎜⎝ 1 − ( n − 1) d ⎟⎠
1 − e −2α z
, α is the fiber attenuation, z is the fiber length and K is the number of steps.
K
3
(7)
Załącznik 1.2
ICTON-MW'08
Fr2A.1
If ∆f max << f p1 , the spurious FWM efficiency η ′ for uniform distribution is only slightly higher than for
logarithmic distribution η ′′ . However, step-size hp1 is typically very low (e.g. of the order of 1 m for
15×40 Gbit/s system with 1 nm distance between channels) and larger step-size could be used to obtain global
relative error level of 10-3, which is typically sufficient for evaluation of WDM system properties [5]. On the
other hand, spurious efficiency of uniform step-size distribution η ′ grows sharply for step-size higher than hp1 .
D. Local-Error-Method (LEM)
In this method the simulation step-size automatically adjusts for required local accuracy [6]. Step-size is selected
by calculating the relative local error δL of each single step by comparing coarse (2h) and fine (h) steps which are
carry out simultaneously. LEM provides higher accuracy than S-SSFM method, because it is of order O(h4) due
to linear extrapolation of coarse and fine steps. LEM method provides near constant relative local error, which is
a good strategy to minimize the relative global error, but is slower than the walk-off method (with uniform stepsize distribution) due to required parallel calculation of coarse and fine solutions.
E. Modified Logarithmic Step-Size Distribution
We have found out that the step-size distribution obtained in LEM method is very close to logarithmic, with
exception of local fluctuations caused by an algorithm used to maintain the optimal step (see Fig. 4). We have
performed several simulations, and each time logarithmic step-size distribution was better than the uniform one,
under the assumption that its slope was optimized. Our conclusion is in contradiction of one given in [6], which
stated that logarithmic step-size method is somewhat poorer than that of the nonlinear phase and walk-off
methods, but not optimal slope of logarithmic step-size distribution was used in [6].
It can be shown that when the local signal power is P ( z ) = P0 e −α z , and the relative local error δ ( z ) is
proportional to P ( z ) , where A is some constant, then δ ( z ) is uniform in each simulation step, if the following
Aα
relations
z1
z2
zK
1
∫0 δ ( z ) dz = ∫z δ ( z ) dz = … = z ∫ δ ( z ) dz = K
1
K −1
zK
∫ δ ( z ) dz =
0
1 − e − Aα z
d
1 − e− Aα z
, where d =
,
=
Aα K
Aα
K
(8)
are satisfied, which, in turn, occurs when the step-size distribution has a form:
hn = zn +1 − zn =
⎛ 1 − nd ⎞
1
ln ⎜⎜
⎟ , n ∈ 1, K .
Aα ⎝ 1 − ( n − 1) d ⎟⎠
(9)
As can be seen, equation (6) is a general form of (2), with additional parameter A, which represents a slope of
logarithmic step-size distribution.
1E-3
100000
-2
Local error =10
1E-4
=10
Global error
Step-size (m )
10000
-3
1000
=10-4
1E-5
100
10
0
1E-6
20
40
60
80
500
100
1000
5000
Number of steps
Fiber length (km)
Figure 4. Step-size distributions obtained in LEM
Figure 5. Global error as a function of number of steps
method and its logarithmic approximations for various for modification of NPS [3](black line) and ML (red
levels of relative local error.
line) method for simulation of 5 channels 10×100 km
WDM RZ system.
In Fig. 5 the global error as a function of the number of steps for modification of NPS [3] and ML method are
compared, for simulation of 5 channels 10×100 km WDM RZ system. As can be seen, ML method is always
better then modification of NPS [3], especially in the important for WDM system evaluation region of errors
between 10-4 and 10-5, due to optimisation of step-size distribution slope in ML method (Fig. 6b and 6c). The
modification of NPS [3] does not accommodate to specific to WDM simulation conditions described in
section 3B.
4
Załącznik 1.2
ICTON-MW'08
Fr2A.1
500
Step-size (m)
100
10
5
0
5k
10k
15k
20k
25k
30k
35k
40k
45k
50k
55k
60k
50k
55k
Distance (m)
60k
65k
70k
75k
80k
85k
90k
95k
Distance (m)
a)
500
100
10
5
5k
0
10k
15k
20k
25k
30k
35k
40k
45k
65k
70k
75k
80k
85k
90k
95k
b)
1000
Step-size(m)
100
10
1
0
50k
100k
150k
200k
250k
300k
350k
400k
450k
500k
550k
Distance (m)
600k
650k
700k
750k
800k
850k
900k
950k
1M
c)
Figure 6. Step size distributions for simulation of 5 channels 100 km WDM RZ system for: a) modification of
NPS [3], b) ML method, one span, c) ML method, 10 spans. Global error varied from 10-2 to 10-6.
5
ICTON-MW'08
Załącznik 1.2
Fr2A.1
4. CONCLUSIONS
We have proposed novel Modified Logarithmic (ML S-SSFM) method of step-size distribution optimised to
improve S-SSFM numerical efficiency. In ML S-SSFM the slope of logarithmic step-size distribution is
optimised by performing several pre-simulations of averaged optical field. The ML S-SSFM is a generalisation
of the logarithmic method used to suppress spurious FWM tones [1]. The ML S-SSFM method is always better
then modification of NPS [3], especially in the important for WDM system evaluation region of errors between
10-4 and 10-5.
REFERENCES
[1] G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto: Suppression of spurious tones
induced by the split-step method in fiber systems simulation, IEEE Photon. Technol. Lett., vol. 12,
pp. 489-491, May 2000.
[2] M. Jaworski, Methods of step-size distribution optimisation used in S-SSFM simulations of WDM systems,
to be published in Journal of Telecommunications and Information Technology.
[3] Q. Zhang, M.I. Hayee: Symmetrized split-step Fourier scheme to control global simulation accuracy in
fiber-optic communication systems, J. of Lightwave Technology, vol. 26, no. 2, pp. 302-316, Jan. 2008.
[4] G.P. Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA, Academic Press, 2001.
[5] C.J. Rasmussen: Simple and fast method for step size determination in computations of signal propagation
through nonlinear fibres, in Proc. of OFC 2001, WDD29-1.
[6] O.V. Sinkin, R. Holzlöhner, J. Zweck, C.R. Menyuk: Optimization of the split-step Fourier method in
modeling optical-fiber communications systems, J. of Lightwave Technology, vol. 21, no. 1, pp. 61-68,
Jan. 2003.
6
Załącznik 1.3
1. COST291 Final Report
Part III
Chapter 1: Software Tools and Methods for Modelling Physical
layer Issues
1.3
Split-Step-Fourier-Method in Modeling of WDM Links
Author: Marek Jaworski, National Institute of Telecommunications, Department of Transmission and
Fiber Optics,
single-band [9]-[15], [20] – in which full-bandwidth of WDM transmission is simulated, and multi-band [16]-[19]
– in which separate channels are simulated, taking into consideration an influence of adjacent channels (Fig. 12).
Single-band methods give an exact solution of the nonlinear Schrödinger equation (NLSE), i.e. include the impact
of nonlinear phenomena, like: SPM, XPM, FWM, but on the other hand are used mainly in narrow bandwidth cases
due to its high simulation time. Multi-band methods are faster, but give only limited information of nonlinear
phenomena (SPM, XPM but not FWM) derived from other channels and are more flexible.
Split-step-Fourier-method (SSFM) is commonly used for simulating of light propagation in an optical fibre,
described by the nonlinear Schrödinger equation (NLSE) [9], due to its high numerical efficiency. In many
publications optimisation of the simulation time and accuracy is considered [10-20]. Higher order numerical
methods (i.e. explicit Adams–Bashforth and implicit Adams–Moulton, etc.) or predictor-corrector methods [10] are
used. Comparing to conventional symmetrical SSFM, the numerical effectiveness of higher order methods
increases with higher required accuracy. These methods are especially useful for simulations of soliton
propagation, where linear (L) and nonlinear (N) operators in SSFM are self-balanced.
Typically, there are higher dispersion and lower nonlinearity in WDM transmission, comparing to soliton
transmission. As a consequence, special tailored methods should be applied to simulation of signal propagation in
WDM links. Additionally, due to relatively low required accuracy (of the order of 10-2 – 10-3), the symmetrized
SSFM (S-SSFM) of order O(h2) is preferred for WDM signal simulations. Besides common used S-SSFM, another
methods are used in special cases, e.g. split-step wavelet collocation is faster then S-SSFM in very wideband
simulations [11], but is applicable only for zero dispersion slope ( β 3 = 0 ).
Załącznik 1.3
Simulations
Full Band
Finite Difference
Multi Band
Split Step (SS)
Fourier
XPM Standard [16]
Wavelet [11]
XPM with Spatial
Integration [17]
XPM Simplified [18]
XPM Local-Error [19]
Higher Order [10]
Fixed Step
SSFM
Non-linear phase
S-SSFM [9]
Log Step [15]
Analytical Optimization [12]
Walk-off
Local-Error [13]
Pre-Simulation [14]
Pre-Simulated Local-Error [20]
Fig. 12. Review of WDM Signal Propagation Simulations.
Local-Error-Method (LEM) is especially useful in single-band simulations, because it automatically adjust
simulation step for required accuracy [13]. In this method step size is selected by calculating the relative local error
of each single step, taking into account the error estimation and linear extrapolation. Provides higher accuracy than
above-mentioned methods, since it is method of third order. Simulations are conducted simultaneously with coarse
(2h) and fine (h) steps.
For large number of WDM channels all single-band methods, including LEM, show prohibitively long simulation
time [19]. In this case multi-band methods are used [16]-[19]. Different multi-band methods have been evaluated in
[19] and application of LEM method to cross-phase modulation (XPM) simulation in place of fixed step was
proposed, which improves simulation accuracy and speed up to 30%.
Optimal step size in S-SSFM is of uttermost importance to improve numerical efficiency. Lately, methods known
in quantum mechanics was used to step size calculation [12]. The optimal step size hoptimal can be estimated
analytically for required global error δG. This procedure is fast in the case of lossless fiber. In more realistic case
with lossy fiber, the optimal step size can be estimated as well, but with additional computational effort [12].
In pre-simulation method the step size is selected by calculating the global error δ G in a series of fixed-step
S SSFM pre-simulations with signal spectrum averaging [14]:
U nred =
n ⋅ N red + N red −1
∑
i = n⋅ N red
⎡ n⋅ Nred + Nred −1
⎤
2
U i , arg (U nred ) = arg ⎢ ∑ ( U i ⋅ U i ) ⎥ ,
⎣ i = n⋅ Nred
⎦
(1)
where U = ℑ ( u ) is the Fourier transform of the signal. For reduced number of samples Nred, split-step presimulation on the test signal can be much faster (> Nred ) than the corresponding simulation on the full signal.
Several pre-simulations must be carried-out iteratively to calculate optimal step size hoptimal , required to achieve
desired global accuracy. Pre-simulations typically takes 30% of full spectrum simulation time [14].
Pre-Simulated Local-Error S-SSFM
We proposed novel simulation method which comprises two stages: step optimization hoptimal ( z ) is carried out in the
initial stage, combining local-error and pre-simulation methods and in the second stage conventional S-SSFM is
used, applying optimal steps obtained in the initial stage. Overall time savings up to 50% are realistic, depending of
simulated system scenario. We called this novel procedure Pre-simulated Local Error S-SSFM (PsLE S-SSFM).
In PsLE S-SSFM LEM algorithm [13] is used with averaged signal spectrum (1) [14]. In [13] method of order
O(h3) is utilized by taking fraction of coarse uc and fine uf solutions to calculate the next step. In PsLE S-SSFM
only fine solution uf is used, which gives better stability and does not degrade accuracy in the case of WDM
simulations, where the global error is low, of the order of 10-3. The initial stage duration is only small percentage
(2%) of the second stage, in which full-band simulation is carried on using fixed-step method.
Załącznik 1.3
Results
We have explored the applicability of PsLE method to WDM systems with different number of channels. The
method was used for simulation of WDM link with various number of channels and the following parameters: bit
rate of 40 Gb/s, channel spacing of 100 GHz, channel power of 1 mW, simulated bandwidth of 320 GHz/channel
and bit sequence length of 29. Transmission line comprises 100 km of Standard Single Mode Fibers (SSMF), with
parameters given in Table 1.
Table 1. Fiber parameters used in the simulation.
Parameter
Attenuation
Dispersion
Dispersion slope
Nonlinear coefficient
dB/km
ps/(nm·km)
ps/(nm·km)2
1/(W·km)
SSMF
0.22
16.00
0.08
1.32
Results shown in Fig. 13 indicate that PsLE S-SSFM is up to 50% faster than walk-off method in all simulated
cases in important global error range of 10-2 – 10-3. Relation between method parameter and global error was
considered for fixed-step and PsLE methods (Fig. 14). The method parameter is the parameter in a split-step
method that should be varied to obtain required accuracy. For required global error δG = 10-3 the local error (i.e. the
parameter of PsLE method) varies from 2·10-5 to 3·10-4 for different number of simulated channels, in the same
conditions the step size (i.e. the parameter of fixed-step method) varies in wider range – from 8 m to 5000 m. It is
clear that local error in PsLE method is better criterion to assess global error than step size in fixed-step method.
The same is true for walk-off method, which in fact, is fixed-step method with automatically adjusted the step size.
104
# of channels = 15
10
=7
102
=3
101
100
-1
Global Relative Error
Simulation Time [a.u.]
103
1
PsLE
Fixed Step
=1
Fixed Step [m]
10-2
-3
15
10
10-4
10-5
-6
10
# of channels = 1
3
-7
10
10-8
10-1
1
3
7
PsLE
7
10-9
10-2 -5
10
-4
10
-3
10
-2
10
Fig. 13. Simulation time vs. global relative error
for fixed-step (dashed line) and PsLE (solid line)
methods
10
-1
15
10-10
10-6 10-5 10-4 10-3 10-2 10-1 1 101 102 103 104
Parameter of Method
Fig. 14. Global relative error vs. method
parameter: local error for PsLE and step size for
fixed-step.
PsLE method has two basic advantages: shorter simulation time of up to 50% in comparison with walk-off method,
which is known as the most efficient in WDM simulations [13] and offers simply accuracy criterion i.e. local error,
which is a good indicator of the global accuracy.
Conclusions
Pre-simulated local-error S-SSFM halves simulation time of conventional S-SSFM. Moreover, local-error used in
pre-simulation seems to be a good indicator of the global accuracy. To the best of our knowledge PsLE S-SSFM is
the fastest method for simulations of light propagation in WDM links.
References
[9]
G.P. Agrawal, “Nonlinear Fiber Optics”, 3rd ed. San Diego, CA: Academic, 2001.
Załącznik 1.3
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
X. Liu, B. Lee, “A fast method for nonlinear Schrödinger equation, IEEE Photon. Technol. Lett.,
vol. 15, no. 11, Nov. 2003.
T. Kremp, “Split-step wavelet collocation methods for linear and nonlinear optical wave
propagation”, Ph.D. dissertation, High-Frequency and Quantum Electronics Laboratory, University
of Karlsruhe, Cuvillier Verlag Göttingen, Feb. 2002.
A.A. Rieznik, T. Tolisano, F.A. Callegari, D.F. Grosz, H.L. Fragnito “Uncertainty relation for the
optimization of optical-fiber transmission systems simulations, Optics Express 3834, vol. 13, no.
10, 16 May, 2005.
O.V. Sinkin, R. Holzlöhner, J. Zweck, C.R. Menyuk, “Optimization of the split-step Fourier
method in modeling optical-fiber communications systems, J. of Lightwave Technology, vol. 21,
no. 1, Jan. 2003.
C.J. Rasmussen, “Simple and fast method for step size determination in computations of signal
propagation through nonlinear fibres, in Proc. of OFC 2001,WDD29-1.
G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, “Suppression of spurious
tones induced by the split-step method in fiber systems simulation, IEEE Photon. Technol. Lett.,
vol. 12, pp. 489-491, May 2000.
T. Yu, W.M. Reimer, V.S. Grigoryan, C.R. Menyuk, “A mean field approach for simulating
wavelength-division multiplexed systems, IEEE Photon. Technol. Lett, vol. 12, no. 4, pp. 443-445,
Apr. 2000.
J. Leibrich, W. Rosenkranz, “Efficient numerical simulation of multichannel WDM transmission
systems limited by XPM, IEEE Photon. Technol. Lett., vol. 15, no. 3, pp. 395-397, Mar. 2003.
G.J. Pendock, W. Shieh, “Fast simulation of WDM transmission in fiber, IEEE Photon. Technol.
Lett., vol. 18, no. 15, pp.1639-1641, Aug. 1, 2006.
M. Jaworski, M. Chochol, “Split-step-Fourier-method in modeling wavelength-divisionmultiplexed links, in Proc. of ICTON 2007, Rome, Italy, paper Mo.P.13, vol. 4, pp. 47-50, July 1-5,
2007.
M. Jaworski, M. Marciniak, “Pre-simulated Local-Error-Method for modelling of light propagation
in Wavelength-Division-Multiplexed links, in Proc. of ICTON-MW 2007, Sousse, Tunisia, paper
Fr4B.4, pp. 1-4, Dec. 6-8 2007.
Załącznik 1.4
Methods of Step-Size Distribution Optimisation
Used in S-SSFM Simulations of WDM Systems
Marek Jaworski
ABSTRACT
Brief review of methods used for simulation of signal propagation in Wavelength-Division-Multiplexed (WDM)
links is presented. We propose two novel methods of step-size distribution optimisations used to improve
Symmetrized-Split-Step-Fourier-Method (S-SSFM) numerical efficiency: Pre-simulated Local Error S-SSFM
(PsLE S-SSFM) and Modified Logarithmic (ML S-SSFM). PsLE S-SSFM contains two stages: in the initial
stage step-size distribution optimisation is carried out by combining local-error method and pre-simulation with
signal spectrum averaging; in the second stage conventional SSFM is used, applying optimal step-size
distribution obtained in the initial stage. ML S-SSFM is a generalisation of logarithmic method proposed to
suppress spurious FWM tones, in which a slope of logarithmic step-size distribution is optimised. Overall time
savings exceed 50%, depending of a simulated system scenario.
Keywords: Split-Step-Fourier-Method, Local Error Method, logarithmic step, simulation, DWDM systems.
1. INTRODUCTION
Split-Step-Fourier-Method (SSFM) is commonly used for simulating of light propagation in an optical fibre,
described by the nonlinear Schrödinger equation (NLSE) [1], due to its high numerical efficiency. Optimisation
of simulation time and accuracy is considered in many publications [2-12]. Higher order numerical methods (i.e.
explicit Adams–Bashforth and implicit Adams–Moulton, etc.) or predictor-corrector methods [2] are used when
the highest accuracy is needed. In this case the numerical effectiveness is better than for conventional
symmetrized SSFM (S-SSFM). These methods are especially useful for simulations of soliton propagation,
where linear (L) and nonlinear (N) operators in SSFM are self-balanced.
Typically, there are higher dispersion and lower nonlinearity in WDM transmission, when comparing to
soliton transmission. As a consequence, special tailored methods should be applied for simulation of signal
propagation in WDM links. In this case, S-SSFM is especially effective. It is a method of order O(h2), which is
adequate for relatively low accuracy required (of the order of 10-2 – 10-3). Besides common used S-SSFM,
another methods are used in special cases, e.g. split-step wavelet collocation is faster then S-SSFM in very
wideband simulations [3], but is applicable only for zero dispersion slope ( β 3 = 0 ).
single-band [1]-[7], [12] – in which full-bandwidth of WDM transmission is simulated, and multi-band [8]-[11]
– in which separate channels are simulated by taking into consideration an influence of adjacent channels
(Fig. 1). The single-band methods give an exact solution of the nonlinear Schrödinger equation (NLSE),
including the impact of nonlinear phenomena, like: SPM, XPM, FWM, but on the other hand, these methods are
used mainly in narrow bandwidth cases due to its high simulation time. The multi-band methods are faster and
more flexible, but give only limited information of nonlinear phenomena (i.e. SPM, XPM but not FWM) derived
from other channels.
An optimal step-size in S-SSFM is of uttermost importance to improve the numerical efficiency. Local-ErrorMethod (LEM) is especially useful for step-size optimisation, because it automatically adjusts simulation step for
required accuracy [5]. In this method step-size is selected by calculating the relative local error δL of each single
step, taking into account the error estimation and linear extrapolation. LEM provides higher accuracy than
S-SSFM method, because it is of order O(h3). Simulations are conducted simultaneously with coarse (2h) and
fine (h) steps, which needs additional 50% operations comparing with S-SSFM. Different multi-band methods
have been evaluated in [11] and application of LEM method to cross-phase modulation (XPM) simulation in
place of fixed-step was proposed, which improves simulation accuracy and efficiency up to 30%.
Lately, methods known in quantum mechanics was used for step-size calculation [4]. The optimal step-size
hoptimal can be estimated analytically for required global error δG. This procedure is fast in the case of lossless
fiber. In a more realistic case with lossy fiber, the optimal step-size can be estimated as well, but with an
additional computational effort [4].
1
Załącznik 1.4
Simulations
Full Band
Finite Difference
Multi Band
Split Step (SS)
Fourier
XPM Standard [8]
Wavelet [3]
XPM with Spatial
Integration [9]
XPM Simplified [10]
XPM Local-Error [11]
Higher Order [2]
Fixed Step
SSFM
S-SSFM [1]
Non-linear phase
Log Step [7]
Walk-off
Analytical Optimization [4]
Local-Error [5]
Pre-Simulation [6]
Pre-Simulated Local-Error [12]
Figure 1. Review of WDM signal propagation simulation methods.
In pre-simulation method the step-size is selected by calculating the global error δ G in a series of fixed-step
S-SSFM pre-simulations with signal spectrum averaging [6]:
U nred =
n ⋅ N red + N red −1
∑
i = n⋅ N red
⎡ n⋅ Nred + Nred −1
⎤
2
U i , arg (U nred ) = arg ⎢ ∑ ( U i ⋅ U i ) ⎥ ,
⎣ i = n⋅ Nred
⎦
(1)
where U = ℑ ( u ) is the Fourier transform of the original signal. For reduced number of samples Nred, split-step
pre-simulation of the test signal can be much faster (> Nred ) than the corresponding simulation of the original
signal. Several pre-simulations must be carried-out iteratively to calculate optimal step size hoptimal , required to
achieve desired global accuracy. Pre-simulations typically takes 30% of full spectrum simulation time [6].
2. PRE-SIMULATED LOCAL-ERROR S-SSFM
We proposed novel simulation method which comprises two stages: step-size optimization is carried out in the
initial stage, combining local-error and pre-simulation methods and in the second stage conventional S-SSFM is
used by applying optimal step-size distribution hoptimal ( z ) , obtained in the initial stage. Overall time savings up
to 50% are realistic, depending of simulated system scenario. We called this novel procedure Pre-simulated
Local Error S-SSFM (PsLE S-SSFM).
Modified LEM algorithm with averaged signal spectrum (1) is used in PsLE S-SSFM. Method of order O(h3)
is utilized in [5] by combining a fractions of coarse uc and fine uf solutions to calculate the next step. In our
method only fine solution uf is used in pre-simulation and uc is utilized only to calculate local error, which gives
better stability and does not degrade accuracy considerably in the case of WDM simulations, where the global
error δ G is low – of the order of 10-3. Contrary to original pre-simulation method [6], the duration of the initial
stage is only a small percentage (2%) of the second stage, in which the full-band simulation is carried out.
2.1 Results
We have explored the applicability of PsLE S-SSFM method to WDM systems with different number of
channels. The method was used for simulation of WDM link with the following parameters: RZ modulation
format, bit rate of 40 Gb/s, channel spacing of 100 GHz, channel power of 1 mW, simulated bandwidth of
320 GHz/channel and bit sequence length of 29, and various number of channels. Transmission line comprises
two types of fiber, with parameters given in Table 1.
Table 1. Fiber parameters used in the simulations.
Parameter
Length
Attenuation
Dispersion
Dispersion slope
Nonlinear coefficient
km
dB/km
ps/(nm·km)
ps/(nm·km)2
1/(W·km)
SSMF1
100
0.22
16.00
0.08
1.32
SSMF2
100
0.22
5.00
0.00
1.32
2
Załącznik 1.4
Results shown in Fig. 2 indicate that the PsLE S-SSFM is up to 50% faster than the walk-off method in all
simulated cases, in critical global error range of 10-2 – 10-3. Relation between the method parameter and the
global error was considered for fixed-step and PsLE methods (Fig. 3). The method parameter is a parameter in a
split-step method that should be varied to obtain required accuracy. For required global error δG = 10-3 the local
error (i.e. the parameter of PsLE method) varies from 2·10-5 to 3·10-4 for different number of simulated channels,
in the same conditions the step size (i.e. the parameter of fixed-step method) varies in a much wider range – from
8 m to 5000 m. As a rule of thumb, the global relative error equals δ G = N ⋅ δ L , where N is the number of
steps and δ L is the local relative error. It is clear that the local relative error δ L in PsLE method is better criterion
to assess global error than the step-size in fixed-step method. The same is true for walk-off method, which in
fact, is fixed-step method with automatically adjusted the step-size.
104
# of channels = 15
=7
=3
1
100
1
PsLE
10-2
102
10
-1
10
Simulation Time (a.u.)
103
1
PsLE
Fixed Step
=1
Fixed Step (m)
3
7
15
10-3
10-4
10-5
# of channels = 1
-6
10
3
10-7
7
10-8
10-1
10-9
10
15
10-10
-6
-5
-4
-3
-2
-1
10 10 10 10 10 10 1 101 102 103 104
Parameter of Method
-2
10-5
10-4
10-3
10-2
10-1
Figure 2. Simulation time vs. global relative error for
fixed-step (dashed line) and PsLE (solid line) methods.
Figure 3. Global relative error vs. method parameter:
local error for PsLE and step size for fixed-step.
PsLE method has two basic advantages: shorter simulation time of up to 50% in comparison with walk-off
method, which is known as the most efficient in WDM simulations [5] and offers simply accuracy criterion,
i.e. the local error, which is a good indicator of the global accuracy.
3. ROLE OF FWM SPURIOUS TONES ON ACCURACY OF S-SSFM SIMULATIONS
Four wave mixing (FWM) fictitious tones generated during S-SSFM simulations are one of the main sources of
errors. Detailed knowledge of their properties is the key factor to improve S-SSFM simulations speed and
accuracy.
Actual FWM efficiency η decreases versus the channel separation ∆f [1]. Fixed-step S-SSFM with uniform
distribution of step-size leads to fictitious FWM efficiency η ′ , presenting several peaks at frequencies f pi ,
which was analysed analytically in [7].
0
uniform
FWM efficiency [dB]
-10
-20
optimal log
-30
-40
theoretical
-50
-60
0
100
200
Channel separation ∆f (GHz)
300
Fig. 4. FWM efficiency as a function of channel separation ∆f : true – theoretical, and spurious for optimal-log
and uniform distributions, respectively.
3
Załącznik 1.4
Fig. 4 shows the FWM efficiency versus the channel separation ∆f after the propagation through a fiber
span. The first peak ( ∆f = f p1 ) on η ′ curve was shown around 270 GHz . Whatever (signal or noise) is at that
spectral distance from a carrier acts like an unrealistic pump for spurious tones. In the walk-off method, uniform
step-size distribution is used, in the same way as in the fixed-step method, but the step-size h is adjusted to
maintain frequency f p1 of the first fictitious peak at spurious FWM efficiency curve η ′(∆f ) outside simulated
bandwidth ∆f max , which is fulfill for h
1 ( 2π β 2 ∆f max 2 ) .
In case of the logarithmic step-size distribution, FWM spurious distortions η ′′ follows proper value of η , up
to the critical step-size hp1 and then, for higher number of steps K , η ′′ behaves like a white noise, with RMS
value inverse-proportional to K . In [7] an analyse was carried out for a simplified case with comb of CW
carriers, leading to the following logarithmic step-size distribution:
hn = zn +1 − zn =
1 ⎛ 1 − nd ⎞
ln ⎜
⎟ , n ∈ 1, K
2α ⎜⎝ 1 − ( n − 1) d ⎟⎠
(2)
1 − e −2α z
, and K is the number of steps.
K
<< f p1 , spurious FWM efficiency η ′ for uniform distribution is only slightly higher than for
where d =
If ∆f max
logarithmic distribution η ′′ . However, step-size hp1 is typically very low (e.g. of the order of 1 m for
15×40 Gbit/s system with 1 nm distance between channels) and larger step-size could be used to obtain global
relative error level of 10-3, which is typically sufficient for analysis of DWDM system properties [6]. On the
other hand, uniform step-size distribution spurious efficiency η ′ grows sharply for step-size higher than hp1 .
The accuracy gain δ fix/log obtained in S-SSFM simulations with logarithmic step-size distribution compared
with uniform one, increases as square root of the number of simulation steps K:
δ fix/log = K
and reaches maximum δ
Max
fix/log
(3)
for the step-size hp1 , corresponding to the resonant frequency f p1 , which is shown
Max
at critical step-size hp1 may exceed 30 dB, which means that the uniform
in fig. 5. The maximum ratio δ fix/log
step-size distribution is not applicable for this step-size, contrary to logarithmic one. Moreover, for step-size far
from critical step-size hp1 , e.g. for 5hp1 , logarithmic distribution is still more accurate than uniform one, for the
same number of steps K, and accuracy gain is always consistent with the following limit
Max
δ fix/log
≥
L
αL
=
Leff 1 − e −α L
.
(4)
The step-size h is a compromise between the global error δ G and the simulation time in a real DWDM system.
In such a system, additional effects, not only FWM, are the source of errors, i.e. SPM and XPM. Moreover, an
inter-channel effects (IFWM, IXPM) are generated even in a single channel system.
4
Załącznik 1.4
100
18
10
Step-size (km)
hp1
1
0.1
0.01
1.8
16
12
1.0
10
8
Optimal A
Accuracy gain (dB)
14
6
4
2
0
1
10
K p1
1000
100
Number of simulations steps
10000
Fig. 5. Accuracy gain of logarithmic distribution over uniform one as a function of number of simulation steps K
(or alternatively step-size). Simulation – solid line and theoretical approximation (3) – dashed line.
Additionally, optimal value of parameter A is shown. FWM efficiencies are shown in insets.
As can be seen in fig. 6, optimal value of parameter A tends to 2 for short simulated fiber spans, and this value
was been chosen in [5], which was the source of worsen results of logarithmic distribution, because A = 2 is far
from optimal value in S-SSFM simulation of actual DWDM systems, which is shown in the next section.
30
3
25
20
2
15
10
Optimal A
Log/fix accuracy gain (dB)
35
1
5
0
0
100
Span [km]
200
Fig. 6. Accuracy gain of logarithmic distribution over uniform one as a function of fiber span.
Additionally, optimal value of parameter A is shown.
4. MODIFIED LOGARITHMIC STEP-SIZE DISTRIBUTION
Step-size distribution (2) is used as reference in [5], with conclusion that logarithmic step-size method is
somewhat poorer than that of the nonlinear phase and walk-off methods in a single-channel simulations and even
further deteriorates in a multi-channel simulations, because the step-size choice is only based on limiting
spurious FWM, which is only one of the potential sources of error.
On the other hand, LEM method [5] provides near constant relative local error, which is good strategy to
minimize the relative global error, but is slower than the walk-off method (with uniform step-size distribution)
due to required parallel calculation of coarse and fine solutions.
We have found out that the step-size distribution obtained in LEM method is very close to logarithmic, with
exception of local fluctuations caused by an algorithm used to maintain the optimal step (see fig. 7). We have
performed several simulations, and each time logarithmic step-size distribution was better than the uniform one,
under the assumption that it slope was optimized. Our conclusion is contradiction of that obtained in [5], but in
that case not optimal slope of logarithmic step-size distribution was used.
It can be shown that when the local signal power is P ( z ) = P0 e −α z , and the relative local error δ ( z ) is
proportional to P ( z ) , where A is some constant, then the relative local error is uniform in each simulation
Aα
step, if the following relations
5
Załącznik 1.4
z1
z2
zK
0
z1
z K −1
∫ δ ( z ) dz = ∫ δ ( z ) dz = … =
∫
δ ( z ) dz =
1
K
zK
∫ δ ( z ) dz =
0
1 − e− Aα z
1 − e − Aα z
d
=
, for d =
,
Aα K
Aα
K
(5)
are satisfied, which, in turn, occurs when
hn = zn +1 − zn =
⎛ 1 − nd ⎞
1
ln ⎜⎜
⎟ , n ∈ 1, K .
Aα ⎝ 1 − ( n − 1) d ⎟⎠
(6)
As can be seen, equation (6) is general form of (2), with additional parameter A, which represents a slope of
logarithmic step-size distribution.
100000
Step-size (m)
10000
Local error =10-2
=10-3
1000
=10-4
100
10
0
20
40
60
80
100
Fiber length (km)
Figure 7. Step-size distributions obtained in LEM method and its logarithmic approximations for various levels
of relative local error.
(Fiber SSMF1, 7 channels, system parameters given in p. 2.1).
3.1 Results
The global relative error was calculated for S-SSFM simulation with the following step-size distributions:
uniform, logarithmic obtained by PsLE and optimal logarithmic, taking into account various WDM system
scenarios. Results are summarized in table 2.
Table 2. Results of S-SSFM simulation for various WDM system scenarios, with the following step-size
distributions: uniform, logarithmic obtained by PsLE and optimal logarithmic, for δ G = 2 ⋅10−3 .
Number of Dispersion
channels [ps/(nm·km)]
1
3
7
15
31
63
1
3
7
15
31
1
3
7
15
5
5
5
5
5
5
16
16
16
16
16
5
5
5
5
Number of steps
Span [km]
100
100
100
100
100
100
100
100
100
100
100
50
50
50
50
Log
(optimal A)
8 (0.5)
122 (0.5)
725 (0.6)
3420 (0.5)
14600 (0.6)
60000 (0.5)
17 (0.7)
280 (0.7)
1600 (0.7)
7600 (0.7)
32500 (0.7)
6 (0.5)
92 (0.5)
550 (0.5)
2570 (0.4)
Log PsLEM
Fixed-Step
8
126
740
3480
14700
61000
17
300
1780
7900
34000
6
93
560
2590
16
225
1400
6400
27300
110600
36
517
3150
14200
60800
8
111
720
3150
Fixed/Log
2.00
1.84
1.93
1.87
1.87
1.84
2.12
1.85
1.96
1.87
1.87
1.33
1.21
1.31
1.23
The optimal value of parameter A for typical simulated WDM systems lays between 0.4 and 0.7 for δ G = 2 ⋅10−3 ,
depending of the influence of spurious FWM on the global error. Optimal value of parameter A should be
calculated for each simulation and it is time consuming task. PsLE S-SSFM method can be helpful here. In this
case, modified logarithmic step-size distribution is a smoothed version of distribution obtained in PsLE S-SSFM
6
Załącznik 1.4
pre-simulation. Up to 2 times less steps are needed when optimal logarithmic step-size distribution is used,
comparing with walk-off method – known as the most efficient to date.
The optimal logarithmic step-size distribution gives always better results than the uniform one, which is
shown in fig. 8. Logarithmic step-size distribution obtained by Pre-simulation Local Error method is very close
to the optimal one in an important global error range of 10-2 – 10-3, but for lower levels of global error the results
is even slightly worse than for the uniform distributions, due to the bigger than optimal value of the parameter
A, which occurs for global relative error lower than 5·10-4 (see fig. 9).
1E-1
1E-2
Global relative error
uniform
1E-3
1E-4
PsLE log
optimal log
1E-5
K p1
1E-6
0
400
800
1200
1600
2000
Number of steps
Figure 8. Global relative error vs. number of steps in S-SSFM for various step-size distributions.
1.0
Coefficient A
0.8
0.6
PsLE log
0.4
0.2
optimal log
K p1
0.0
0
400
800
1200
1600
2000
Number of steps
Figure 9. a) Optimal and b ) obtained by PsLE method, coefficient A of logarithmic step-size distributions
vs. number of steps in S-SSFM.
Dependence between the relative global error and the coefficient A is presented in fig. 10.
7
Załącznik 1.4
1E-2
9E-3
Global relative error
8E-3
7E-3
6E-3
uniform
5E-3
optimal log
4E-3
LEM
3E-3
PsLE log
2E-3
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Coefficient A
Figure 10. Relative global error as a function of coefficient A for S-SSFM simulation.
Results of fixed-step (uniform) and LEM methods are presented for comparison.
(Fiber SSMF1, 7 channels, system parameters given in p. 2.1.)
As can be seen in fig. 10 optimal value of parameter A lays between 0.5 ÷ 1.0 and for A = 2 used in [5], error is
two times higher than obtained for uniform step-size distribution. The step-size distributions corresponding to
various values of parameter A, for 100 km of fiber with α = 0.22, are shown in fig. 11.
100000
Step-size (m)
10000
A = 1.8
1.5
1.2
0.9
0.6
1000
0.3
100
10
0
20
40
60
80
100
Fiber length (km)
Figure 11. Step-size distributions as a function of fiber length for various values of parameter A.
(100 km of fiber with α = 0.22)
As a rule of thumb, logarithmic step-size distribution improves global relative accuracy by
L
αL
∆δ G =
=
Leff 1 − e −α L
as compared to uniform step-size distribution, which is illustrated in fig. 12.
10
Accuracy Gain (dB)
8
α=0.45 dB/km
6
4
α=0.22 dB/km
2
0
0
20
40
60
Distance (km)
80
100
Figure 12. Step-size distributions.
Our future work is concentrated on finding more accurate and faster methods to chose optimal values of the
parameter A and the number of steps K, needed for a given relative global error δ G .
8
Załącznik 1.4
5. CONCLUSIONS
Pre-simulated local-error S-SSFM typically halves simulation time of WDM links, comparing to conventional
fixed-step S-SSFM. Moreover, local-error used in pre-simulation seems to be a good indicator of the global
accuracy. Even more effective step-size distribution can be achieved using modified logarithmic method,
although in this case, methods to found the optimal value of slope for logarithmic step-size distribution and the
number of steps, for a given global accuracy, should be further studied. To the best of our knowledge proposed
two novel methods are faster than other methods for simulations of light propagation in WDM links. Up to 2
times less steps are needed when optimal logarithmic step-size distribution is used, comparing with walk-off
method – known as the most efficient until now.
6. REFERENCES
[1] G.P. Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA, Academic Press, 2001.
[2] X. Liu, B. Lee: A fast method for nonlinear Schrödinger equation, IEEE Photon. Technol. Lett., vol. 15,
no. 11, Nov. 2003.
[3] T. Kremp: Split-step wavelet collocation methods for linear and nonlinear optical wave propagation, Ph.D.
dissertation, High-Frequency and Quantum Electronics Laboratory, University of Karlsruhe, Cuvillier
Verlag Göttingen, Feb. 2002.
[4] A.A. Rieznik, T. Tolisano, F.A. Callegari, D.F. Grosz, H.L. Fragnito: Uncertainty relation for the
optimization of optical-fiber transmission systems simulations, Optics Express 3834, vol. 13, no. 10,
16 May, 2005.
[5] O.V. Sinkin, R. Holzlöhner, J. Zweck, C.R. Menyuk: Optimization of the split-step Fourier method in
modeling optical-fiber communications systems, J. of Lightwave Technology, vol. 21, no. 1, pp. 61-68,
Jan. 2003.
[6] C.J. Rasmussen: Simple and fast method for step size determination in computations of signal propagation
through nonlinear fibres, in Proc. of OFC 2001,WDD29-1.
[7] G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto: Suppression of spurious tones
induced by the split-step method in fiber systems simulation, IEEE Photon. Technol. Lett., vol. 12,
pp. 489-491, May 2000.
[8] T. Yu, W.M. Reimer, V.S. Grigoryan, C.R. Menyuk: A mean field approach for simulating wavelengthdivision multiplexed systems, IEEE Photon. Technol. Lett, vol. 12, no. 4, pp. 443-445, Apr. 2000.
[9] J. Leibrich, W. Rosenkranz: Efficient numerical simulation of multichannel WDM transmission systems
limited by XPM, IEEE Photon. Technol. Lett., vol. 15, no. 3, pp. 395-397, Mar. 2003.
[10] G.J. Pendock, W. Shieh: Fast simulation of WDM transmission in fiber, IEEE Photon. Technol. Lett.,
vol. 18, no. 15, pp.1639-1641, Aug. 1, 2006.
[11] M. Jaworski, M. Chochol: Split-step-Fourier-method in modeling wavelength-division-multiplexed links,
in Proc. of ICTON 2007, Rome, Italy, paper Mo.P.13, vol. 4, pp. 47-50, July 1-5, 2007.
[12] M. Jaworski, M. Marciniak: Pre-simulated Local-Error-Method for modelling of light propagation in
Wavelength-Division-Multiplexed links, in Proc. of ICTON-MW 2007, Sousse, Tunisia, paper Fr4B.4,
pp. 1-4, Dec. 6-8 2007.
9
Etap 2:
Badania zintegrowanych elementów całkowicie optycznego
przetwarzania pakietów
Praca nr 14310028
Etap 2: Badania zintegrowanych elementów całkowicie optycznego przetwarzania pakietów
Praca nr 14310028
Kierownik pracy: doc. dr hab. Marian Marciniak
Wykonawcy pracy:
dr inż. Mirosław Klinkowski
dr inż. Marek Jaworski
spec. Hanna Skrobek
mgr inż. Olga Bolszo
mgr inż. Mariusz Zdanowicz
SPIS TREŚCI
1.
2.
Wprowadzenie..................................................................................................................... 4
Badanie algorytmów routingu w sieciach OBS .................................................................. 4
2.1
Streszczenie................................................................................................................ 4
2.2
Wprowadzenie............................................................................................................ 4
2.3
Cel pracy .................................................................................................................... 5
2.4
Wyniki pracy .............................................................................................................. 5
3. Badanie charakterystyk wydajnościowych i funkcjonalności architektur OBS ................. 6
3.1
Streszczenie................................................................................................................ 6
3.2
Wprowadzenie............................................................................................................ 6
3.3
Cel pracy .................................................................................................................... 7
3.4
Wyniki pracy .............................................................................................................. 7
3
1. Wprowadzenie
Rozwoju sieci transportowych zorientowanych na przesyłanie danych wynika z faktu, że
Internet jest bezpołączeniową siecią opartą na transmisji pakietów. W tym kontekście
obiecującym rozwiązaniem jest model sieci z komutacją grupową pakietów (OBS, ang.
optical burst switching). Korzyści płynące z elastycznego przełączania stosunkowo krótkich
grup pakietów optycznych (ang. bursts) w modelu OBS są okupione znaczną złożonością
systemu i trudnościami w implementacji. Stąd istnieje potrzeba opracowania skutecznych
metod pozwalających na działanie sieci OBS.
Praca badawcza dotyczyła gwarantowania jakości usług (QoS, ang. Quality of Service)
w sieciach OBS, oraz w sieciach z komutacją pojedynczych pakietów optycznych (OPS, ang.
Optical Packet Switching). Analizowane były zarówno mechanizmy działające na poziomie
pojedynczych przełączników optycznych jak i algorytmy routingu na poziomie sieci.
2. Badanie algorytmów routingu w sieciach OBS
2.1 Streszczenie
Etap B poświęcony jest problemowi routingu w sieciach OBS. W szczególności wyróżnione
zostały dwa tematy:
Temat 1: Strategie izolowanego alternatywnego routingu w etykietowanych, zorientowanych
połączeniowo sieciach OBS (ang. labeled OBS, LOBS) z emulacją czasów offsetowych (ang.
offset time-emulated OBS, E-OBS).
Temat 2: Optymalizacja routingu wielościeżkowego (ang. multi-path routing) w sieciach
OBS.
2.2 Wprowadzenie
Architektury OBS nie posiadające zdolności buforowania pakietów optycznych są wrażliwe
na przeciążenia sieci. Obecność kilku nadmiernie przeciążonych łączy może poważnie
pogorszyć przepływność w sieci. Prawdopodobieństwo utraty wiązki pakietów (ang. burst
loss probability, BLP), które odzwierciedla stan przeciążenia całej sieci jest podstawową
miarą jakości w sieciach OBS.
Przeciążenia mogą być redukowane bądź poprzez odpowiednie wymiarowanie sieci lub
przez właściwy routing. W pierwszym przypadku pojemności węzłów oraz łączy są dobierane
na podstawie macierzy obciążeń ruchowych pomiędzy węzłami i po takiej optymalizacji
proste mechanizmy routingu (np. najkrótszej ścieżki) są zwykle stosowane. Niemniej jednak,
w przypadku gdy obciążenia ruchowe ulegają zmianie, niektóre obszary sieci mogą
w dalszym ciągu doświadczać przeciążenia. Z drugiej strony, właściwy routing może ułatwić
dostosowanie się sieci do zmian w obciążeniu ruchowym. Problemem jest jednak dodatkowa
złożoność mechanizmów routingu, który często wymaga wsparcia ze strony protokołów
sygnalizacyjnych. Ponieważ obydwa rozwiązania uzupełniają się raczej niż wykluczają,
jakakolwiek sieć OBS powinna być projektowana zarówno z uwzględnieniem właściwego
wymiarowania pojemności łączy jak i odpowiednią strategią routingu działającego wewnątrz
sieci.
Wysoce dynamiczny charakter transmisji grup pakietów w sieciach OBS może
wprowadzać nieścisłość informacji o stanie sieci. Poza tym występuje konieczność obsługi
ogromnej liczby stosunkowo krótkich grup pakietów optycznych. Innym zagadnieniem jest
duża przepustowość technologii komutacji optycznej, która wprowadza dodatkowe
wymagania na szybkości przetwarzania w sterowniku węzła optycznego (np. szybkie
przeglądanie tablic routingu). Wszystkie te czynniki zwiększają złożoność sieci i wymagają
4
wprowadzenia dodatkowych mechanizmów. Zastosowanie zorientowanej połączeniowo
techniki przełączania etykiet (ang. multi-protocol label switching, MPLS) z jej z góry
zdefiniowanymi ścieżkami logicznymi oraz szybkim przeszukiwaniem etykiet znacznie
ułatwia przedstawione problemy. W rezultacie wiele z proponowanych strategii routingu
wykorzystuje koncepcję etykietowanego OBS (ang. labeled OBS, LOBS) dla potrzeb
inżynierii ruchu (ang. traffic engineering TE) w sieci. Także zastosowanie architektury z
emulacją czasów offsetowych E-OBS pozwala na nieograniczony ze względu na wielkość
offsetu routing alternatywny w sieci.
Routing wielościeżkowy reprezentuje grupę strategii routingu, które mają na celu
balansowanie obciążenia sieci. W przypadku sieci OBS, większość z proponowanych
w literaturze rozwiązań routingu wielościeżkowego zakłada predefiniowany zbiór ścieżek
obliczanych za pomocą algorytmu Dijkstry (tzn. najkrótszej ścieżki). Gdy zbiór dostępnych
ścieżek jest zdefiniowany, wybór odpowiedniej ścieżki dla transmisji wiązki pakietów
odbywa się na podstawię pewnej heurystycznej, bądź poddawanej optymalizacji funkcji
kosztu.
2.3 Cel pracy
Badanie całej sieci stanowi następny krok po badaniu węzła, a zagadnienie routingu jest
jednym z najistotniejszych problemów sieci. Zagadnienie to w sieciach OBS wydaje się
bardziej złożone niż np. w sieciach OPS (Optical Packet Switching – z komutacją pakietów).
W szczególności grupy pakietów mają większe rozmiary niż pojedyncze pakiety, co może
zarówno zwiększyć prawdopodobieństwo ich utraty w pozbawionych buforów optycznych
węzłach sieci OBS jak i generować dodatkowy ruch podczas przysyłania grup pakietów
dłuższymi ścieżkami. Celem tej pracy jest badanie algorytmów routingu równoważących
natężenie ruchu i ograniczających stopień utraty danych w sieci OBS.
W przypadku routingu wielościeżkowego w sieciach OBS, metody optymalizacyjne
wykorzystują funkcję kosztu, która reprezentuje całkowite prawdopodobieństwo utraty wiązki
pakietów i która obliczana jest na podstawie modelu stratnego sieci OBS. Ponieważ ta funkcja
ma charakter nieliniowy do jej optymalizacji wykorzystywane są nieliniowe metody
gradientowe. Dla potrzeb tych metod konieczne jest znalezienie pochodnych cząstkowych
funkcji kosztu.
2.4 Wyniki pracy
A) Jakkolwiek w literaturze można znaleźć wiele propozycji dla problemu routingu
w sieciach OBS, brak jest publikacji stanowiącej przegląd porównawczy różnych
metod routingu. Dlatego w pracy przedstawiamy szczegółową terminologię dla metod
routingu i w oparciu o te definicje wprowadzamy klasyfikację strategii routingu
w sieciach OBS.
B) W pracy proponujemy oraz badamy dwa algorytmy routingu izolowanego
alternatywnego dla zorientowanych połączeniowo sieci E-OBS, mianowicie: routing
z wykluczaniem ścieżki (ang. path excluding routing, PER) oraz routing z obejściem (ang.
bypass routing, BPR). Jak pokazują otrzymane wyniki, nasze rozwiązania pomagają
zmniejszyć liczbę utraconych wiązek pakietów w sieci OBS. W szczególności BPR
zapewnia znaczną poprawę wydajność w stosunku do powszechnie stosowanego routingu
najkrótszej ścieżki, w sieciach o małych oraz średnich rozmiarach, a także przy niskich
oraz średnich obciążeniach ruchowych. Jakkolwiek wydajność PER jest nieznacznie
słabsza w tych scenariuszach (w porównaniu do BPR), ten algorytm z kolei pracuje lepiej
przy wyższych obciążeniach ruchowych.
5
C) Zaproponowano także metodę optymalizacji routingu wielościeżkowego w sieci OBS
w oparciu o teorię optymalizacji nieliniowej. W szczególności rozważane są dwa
modele stratne sieci OBS z prawdopodobieństwem utraty pakietów jako podstawową
miarą jakości. Dla modelu bez redukcji obciążenia łącza (ang. non-reduced link load
model) zaproponowano metodę szybkiego i dokładnego obliczania pochodnych
cząstkowych dla potrzeb procedury optymalizacyjnej. W modelu z redukcją obciążenia
łącza (ang. reduced link load model) zastosowano przybliżone wzory na pochodne
cząstkowe, obliczane jak dla modelu sieci z przełączaniem obwodów (ang. circuit
switching). Wyniki obliczeń numerycznych jak i symulacji komputerowej pokazują, że
zoptymalizowany routing wielościeżkowy skutecznie redukuje prawdopodobieństwo
utraty pakietów w sieci w porównaniu z routingiem najkrótszej ścieżki. Co więcej,
w przypadku gdy zbiór dostępnych ścieżek jest ustalony i niewielki, zoptymalizowany
routing wielościeżkowy jest w stanie skuteczniej rozwiązywać problem przeciążenia sieci
niż routing alternatywny.
Wyniki uzyskano w oparciu o analizę matematyczną, obliczenia numeryczne w programie
Matlab oraz z wykorzystaniem stworzonego programu komputerowego symulującego
mechanizmy routingu w sieciach OBS.
3. Badanie charakterystyk wydajnościowych i funkcjonalności architektur OBS
3.1 Streszczenie
Etap C poświęcony jest badaniu charakterystyk wydajnościowych i funkcjonalności
architektur OBS. W szczególności wyróżnione zostały dwa tematy:
Temat 1: Porównanie dwóch podstawowych architektur OBS: konwencjonalnej (C-OBS)
i z emulacją czasu offsetowego (E-OBS, ang. offset time-Emulated OBS).
Temat 2: Modelowanie płaszczyzny sterowania architektury OBS z emulacją czasu
offsetowego.
3.2 Wprowadzenie
Od momentu wprowadzenia modelu OBS rozważane były dwie różne koncepcje zapewniania
czasu offsetowego w tego typu sieciach. W konwencjonalnych sieciach OBS (C-OBS), czas
offsetowy wprowadzany jest w węzłach brzegowych (ang. edge node) poprzez opóźnienie
transmisji wiązki pakietów w odniesieniu do pakietu kontrolnego. W sieciach z emulacją
czasu offsetowego (E-OBS), czas offsetowy wprowadzany jest w każdym węźle
przełączającym (ang. core node) za pomocą dodatkowego światłowodowego elementu
opóźniającego. Jakkolwiek koncepcja C-OBS cieszy się ogromnym zainteresowaniem
i poświęcono jej do dzisiaj wiele prac badawczych, w naszej pracy pokazujemy, że posiada
ona liczne wady, które można uniknąć po zastosowaniu koncepcji E-OBS. W tym miejscu
należy zaznaczyć, że brak jest szerokich badań nad E-OBS i jak do tej pory ta koncepcja
rozważana była jedynie w sporadycznych przypadkach.
Ze względu na rozdzieloną transmisję pakietów kontrolnych oraz właściwej grupy
pakietów optycznych przenoszących dane, zarówno opto-elektroniczna płaszczyzna kontroli
jak i całkowicie optyczna płaszczyzna danych mogą być postrzegane jako dwie równoległe
sieci – w szczególności można rozróżnić sieć danych i sieć kontrolną (sterującą). Grupa
pakietów optycznych jest tracona jeżeli tracony jest jej pakiet kontrolny albo też utracie
ulegają same dane. Taka sytuacja ma miejsce w chwili zajętości zasobów, w stanach
przeciążenia (ang. congestion).
Problem przeciążenia w płaszczyźnie danych rozwiązywany jest z pomocą mechanizmów
rozwiązywania konfliktów (ang. contention resolution mechanisms) oraz algorytmów
6
szeregowania (ang. scheduling algorithms) grup pakietów. Przeciążenie w płaszczyźnie
kontroli jest rozwiązywane z pomocą kolejkowania pakietów w buforach elektronicznych
sterownika przełącznika (węzła) optycznego.
Grupa pakietów optycznych może zostać utracona także w wyniku zbyt wczesnego
przybycia pakietów z danymi do węzła przełączającego. Ten efekt ma miejsce jeżeli
całkowity czas przetwarzania pakietu kontrolnego w sterowniku węzła jest dłuższy niż czas
offsetowy. Całkowity czas przetwarzania pakietu kontrolnego określany jest na podstawie
czasu buforowania oraz czasu przetwarzania pakietu w procesorze, jak i czasu potrzebnego na
zestawienie połączenia w matrycy optycznej. Ponieważ pakiety kontrolne podlegają różnym
czasom buforowania, w zależności od obciążenia, całkowity czas przetwarzania jest zmienny.
W rezultacie, określenie czasu offsetowego, który będzie zapobiegał utracie grup pakietów
optycznych nie jest zadaniem trywialnym. Warto wspomnieć, że zbyt duże czasy offsetowe są
niepożądane w sieciach OBS zarówno ze względu na nadmierne opóźnianie grup pakietów
optycznych jak i ograniczenie możliwości ich realizacji w sieciach E-OBS za pomocą
światłowodowych linii opóźniających; stąd, powinny one podlegać optymalizacji.
3.3 Cel pracy
Celem pracy jest rozpoznanie podstawowych charakterystyk architektur C-OBS i E-OBS.
W pierwszej kolejności przedstawiamy ogólną klasyfikację architektur OBS ze względu na
metodę zapewnienia czasu offsetowego, w tym w szczególności, przedstawiamy podstawy
architektury E-OBS. Ponieważ architektura C-OBS była szczegółowo opisana w poprzednich
opracowaniach, zakładamy, że podstawy jej działania są znane. W dalszej kolejności
prowadzimy dyskusję porównawczą dotyczącą kilku zagadnień związanych zarówno
z funkcjonalnymi jak i wydajnościowymi charakterystykami C-OBS i E-OBS.
W drugiej części pracy zajmujemy się modelowaniem płaszczyzny sterowania OBS.
W szczególności analizujemy zakresu zastosowania światłowodowych elementów
opóźniających zapewniających czas offsetowy w sieciach E-OBS. W pierwszej kolejności
analizowane są czynniki mające wpływ na działanie sieci OBS w płaszczyźnie kontroli.
W celu zbadania problemu przeciążenia w płaszczyźnie kontroli wprowadzamy 2 modele
kolejkowe, które reprezentują działanie przykładowego sterownika węzła OBS. Zastosowane
modele pozwalają na zbadanie zależności jakie istnieją pomiędzy kluczowymi parametrami
systemu OBS. W szczególności możliwe jest stwierdzenie zakresu działania architektur
E-OBS, wykorzystujących światłowodowe elementy opóźniające. Należy wspomnieć,
że przedmiot badań nie był szeroko adresowany w literaturze.
3.4 Wyniki pracy
A) W pracy dokonano analizy właściwości dwóch podstawowych architektur OBS,
mianowicie, konwencjonalnej architektury OBS (C-OBS) i architektury z emulacją czasu
offsetowego (E-OBS). Pokazano, że C-OBS posiada wiele wad, które można uniknąć
po zastosowaniu E-OBE. Problem 'niesprawiedliwego' (ang. unfairness) dostępu do
zasobów transmisyjnych, ograniczenia przy routingu alternatywnym, potrzeba
skomplikowanych algorytmów rezerwacji zasobów z możliwością wypełniania luk (ang.
void-filling), utrudnienia przy gwarantowaniu jakości usług, są jednymi z przykładów.
Z drugiej strony, E-OBS pozwala uniknąć wyżej wspomniane problemy. Jak pokazują
najnowsze prezentacje testowych przełączników OBS (dla przykładu, na konferencji
ECOC 2006), emulacja czasów offsetowych za pomocą dodatkowych światłowodowych
elementów opóźniających wprowadzonych w węzłach przełączających jest realizowalna
praktycznie.
7
B) W pracy zajęto się także modelowaniem płaszczyzny sterowania sieci E-OBS.
W szczególności analizowany był problem przeciążenia w płaszczyźnie kontroli i jego
wpływ na problem niedostatecznego offsetu (ang. insufficient offset). W tym celu
zaproponowano dwa modele kolejkowe reprezentujące działanie płaszczyzny
sterowania przykładowego systemu E-OBS, z jednym procesorem przetwarzającym
w sterowniku węzła. W zależności od przyjętego rozkładu czasów przetwarzania,
rozważany jest system kolejkowy M/M/1 z rezygnacją (ang. reneging) oraz system
kolejkowy M/D/1/K (bez rezygnacji). Otrzymane wyniki pokazują, że przy odpowiednim
ustaleniu długości grupy pakietów optycznych możliwe jest ograniczenie
przeciążenia w płaszczyźnie kontroli. Co więcej, w przypadku analizowanego
sterownika, o średnich czasach przetwarzania pakietów kontrolnych, pokazano, że
światłowodowe elementy opóźniające są w stanie zapewnić właściwe czasy offsetowe,
przy jednoczesnym zachowaniu wydajności węzła przełączającego.
Biorąc pod uwagę argumenty zaprezentowane w tym opracowaniu, zasadnym jest uznanie
architektury E-OBS jako wydajnej i funkcjonalnej opcji dla konwencjonalnych sieci
OBS.
Szczegółowe rezultaty prac prowadzonych w ramach Etapu 2 "Badania zintegrowanych
elementów całkowicie optycznego przetwarzania pakietów" w roku 2008 przedstawione
zostały w 5 publikacjach:
[1] M. Klinkowski, M. Marciniak, M. Pióro: Routing optimization in optical burst switching
networks: A multi-path routing approach, to be published in COST293 Final Report, Part
II, Chap. 1. (Załącznik 2.1)
[2] M. Klinkowski, M. Marciniak: Optimization of multi-path routing in optical burst
switching networks, to be published in COST291 Final Report, Chap. 4. Section 7
(Załącznik 2.2)
[3] D. Careglio, M. Klinkowski, J. Sole-Pareta: Preemption window mechanism for efficient
QoS support in E-OBS network architecture, in Proceedings of 5th International
Conference on Broadband Communications, Networks and Systems, BROADNETS
2008, London, UK, 8-11 Sep. 2008, CD version, IEEE, 2008, pp. 1-8. (Załącznik 2.3)
[4] P. Pedroso, D. Careglio, R. Casellas, M. Klinkowski, J. Sole-Pareta: An interoperable
GMPLS/OBS control plane RSVP and OSFP extensions proposal, in Proceedings of 6th
International Symposium; Communication Systems, Networks and Digital Signal
Processing, CSNDSP 2008, Graz University of Technology, Austria, 23-25 July 2008,
IEEE, 2008, pp. 418-422. (Załącznik 2.4)
[5] O. Pedrola, S. Rumley, M. Klinkowski, D. Careglio, C. Gaumier, J. Sole-Pareta: Flexible
simulators for OBS network architectures, in Proceedings of 10th Anniversary
International Conference on Transport Optical Networks, ICTON 2008, Athens, Greece,
22 - 26 June 2008, IEEE, 2008, vol. 3, pp. 117-122. (Załącznik 2.5)
[6] M. Klinkowski, M. Pióro, D. Careglio, M. Zolkiewicz, F. Solano Donado, J. Sole-Pareta:
Physical layer impairment aware routing and wavelength assignment in optical networks,
COST GRAAL Workshop (co-located with DISC 2008) Arcachon, France, Sep. 2008.
[7] M. Klinkowski, D. Careglio, D. Morató, J. Solé-Pareta: Preemption window for burst
differentiation in OBS, in Proceedings of Optical Fiber Communication Conference and
the Fiber Optic Engineers Conference (OFC/NFOEC 2008), San Diego, USA, 24-28
Feb. 2008, Optical Society of America, San Diego, USA, CD version, 2008, pp. 1-3
8
Załącznik 2.1
Contents
Part I Studies in Broadband
and Optical Networks
1
Routing Optimization in Optical Burst Switching Networks: a
Multi-Path Routing Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mirosław Klinkowski, Marian Marciniak, and Michał Pióro
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
OBS technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1
Routing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3
Network modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1
Link loss calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2
Network loss calculation . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3
Multi-path source routing . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4
Resolution methods and numerical examples . . . . . . . . . . . . . . . . . .
1.4.1
Formulation of the optimization problem . . . . . . . . . . . . . .
1.4.2
Calculation of partial derivatives . . . . . . . . . . . . . . . . . . . . .
1.4.3
Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1
Accuracy of loss models . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.2
Properties of the objective function . . . . . . . . . . . . . . . . . . .
1.5.3
Computational effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
4
5
5
6
7
9
10
10
10
11
13
15
15
16
16
17
17
v
Załącznik 2.1
Part I
Studies in Broadband
and Optical Networks
Załącznik 2.1
Załącznik 2.1
Chapter 1
Routing Optimization in Optical Burst
Switching Networks: a Multi-Path Routing
Approach
Mirosław Klinkowski, Marian Marciniak, and Michał Pióro
Abstract This chapter concerns routing optimization in optical burst switching networks (OBS). OBS is a photonic network technology aiming at efficient transport of
IP traffic. OBS architectures are in general bufferless and therefore they are sensitive
to burst congestion. An overall burst loss probability (BLP) which adequately represents the congestion state of the entire network is the primary metric of interest in
an OBS network. The network congestion can be reduced by using proper routing.
We consider multi-path source routing and aim at optimal distribution of traffic over
the network. In this context, we study three network loss models, a well-known loss
model of an OBS network and two original approximate models. Since the objective
function of each model is non-linear, either linear programming formulations with
piecewise linear approximations of this function or non-linear optimization gradient
methods can be used. The presented solution is based on non-linear optimization;
for this purpose we provide the formulas for calculation of partial derivatives. The
main goal of this chapter is to show that the use of approximate models allows
us to speed-up significantly the optimization procedure without losing much accuracy. Moreover we show that our method effectively distributes the traffic over the
network, and the overall BLP can be reduced as compared with both shortest path
routing and alternative routing.
Mirosław Klinkowski
Departament D’Arquitectura de Computadors, Universitat Politècnica de Catalunya, Barcelona,
Spain, and
Department of Transmission and Optical Technology, National Institute of Telecommunications,
Warsaw, Poland, e-mail: [email protected]
Marian Marciniak
Department of Transmission and Optical Technology, National Institute of Telecommunications,
Warsaw, Poland, e-mail: [email protected]
Michał Pióro
Institute of Telecommunications, Warsaw University of Technology, ul. Nowowiejska 15/19, 00665 Warsaw, Poland, and
Lund University, Lund, Sweden, e-mail: [email protected]
3
Załącznik 2.1
4
M. Klinkowski et al.
Key words: multi-path routing, network optimization, non-linear optimization, optical burst switching
1.1 Introduction
Optical Burst Switching (OBS) is a photonic network technology aiming at efficient
transport of IP traffic [20]. OBS architectures are in general bufferless and as such
are sensitive to burst congestion. An overall burst loss probability (BLP) which adequately represents the congestion state of entire network is the primary metric of
interest in an OBS network. The network congestion can be reduced by using proper
routing; in this context alternative (or deflection) routing (e.g., [1]), a common routing strategy in OBS, has been considered. Although deflection routing improves
network performance under low traffic loads, still it may increase burst losses under
moderate and high loads.
In this chapter we consider another approach – multi-path source routing – and
use network optimization theory to distribute the traffic in an optimal way. This
work completes and extends our previous works [11] and [12]. We investigate three
different network loss models, a well-known loss model of an OBS network [21]
and two approximate models developed by ourselves. As the cost function, which
represents the overall burst loss probability, is non-linear, either linear programming formulations with piecewise linear approximations of this function [22] or
non-linear optimization gradient methods [7] can be used. We make use of the latter
approach.
In our non-linear optimization problem we assume that there is a pre-established
virtual path topology consisting of a limited number of paths between each pair
of source-destination nodes. Using a gradient optimization method we calculate a
traffic splitting vector that determines the distribution of traffic over these paths. In
order to support the gradient method we provide straightforward formulas for calculation of partial derivatives. The main goal of this chapter is to show that the use
of approximate models allows us to speed-up significantly the optimization procedure without losing much accuracy. Moreover we show that our method effectively
distributes the traffic over the network, and the overall BLP can be reduced as compared with both shortest path routing and alternative routing. The proposed solution
can be used, in particular, for static (pre-planned) multi-path source routing, where
the traffic distribution is calculated based on a given (long-term) traffic demand matrix. Then either a periodic or a threshold-triggered update of the splitting vector can
be performed if the traffic demand matrix is subject to a change.
The chapter is structured as follows. In Section 1.2 we provide a description
of OBS technology and briefly review routing methods considered for OBS networks. In Section 1.3 we discuss OBS network loss models and introduce a multipath source routing model. In Section 1.4, for each of the introduced network loss
models, we formulate the objective function, calculate the partial derivatives, and
present some numerical results. In Section 1.5 we investigate the accuracy of net-
Załącznik 2.1
1 Routing Optimization in OBS Networks
5
work loss models and the characteristics of the objective function, and discuss the
computational effort of the optimization method. Finally, Section 1.6 contains the
conclusions.
1.2 OBS technology
OBS technology is a promising solution for reducing the gap between transmission and switching speed in future networks. The principal design objective for an
OBS network is that the aggregated user data, called the burst, is carried transparently through the network as an optical signal, i.e., without any optical-to-electrical
conversion. This optical signal passes through the switches that have either none
or very limited buffering capabilities. The control information is carried on a dedicated wavelength and separately from the user data. This information is delivered to
switching nodes with some offset time, prior to the data burst, so that the node can
process it and setup the switching matrix in advance. In such a network the wavelength resources are allocated temporarily and shared between different connections. Such an operation increases network flexibility and adaptability to the bursty
characteristics of IP traffic. Moreover, the aggregation of user data helps to reduce
the scale of control information processed in the network as well as it relaxes the
switching requirements. Since the control information and the user data are separated they can be encoded with different modulation formats and transmitted at different rates. Such division improves network management and provides additional
flexibility.
A conventional OBS network operates with a one-way signalling mode and it
allocates transmission resources on-the-fly, a while before the burst arrives to the
node. Since there is no acknowledgement about the availability of network resources
it may happen that two bursts want to access the same wavelength resources at the
same time. The problem of such a burst contention is crucial in OBS networks. The
conversion of wavelength is a natural mechanisms used to solve this problem [4].
In this mechanism, the carrier frequency of a contending optical signal is converted
to another available one. Deflection (or alternative) routing is another contention
resolution mechanism considered for OBS network. In this case, a contending burst
is forwarded spatially, in the switching matrix, to another output port (fibre).
1.2.1 Routing methods
Static shortest path routing based on Dijkstra’s algorithm is the primary routing
method frequently explored in OBS networks (e.g., [24]). Such routing reduces
overall network utilization when calculated with respect to the number of hops. On
the other hand, some links may be overloaded, while others may be spare, leading to
excessive burst losses. Therefore several both reactive and proactive routing strate-
Załącznik 2.1
6
gies, based on alternative, multi-path, and single-path routing, have been proposed
with the objective of the reduction of burst congestion.
Although alternative routing can improve the network performance under low
traffic load conditions, still it may intensify the burst losses under moderate and
high loads [25]. Indeed the general problem of alternative routing in bufferless OBS
networks is the over-utilization of link resources, what happens if an alternative
path has more hops than a primary path. Hence, whereas first proposals were based
on static route calculation and selection (e.g., [8]), in the next step some authors
proposed an optimized calculation of the set of alternative routes [15] as well as
an adaptive selection of paths [2]. The assignment of lower priorities to deflected
bursts is another important technique which protects against excessive burst losses
on primary paths [1].
Multi-path routing represents another group of routing strategies which aim at
the traffic load balancing in OBS networks. Most of the proposals are based on a
static calculation of the set of equally-important routes, usually with the Dijkstra
algorithm. Then the path selection is performed adaptively and according to some
heuristic [18] or optimized cost function [22][16]. Both traffic splitting [14] and path
ranking [23] techniques are used in the path selection process.
The network congestion in single-path routing can be avoided thanks to a proactive route calculation. Although most of the strategies proposed for OBS networks
consider centralized calculation of single routes [22], still some authors focus on
distributed routing algorithms [5]. Both optimization [26] and heuristic [3] methods
are used.
1.3 Network modelling
We use G = (V, E) to denote the graph of an OBS network; the set of nodes is
denoted as V , and the set of links is denoted as E. Link e ∈ E comprises Ce wavelengths. P denotes the set of paths predefined between source s and destination t
nodes, s,t ∈ V , and s 6= t. Each individual path p ∈ P is identified with a subset
p ⊆ E. Subset Pst ⊆ P identifies all paths from source s to destination t; the sets
Pst are disjoint in our model. Subset Pe ⊆ P identifies all paths that go through
link e.
The reservation (holding) times on each link are independent and identically distributed random variables with the mean equal to the mean burst duration h; for
simplicity we assume h = 1. We assume that the network is capable of full wavelength conversion, i.e. a burst can be transmitted on any available wavelength in
each link. The demand traffic pattern is described by matrix [γst ]s,t∈V and bursts destined to given node t arrive at node s according to a Poisson process of (long-term)
rate γst /h = γst .
Later we use ρ p and ρe to denote the traffic offered to path p ∈ P and the traffic
offered to link e ∈ E, respectively.
Załącznik 2.1
7
re=vp(1-Ei)(1-Ej)
re=vp(1-Ei)(1-Ej)(1-El)(1-Em)
vp
s
Ei
El
Ej
vp
Em
link e
Ei
Ej
link e
s
d
d
(a) Reduced CS
(b) Reduced OBS
re=v1+...+vp
v1
s
vp
...
link e
s
(c) Non-reduced OBS
Fig. 1.1 Link load models
In the following two subsections we deal with the modelling of the volume of
burst traffic lost in the OBS network. The procedure consists, in the first step, of the
calculation of burst loss probabilities Ee on individual links, and in the second step,
of the calculation of BLP in the entire network. Finally, we introduce a multi-path
source routing model.
1.3.1 Link loss calculation
By assuming the network has a full wavelength conversion capability, i.e., each
wavelength can be selected whenever is available, the blocking probability Ee on
each link is given by the following Erlang loss formula (see [21]):
ρ Ce
Ee = E(ρe ,Ce ) = e
Ce !
"
ρi
∑ i!e
i=0
Ce
#−1
,
e ∈ E.
(1.1)
In order to determine Ee , e ∈ E we have to calculate the traffic load ρe offered to
individual links; remind that Ce , e ∈ E is given. Below we provide two models of
such a calculation.
Reduced load (RL). A common loss model of an OBS network was proposed by
Rosberg et al. [21] and it makes use of a reduced load calculation. This model is an
extension of the model proposed by Kelly [9] for circuit-switching (CS) networks.
In the OBS network, it is assumed that the traffic offered to link e is obtained as a
Załącznik 2.1
8
sum of the traffic offered to all the paths that cross this link reduced by the traffic
lost in the preceding links along these paths.
This relation can be expressed as:
ρe =
∑
ρ pΛ pe ,
e ∈ E,
(1.2)
p∈Pe
where
Λ pe =
∏
¡
¢
1−Ef ,
p ∈ P, e ∈ E,
(1.3)
f ∈r pe
and subset r pe ⊂ p identifies all links that precede link e along path p.
The difference between this model and the CS network model is that in the latter
the subset r pe contains all the links that succeed link e along path p, on top of all
preceding links. This difference reflects the fact that a burst offered to path p in OBS
uses a single wavelength from each link along the path until the first link where it is
being blocked or until it exists in the network. On the contrary, a connection in CS
either occupies a channel in all the links along the path or is blocked.
The calculation of link loss probabilities Ee , e ∈ E, together with the calculation
of offered burst traffic ρe , given by the reduced load model (1.2), leads to a fixed
point equation with a solution known as the Erlang fixed-point. The fixed point cannot be solved in a closed form but its approximation can be found through repeated
substitution of (1.1) in (1.2). It is known that the fixed point exists in both CS and
OBS networks (see [9] and [21], respectively). Although the fixed point is unique in
CS networks, still, its uniqueness has not been proved in OBS networks.
Although the traffic offered to a route is Poisson, still it may be thinned by blocking at the consecutive links and thus no longer remains Poisson. Since there is no
straightforward solution to this problem we make a simplification that the burst arrival process to each link is Poisson.
Non-reduced load (NRL). Formulation (1.2) may bring some computational difficulty, especially, with regard to the calculation of partial derivatives for optimization
purposes. Therefore, we also consider a simplified non-reduced load model, where
the traffic offered to link e is calculated as a sum of the traffic offered to all paths
that cross this link:
ρe =
∑
ρp,
e ∈ E.
(1.4)
p∈Pe
The rationale behind this assumption is that under low link losses E f , f ∈ E,
observed in a properly dimensioned network, model (1.2) can be approximated by
(1.4).
Figures 1.1a-c present illustrative examples of the reduced load calculation for
both CS and OBS networks, as well as of the non-reduced load calculation.
Załącznik 2.1
9
1.3.2 Network loss calculation
Overall network loss (NL). The calculation of overall burst loss/blocking probability in an OBS network is presented in [21], and it uses the same formulation as
it was proposed for CS networks [9]. In further discussion we name this model an
overall network loss (NL) model.
The main modelling steps include the calculation of:
1. burst loss probabilities Ee on links, given by (1.1),
2. loss probabilities L p of bursts offered to paths
L p = 1 − ∏ (1 − Ee ) ,
p ∈ P,
(1.5)
e∈p
3. and the overall burst loss probability BNL
"
BNL =
∑
p∈P
ρpLp
#−1
∑
ρp
.
(1.6)
p∈P
In order to calculate the path loss probability L p , p ∈ P, we take an assumption
that burst blocking events occur independently at the network links. Then formula
(1.5) accounts for blocking probabilities in all links e that belong to path p.
The overall burst loss probability BNL is calculated simply as the volume of burst
traffic lost in the network normalized to the volume of burst traffic offered to the
network.
Overall link loss (LL). Another method for calculation of burst losses in the entire
network is based on an overall link loss (LL) model [6]. In this method we sum up
the volumes of traffic lost on individual network links.
The main modelling steps include the calculation of:
1. burst loss probabilities Ee on links, given by (1.1),
2. and BLL , a sum of the burst traffic lost on individual links relative to the overall
traffic offered to the network
"
#−1
LLL =
∑ ρe E e ∑
e∈E
ρp
.
(1.7)
p∈P
LL overestimates actual burst losses given by (1.6) in NL because it counts twice
the intersection of blocking events that occur on distinct links. In fact BLL may be
higher than 1 and thus it cannot be considered as the probability metric. Nevertheless, for Ee → 0, e ∈ E, the blocking events that occur simultaneously vanish rapidly
and model (1.7) converges to model (1.6).
Załącznik 2.1
10
path 1
3
2
x1
burst
1
A
4
x2
5
6
path 2
Fig. 1.2 An example of OBS network with source-based routing; x1 and x2 are the traffic splitting
factors and x1 + x2 = 1.
1.3.3 Multi-path source routing
We assume that the network applies source-based routing, so that the source node
determines the path of a burst that enters the network (see Fig. 1.2). Moreover, the
network uses multi-path routing where each subset Pst comprises a (small) number
of paths and a burst can follow one of them. We assume that the selection of a route
from set Pst is random for each burst and is performed according to a given traffic
splitting factor x p , such that
0 ≤ x p ≤ 1,
∑ p∈Pst x p = 1,
p ∈ P,
s,t ∈ V, s 6= t.
(1.8)
(1.9)
Thus traffic ρ p offered to path p ∈ Pst can be calculated as
ρp = xpτp,
(1.10)
where τ p = γst is the total traffic offered between s and t.
Here vector x = (x1 , . . . , x|P| ) determines the distribution of traffic over the network; this vector should be optimized to reduce congestion and to improve overall
performance.
1.4 Resolution methods and numerical examples
1.4.1 Formulation of the optimization problem
Taking into account different methods of the link load and the network loss calculation presented in Section 1.3, several network loss models with corresponding
objective functions can be defined.
Załącznik 2.1
11
1. NL-RL. The link load is calculated according to the RL model given by (1.2),
and the network loss is calculated according to the NL model given by (1.6) with
the objective function given by:
BNL−RL (x) =
∑
xpτpLp.
(1.11)
p∈P
2. NL-NRL. The link load is calculated according to the NRL model given by (1.4),
and the network loss is calculated according to the NL model given by (1.6) with
BNL−NRL (x) =
∑
xpτpLp.
(1.12)
p∈P
3. LL-NRL. The link load is calculated according to the NRL model given by (1.4),
and the network loss is calculated according to the LL model given by (1.7) with
!
Ã
BLL−NRL (x) =
∑ ρe Ee = ∑ Ee ∑
e∈E
e∈E
xpτp .
(1.13)
p∈Pe
The last possible combination of the link load and the network loss calculation
is LL-RL. Because such a model does not bring much gain with respect to the NLRL model, as it does not avoid the complexity of fixed-point calculation, we do not
study it.
£
¤−1
In each case the normalization factor ∑ p∈P ρ p
has been omitted because we
assume it to be a constant value.
The optimization problem is the same for each method, and is formulated as
follows:
min B(x)
x
(1.14)
subject to the multi-path routing constraints given by (1.8) and (1.9).
Since in each case B(x) is a non-linear function of vector x, the optimization problem is non-linear. Taking into account the form of both constraints (1.2) and (1.4),
a particularly convenient optimization method is the Frank-Wolfe reduced gradient
method (algorithm 5.10 in [19]); this algorithm was used for a similar problem in
circuit-switched (CS) networks [7].
1.4.2 Calculation of partial derivatives
In general, gradient methods are iterative methods used in the optimization of convex functions. Gradient methods need to employ the calculation of partial derivatives of the cost function so that to find the direction of improvement of this func-
Załącznik 2.1
12
tion. Below we provide adequate formulas for the partial derivatives for each of the
models.
NL-RL model. The partial derivative of BNL−RL with respect to xq , q ∈ P, can be
derived directly by a standard method involving the solution of a system of linear
equations. It follows from (1.2) and (1.1) that
∂ E f (x)
∂ ρe (x)
,
= αqe τqΛqe + ∑ x p τ pΛ pe ∑ (1 − E f )−1
∂ xq
∂ xq
f ∈r pe
p∈Pe
e ∈ E, q ∈ P,
(1.15)
where αqe = 1 if e ∈ q, and αqe = 0 otherwise, and
¶
µ
Ce − ρe ∂ ρe (x)
∂ Ee (x)
,
= Ee Ee +
∂ xq
ρe
∂ xq
e ∈ E, q ∈ P.
(1.16)
In order to solve the system of equations (1.15)-(1.16) a fixed-point calculation
procedure, i.e., repeated substitution of (1.15) in (1.16), has to be applied.
From (1.5) we have
∂ L p (x)
∂ Ee (x)
,
= (1 − L p ) ∑e∈p (1 − Ee )−1
∂ xq
∂ xq
p, q ∈ P,
(1.17)
q ∈ P.
(1.18)
and finally from (1.11)
∂ L p (x)
∂
,
BNL − RL(x) = τq Lq + ∑ x p τ p
∂ xq
∂ xq
p∈P
The calculation of partial derivatives (1.15)-(1.18) in NL-NRL model is extremely time consuming since it involves an iterative fixed-point approximation procedure.
NL-NRL model. The partial derivative of BNL−NRL with respect to xq , q ∈ P, could
be derived directly from formulae (1.1) and (1.4)-(1.6) by a standard method involving resolution of a system of linear equations, similarly to (1.15)-(1.18). Although
there is no need for a fixed-point calculation in NL-NRL model, still such a computation would be time-consuming.
Therefore we propose instead a straightforward exact calculation based on F. Kelly’s
approach for CS networks [10]; a detailed derivation of formulas is presented in
[11]. In particular, for each path q ∈ P we have
h
i
∂
BNL−NRL (x) = τq Lq + ∑e∈q ce ,
∂ xq
where ce is calculated for each link e ∈ E as
(1.19)
Załącznik 2.1
13
-1
1,E-01
10
-2
Burstloss
loss probability
probability
Burst
1,E-02
10
-3
1,E-03
10
-4
1,E-04
10
SPR (sim)
MR, NL-NRL (sim)
MR, NL-RL (an)
-5
1,E-05
10
MR, NL-NRL (an)
MR, LL-NRL (an)
-6
10
1,E-06
12.8
0,4
16
0,5
19,2
0,6
22,4
0,7
25,6
0,8
Offered
load, Erlangs
Erlangs
Fig. 1.3 Validation of optimization models.
ce = ηe ∑ p∈P ρ p (1 − L p ),
(1.20)
e
and
ηe = E(ρe ,Ce − 1) − E(ρe ,Ce ),
e ∈ E.
(1.21)
Due to assumption (1.4) we have managed to simplify the model (1.2) and make
the calculation of partial derivatives defined by (1.19) and (1.20) straightforward,
not involving any iterations. Indeed, once |E| of unknowns (ce ) are pre-calculated
they can be used in (1.19) to obtain the partial derivatives. Calculating the gradient
in this method, therefore, is not longer an issue.
LL-NRL model. The partial derivative of BLL−NRL with respect to xq , q ∈ P, can
be derived directly from formulae (1.1), (1.4), and (1.13)
i
h
∂
BLL−NRL (x) = τq ∑e∈q (Ee + ηe ρe (1 − Ee )) ,
∂ xq
(1.22)
where ηe is given by equation (1.21).
1.4.3 Numerical results
We evaluated the performance of our multi-path source routing scheme in an eventdriven simulator. In order to find a splitting vector x specifying a near-optimal routing we used a solver fmincon for constrained nonlinear multivariable functions
available in the M ATLAB optimization toolbox. Then we applied this vector in the
simulator.
Załącznik 2.1
14
0
1,E+00
10
-1
Burst loss
loss probability
Burst
probability
1,E-01
10
-2
1,E-02
10
-3
1,E-03
10
SPR, 1 path
-4
1,E-04
10
AR, 2 paths
-5
1,E-05
10
AR, 6 paths
MR, 2 paths
-6
1,E-06
10
12.8
0,4
19,2
0,6
25,6
0,8
32
1
38,4
1,2
Erlangs
Offered
load, Erlangs
Fig. 1.4 Performance comparison of routing strategies (simulation results).
The evaluation was performed for NSFNET, an American backbone network
topology of 15 nodes and 23 links [17]; each link had C = 32 wavelengths and the
transmission bitrate in each wavelength channel was 10 Gbps. Besides the results of
optimized multi-path routing (MR) we provide, as a comparison, the results of two
other routing strategies: a simple shortest path routing (SPR) and a pure alternative
routing (AR). We considered 2 shortest paths per each source-destination pair of
nodes in MR; they were not necessarily disjoint. In SPR only 1 path was available,
whilst in the case of AR we considered 2 different scenarios: with 2 and 6 paths
available. Uniform traffic matrix and exponential burst inter-arrivals and durations
were considered. All the simulation results had 99% level of confidence.
In Fig. 1.3 we show the overall burst loss probability results of the MR strategy,
which was optimized with the assistance of NL-NRL, NL-RL, and LL-NRL models,
successively. The characteristics are obtained in the function of offered traffic load,
which is normalized to the wavelength bitrate and expressed in Erlangs (e.g., 12.8
Erlangs means that each node generates 128 Gbps). As a reference, we provide the
results of SPR.
In the studied scenario, we can see that the burst loss probability results of optimized MR evaluated in the M ATLAB environment are (almost) the same regardless
which network loss model is used. Moreover, the analytical results obtained for NLNRL model agree very well with simulation results (’(sim)’ in Fig. 1.3).
In Fig. 1.4 we compare simulation results obtained for different routing scenarios.
We see that the optimized multi-path routing outperforms the shortest path routing
in the whole range of traffic loads. Also it offers at least as good results as the
alternative routing if the same number of routing paths is available.
Załącznik 2.1
15
Approximation errors relative to NL-RL model
1,E+00
1.0
Relative
Relative
error, error
(BX-BNL-RL)/BNL-RL
NL-NRL, C=8
8,E-01
0.8
LL-NRL, C=8
NL-NRL, C=32
LL-NRL, C=32
6,E-01
0.6
0.4
4,E-01
2,E-01
0.2
0,E+00
0
-0.2
-2,E-01
-4
1,00E-04
10
-3
1,00E-03
10
-2
1,00E-02
10
-1
1,00E-01
10
0
1,00E+00
10
Blocking
Probability,
BNL-RL
Blocking
Probability,
B_NL-RL
Fig. 1.5 Approximation errors relative to NL-RL model vs. blocking probability; NSFNET, shortest path routing, 8 and 32 wavelengths.
1.5 Discussion
In this section we investigate the accuracy of network loss models and the characteristics of the objective function. We also discuss the computational effort of the
optimization procedure.
1.5.1 Accuracy of loss models
We study the accurary of both NR-NRL and LL-NRL network loss approximations
relative to the NL-RL network loss model. To do that we define the approximation
error as:
ErX ,
BX − BNL−RL
,
BNL−RL
(1.23)
where X refers to either NL − NRL or LL − NRL, so BX means the result of the
objective function for model X.
In Fig. 1.5 we present the results of ErX obtained in NSFNET network, with a
different number of wavelengths per link considered and the shortest path routing
used. We can see that the accuracy of both network loss approximate models is very
strict for the blocking probability in the network BNL−RL below 10−2 .
Załącznik 2.1
16
Network Paths Tol.
2 10−6
SIMPLE
4 10−6
SIMPLE
NSFNET 2 10−6
NSFNET 4 10−6
2 10−6
EON
2 10−3
EON
NL-RL
OF SOLV
BLP
2.4 · 10−3 64 sec 1.5 sec
2.4 · 10−3 243 sec 3 sec
> 5h
4.6 · 10−2
> 5h
3.1 · 10−2
−2
> 5h
1.76 · 10
> 5h
1.77 · 10−2
NL-NRL
SOLV
OF
0.1 sec 1.4 sec
0.1 sec 3.4 sec
0.38 sec 22.3 sec
1.6 sec 937 sec
5.5 sec 803 sec
1.1 sec 260 sec
LL-NRL
SOLV
OF
0.1 sec 1.5 sec
0.1 sec 3.1 sec
0.37 sec 24.3 sec
1.5 sec 952 sec
5.3 sec 837 sec
1.0 sec 263 sec
Table 1.1 Comparison of computation times.
1.5.2 Properties of the objective function
NL-RL model. In [10] Kelly demonstrated that the reduced-load loss model of a CS
network is in general not convex. Taking into account an analogy of the reducedload calculation in both CS and OBS networks, we can expect that function (1.11)
is not convex as well. Therefore a solution of optimization problem (1.14) may not
be unique.
NL-NRL model. Similarly as in the case of RL-NL model, it can be shown numerically that the objective function (1.12) is not necessarily convex; in particular, under
high traffic load conditions, there can be found 2 feasible vectors x1 , x2 , such that:
BNL−NRL (λ x2 + (1 − λ )x2 ) > λ BNL−NRL (x2 ) + (1 − λ )BNL−NRL (x1 ),
(1.24)
where 0 ≤ λ ≤ 1.
LL-NRL model. An advantageous property of LL-NRL model is the convexity of
its objective function (1.13); a detailed proof can be found in [13]. For this reason,
a corresponding optimization problem has a unique solution.
1.5.3 Computational effort
In Table 1.1 we compare the computation times of both the objective function (with
the partial derivatives calculation included) and the fmincon solver function of the
M ATLAB environment; in the table they are denoted as OF and SOLV, respectively.
The evaluation is performed on a Pentium D, 3GHz computer. The results are obtained for SIMPLE (6 nodes, 8 links, and 60 paths), NSFNET (15 nodes, 23 links,
and 420 paths), and EON (28 nodes, 39 links, and 1512 paths) network topologies;
the number of wavelengths per link is 32, each source-destination pair of nodes has
2 or 4 shortest paths available, the traffic load is equal to 25.6 Erlangs and 19.2 Erlangs, respectively, for SIMPLE/NSFNET and EON scenarios. In case the iterative
procedure of the Erlang fixed point approximation is used, it ends if the maximal
discrepancy between two consecutive link loss calculations is smaller then 10−6 .
Załącznik 2.1
17
The starting traffic splitting vector is x = 0.5 · (1, ..., 1), meaning that the traffic is
equally distributed on the paths for each demand.
We can see that the calculation of the objective function (and of partial derivatives) is highly time consuming in the NL-RL model even in a small network
scenario. On the contrary, such a calculation is not an issue if either NL-NRL or
LL-NRL model is used. It is worth to see that by decreasing the value of a termination tolerance parameter (’Tol.’ in the table), which decides on the termination of the
solver function, we significantly accelerate the optimization procedure (more than
three times) without substantial decrease of routing performance (compare ’BLP’
value in both EON scenarios). Moreover, we can see that when increasing the number of paths the computation time of the solver function increases considerably in a
larger (NSFNET) network scenario.
1.6 Conclusions
In this chapter we have studied a non-linear optimization method for multi-path
source routing problem in OBS networks. In this method we calculate a traffic splitting vector that determines a near-optimal distribution of traffic over routing paths.
Since a conventional network loss model of an OBS network is complex we have introduced some simplifications. The proposed models are computationally effective
and are still highly accurate compared to the basic model. The obtained formulae
for partial derivatives are straightforward and very fast to compute. It makes the proposed non-linear optimization method a viable alternative for linear programming
formulations based on piecewise linear approximations of the cost function.
The simulation results demonstrate that our method effectively distributes the
traffic over the network and the overall burst loss probability can be significantly
reduced compared with the shortest path routing.
Acknowledgements Part of the results have been achieved during a Short Term Scientific Mission
of COST Actions 293 (”Graphs and Algorithms in Communication Networks”) and 291 (”Towards
Digital Optical Networks”). The work was supported by the Spanish Ministry of Education and
Science under the CATARO project (Ref. TEC2005-08051-C03-01).
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9. Kelly, F.P.: Blocking probabilities in large circuit-switched networks. Advanced Applied Probability 18, 473–505 (1986)
10. Kelly, F.P.: Routing in circuit-switched networks: Optimization, shadow prices and decentralization. Advanced Applied Probability 20, 112–144 (1988)
11. Klinkowski, M., Pioro, M., Careglio, D., Marciniak, M., Sole-Pareta, J.: Non-linear optimization for multi-path source routing in obs networks. IEEE Communications Letters 11(12)
(2007)
12. Klinkowski, M., Pioro, M., Careglio, D., Marciniak, M., Sole-Pareta, J.: Routing optimization in optical burst switching networks. In: Proceedings of the 11th Conference on Optical
Network Design and Modelling (ONDM 2007). Athens, Greece (2007)
13. Krishnan, K.R.: The convexity of loss rate in an erlang loss system and sojourn in an erlang
delay system with respect to arrival and service rates. IEEE Trans. on Comm. 38(9), 1314–
1316 (1990)
14. Li, J., Mohan, G., Chua, K.C.: Dynamic load balancing in ip-over-wdm optical burst switching
networks. Computer Networks 47(3), 393–408 (2005)
15. Long, K., Yang, X., Huang, S., Chen, Q., Wang, R.: Adaptive parameter deflection routing to
resolve contentions in obs networks. In: Proceedings of the 5th International Conference on
Networking (Networking 2006). Coimbra, Portugal (2006)
16. Lu, J., Liu, Y., Gurusamy, M., Chua, K.: Gradient projection based multi-path traffic routing
in optical burst switching networks. In: Proceedings of IEEE High Performance Switching
and Routing workshop (HPSR 2006). Poznan, Poland (2006)
17. Nsfnet-the national science foundation network. http://moat.nlanr.net/
18. Ogino, N., Arahata, N.: A decentralized optical bursts routing based on adaptive load splitting
into pre-calculated multiple paths. IEICE Transactions on Communications E88-B(12), 4507–
4516 (2005)
19. Pioro, M., Medhi, D.: Routing, Flow, and Capacity Design in Communication and Computer
Networks. Morgan Kaufmann (2004)
20. Qiao, C., Yoo, M.: Optical burst switching (obs) - a new paradigm for an optical internet. J.
of High Speed Networks 8(1), 69–84 (1999)
21. Rosberg, Z., Vu, H., Zukerman, M., White, J.: Performance analyses of optical burst switching
networks. IEEE JSAC 21(7), 1187–1197 (2003)
22. Teng, J., Rouskas, G.N.: Traffic engineering approach to path selection in optical burst switching networks. Journal of Optical Networking 4(11), 759–777 (2005)
23. Yang, L., Rouskas, G.: Adaptive path selection in optical burst switched networks. IEEE/OSA
Journal of Lightwave Technology 24(8), 3002–3011 (2006)
24. Yang, L., Rouskas, G.: A framework for absolute qos guarantees in optical burst switched
networks. In: Proceedings of IEEE Broadnets 2006. San Jose, CA (USA) (2006)
25. Zalesky, A., Vu, H., Rosberg, Z., Wong, E., Zukerman, M.: Modelling and performance evaluation of optical burst switched networks with deflection routing and wavelength reservation.
In: Proceedings of IEEE INFOCOM 2004. Hong Kong, China (2004)
26. Zhang, J., Wang, S., Zhu, K., Datta, D., Kim, Y.C., Mukherjee, B.: Pre-planned global rerouting for fault management in labeled optical burst-switched wdm networks. In: Proceedings of
Global Telecommunications Conference (GLOBECOM 2004). Dallas, TX (USA) (2004)
Załącznik 2.2
Chapter 4 / Section 7
”Optimization of multi-path routing in optical
burst switching networks”
MirosÃlaw Klinkowski and Marian Marciniak
National Institute of Telecommunications (Poland)
March 4, 2008
Załącznik 2.2
2
Załącznik 2.2
1. PERFORMANCE ISSUES IN OPTICAL BURST/PACKET SWITCHING
1.1 Optimization of multi-path routing in optical
burst switching networks
1.1.1 Introduction
In this Section we concern on the problem of routing optimization in optical
burst switching networks (OBS). OBS architectures without buffering capabilities are sensitive to burst congestion. An overall burst loss probability (BLP)
which adequately represents the congestion state of entire network is the primary metric of interest in an OBS network. The network congestion can be
reduced by using proper routing; in this context alternative (or deflection)
routing (e.g., see [2]), a common routing strategy in OBS, has been considered.
Although deflection routing improves network performance under low traffic
loads, still, it may increase burst losses under moderate and high loads.
We consider another approach - multi-path source routing - and we use
network optimization theory to improve it. Since an overall BLP has a nonlinear character (see e.g., [3]), either linear programming formulations with
piecewise linear approximations of this function (see e.g., [4]) or non-linear
optimization gradient methods [5] can be used. We make use of the latter
approach.
In our non-linear optimization problem we assume that there is a preestablished virtual path topology consisting of a limited number of paths between each pair of source-destination nodes. Using a gradient optimization
method we calculate a traffic splitting vector that determines the distribution
of traffic over these paths. In order to support the gradient method we use
straighforward formulas for calculation of partial derivatives.
1.1.2 Routing scenario
We use G = (V, E) to denote the graph of an OBS network; the set of nodes
is denoted as V, and the set of links is denoted as E. Link e ∈ E comprises
Ce wavelengths. P defines a set of all paths predefined between each source
nodes s and destination nodes d, where s, d ∈ V and s 6= d. Each individual
PERFORMANCE ISSUES IN OPTICAL BURST/PACKET SWITCHING
3
Załącznik 2.2
path 1
3
2
x1
burst
1
A
4
x2
5
6
path 2
Figure 1-1 Example of OBS network with source-based routing; x1 and x2 are
the traffic splitting factors and x1 + x2 = 1.
path p ∈ P is identified with a subset p ⊆ E. Subset Psd ⊆ P identifies all
paths from source s to destination d. Subset Qe ⊆ P identifies all paths that
go through link e.
We assume that the network applies source-based routing, so that the source
node determines the path of a burst that enters the network (see Fig. 1-1).
Moreover, the network uses multi-path routing where each subset Psd comprises
a (small) number of paths and a burst can follow one of them. Path selection
is performed according to given traffic splitting factor xp , such that
0 ≤ xp ≤ 1, p ∈ P,
and
X
p∈Psd
xp = 1, s, d ∈ V, s 6= d.
(1.1)
The reservation (holding) times on each link are i.i.d. random variables
with the mean equal to the mean burst duration h; for simplicity we assume
h = 1. The demand traffic pattern is described by matrix [tsd ]s,d∈V and bursts
destined to given node d arrive at node s according to a Poisson process of
(long-term) rate tsd /h = tsd . Thus traffic vp offered to path p ∈ Psd can be
calculated as
vp = xp τp ,
(1.2)
where τp = tsd is the total traffic offered between s and d.
Here vector x = (x1 , . . . , x|P| ) determines the distribution of traffic over the
network; this vector should be optimized to reduce congestion and to improve
overall performance.
1.1.3 Formulation
A loss model of OBS network
A loss model of OBS network based on the Erlang fixed-point approximation
was proposed by Rosberg et al. [3]. In particular, the traffic offered to link e
is obtained as a sum of the traffic offered to all the paths that cross this link
reduced by the traffic lost in the preceding links along these paths
4
Załącznik 2.2
ρe =
X
p∈Qe
vp
Y
(1 − Eg ) ,
e∈E
(1.3)
g∈rpe
where subset rpe ⊂ p identifies all links that precede link e along path p.
The formulation of [3] may bring some difficulty in the context of computation of partial derivatives for optimization purposes. Therefore we propose
a simplified non-reduced link load model where the traffic offered to link e is
calculated as a sum of the traffic offered to all the paths that cross this link
X
ρe =
vp , e ∈ E.
(1.4)
p∈Qe
The rationale behind this assumption is that under low link losses Eg ,
observed in a properly dimensioned network, model (1.3) can be approximated
by (1.4).
The main modelling steps include the calculation of
1. burst loss probabilities Ee on links, given by the Erlang loss formula
#−1
"C
e
i
e
X
ρ
ρC
e
, e∈E
(1.5)
Ee = E(ρe , Ce ) = e
Ce ! i=0 i!
2. loss probabilities Lp of bursts offered to paths
Y
Lp = 1 −
(1 − Ee ) , p ∈ P
(1.6)
e∈p
3. and the overall burst loss probability B
#−1
"
X
X
.
B=
vp
vp Lp
(1.7)
p∈P
p∈P
Optimization problem
From equations (1.2) and (1.7) we define a cost function to be the subject of
optimization:
X
B(x) =
xp τp Lp .
(1.8)
p∈P
The optimization problem is formulated as follows:
min B(x)
(1.9)
subject to the constraints given by (1.1).
Since the overall BLP is a non-linear function of vector x the cost function
is non-linear as well. Taking into account the form of constraints (1.4), a particularly convenient optimization method is the Frank-Wolfe reduced gradient
method (algorithm 5.10 in [6]); this algorithm was used for a similar problem
in circuit-switched (CS) networks [5].
OPTIMIZATION OF MULTI-PATH ROUTING IN OPTICAL BURST SWITCHING
NETWORKS
5
Załącznik 2.2
Partial derivatives
Gradient methods need to employ the calculation of partial derivatives of the
cost function. The partial derivative of B with respect to xq , q ∈ P, could
be derived directly from formulae (1.4)-(1.7) by a standard method involving
resolution of a system of linear equations. Such a computation, however, would
be time-consuming.
Therefore instead in [7] we provide a straightforward derivation of the partial derivative that is based on the F. Kelly approach previously proposed for
CS networks in [8]. In particular, for each path q ∈ P we have
i
h
X
∂
ce ,
B(x) = τq Lq +
e∈q
∂xq
(1.10)
where ce is defined for each link e ∈ E as
ce = ηe
X
p∈Qe
vp (1 − Lp ),
(1.11)
and for each link e ∈ E
ηe = E(ρe , Ce − 1) − E(ρe , Ce ).
(1.12)
Due to assumption (1.4) we have managed to simplify the model described
in [8] and make the calculation of partial derivatives defined by (1.11) and
(1.10) straightforward, not involving any iterations. Indeed once |E| unknowns
(ce ) are pre-calculated then they can be used in (1.10) to obtain the partial
derivatives. The calculation of gradient in our method, therefore, is not longer
an issue.
Some remarks
It can be shown (numerically) that the objective function (1.8) is not necessarily
convex; in particular, under high traffic load conditions, there can be found 2
feasible vectors x1 , x2 , such that:
BN L−N RL (λx2 + (1 − λ)x2 ) > λBN L−N RL (x2 ) + (1 − λ)BN L−N RL (x1 ), (1.13)
where, 0 ≤ λ ≤ 1.
Nevertheless, under moderate traffic loads (ρe < Ce , e ∈ E) we have observed that several repetitions of the optimization of (1.8) using formula (1.10)
always give us the same (with a finite numerical precision) near-optimal value
of B.
6
Załącznik 2.2
0
Burst Loss Probability
10
1,E+00
EON (64ls)
-1
1,E-01
10
NSFnet (32ls)
-2
10
1,E-02
-3
1,E-03
10
reduced link load
non-reduced link load
-4
10
1,E-04
13
17
21
25
29
Erlangs
Figure 1-2 Accuracy of non-reduced link load model.
1.1.4 Results
We evaluated the performance of our routing scheme in an event-driven simulator. In order to find a splitting vector x specifying a near-optimal routing we
use a solver fmincon for constrained nonlinear multivariable functions available
in the Matlab environment. Then we apply this vector in the simulator.
The evaluation is performed for NSFnet (15 nodes, 23 links) and EON (28
nodes, 39 links) network topologies; different number of wavelengths (λs) per
link are considered, transmission bitrate is 10Gbps. The optimized routing
(OR) is compared with two other routing strategies: a simple shortest path
routing (SP) and a pure deflection routing (DR). We consider 2 shortest paths
per each source-destination pair of nodes; they are not necessarily disjoint. In
SP routing only 1 path is available. Uniform traffic matrix and exponential
burst inter-arrivals and durations are considered. All the simulation results
have 99% level of confidence.
In Fig. 1-2 we compare the overall burst loss probability B of both reduced
link loss model (1.3) and non-reduced link loss model (1.4), calculated in the
function of offered traffic load, which is normalized to the bitrate and expressed
in Erlangs (e.g., 25Erlangs mean that each node generates 250Gbps), and
with SP routing. We can see that the accuracy of non-reduced link load model
is very strict for B below 10−2 .
In Fig. 1-3 we show B as a function of offered traffic load for different routing scenarios. We see that the optimized routing can achieve very low losses,
particularly, when compared with the shortest path routing. Analytical results
(’OR-an’ in the figure) obtained with (1.7) correspond very well to simulation
results. The optimization takes about 23 sec and 1800 sec for NSFnet network
(of 420 paths) and EON network (of 1512 paths), respectively, when using a
non-commercial Matlab solver on a Pentium D, 3GHz computer.
OPTIMIZATION OF MULTI-PATH ROUTING IN OPTICAL BURST SWITCHING
NETWORKS
7
Załącznik 2.2
-1
-1
1,E-01
10
1,E-01
10
-2
1,E-02
10
-2
1,E-02
10
-3
1,E-03
10
32ls
-4
1,E-04
10
SP
DR
OR
OR-an
-5
1,E-05
10
-3
1,E-03
10
64ls
-4
10
1,E-04
-5
10
1,E-05
SP
DR
OR
OR-an
-6
1,E-06
10
-7
-6
1,E-06
10
0,4
12.8
0,5
16
0,6
0,7
19.2
22.4
Erlangs
0,8
25.6
10
1,E-07
0,15
9.6
0,2
12.8
0,25 19.2
0,3
16
Erlangs
0,35 25.6
0,4
22.4
Figure 1-3 Comparison of routing schemes a) NSFnet, b) EON.
1.1.5 Conclusion
In this Section we have proposed a non-linear optimization method for multipath source routing problem in OBS networks. In our method we calculate
a traffic splitting vector that determines a near-optimal distribution of traffic
over routing paths. The presented formulae for partial derivatives are straightforward and very fast to compute. It makes the proposed non-linear optimization method a viable alternative for linear programming formulations based on
piecewise linear approximations.
The simulation results demonstrate that our method effectively distributes
the traffic over the network and the network-wide burst loss probability can be
reduced compared with the shortest path routing.
8
Załącznik 2.2
BIBLIOGRAPHY
[1] C. Qiao and M. Yoo, ”Optical Burst Switching (OBS) - a New Paradigm
for an Optical Internet”, J. High Speed Networks, vol. 8, no. 1, Mar. 1999,
pp. 69-84.
[2] C. Cameron, et al, ”Prioritized Deflection Routing in Optical Burst Switching Networks”, IEICE Trans. on Comm., vol. E88-B, no. 5, pp. 1861-1867,
May 2005.
[3] Z. Rosberg, et al, ”Performance Analyses of Optical Burst Switching Networks”, IEEE JSAC, vol. 21, no. 7, Sep. 2003, pp. 1187-1197.
[4] J. Teng, G. Rouskas, ”Traffic Engineering Approach to Path Selection in
Optical Burst Switching Networks”, J. Opt. Net., vol. 4, no. 11, 2005.
[5] R. J. Harris, ”The Modified Reduced Gradient Method for Optimally Dimensioning Telephone Networks”. Australian Telecom. Research. vol. 10,
no. 1, 1976, pp. 30-35.
[6] M. Pioro and D. Medhi, ”Routing, Flow, and Capacity Design in Communication and Computer Networks”, Morgan Kaufmann, 2004.
[7] M. Klinkowski, M. Pioro, D. Careglio, M. Marciniak, and J. Sole-Pareta,
“Non-linear Optimization for Multipath Source-Routing in OBS Networks”,
IEEE Communications Letters, vol. 11, no. 12, Dec. 2007.
[8] F. P. Kelly, ”Routing in Circuit-Switched Networks: Optimization, Shadow
Prices and Decentralization”, Advanced Applied Probability, vol. 20, 1988,
pp. 112-144.
BIBLIOGRAPHY
9
Załącznik 2.3
Preemption Window mechanism for efficient QoS
support in E-OBS network architecture
Davide Careglio∗ , Miroslaw Klinkowski∗ ,† , Josep Solé-Pareta∗
∗ Advanced
Broadband Communication Center
Universitat Politècnica de Catalunya, Barcelona, Catalunya, 08034 Spain
Email: {careglio, mklinkow, pareta}@ac.upc.edu
† National Institute of Telecommunications
Warsaw, 04-894 Poland
Abstract—This paper focuses on the problem of quality of
service (QoS) provisioning in optical burst switching (OBS)
networks. OBS is a promising photonic network technology
aiming at efficient transport of IP traffic by means of statistical
multiplexing. The lack of optical memories, however, makes this
operation quite complicated. Problems such as unfairness in
access to the shared transmission resources, facility in adopting
alternative and backup routing, scheduling complexity and so on
arise in the conventional OBS architecture. In [1] we proposed the
offset-time emulated OBS (E-OBS) architecture, which overcomes
all these drawbacks by means of distributed provisioning of
the offset time in core nodes. Nonetheless it is still difficult to
guarantee a certain level of service quality. Burst preemption
mechanism, which, alongside with offset-time differentiation, was
proven to be the most effective technique for QoS provisioning in
OBS networks. The general drawback of any burst preemptionbased mechanism is that, in case of successful preemption, either
the resources reserved for the preempted bursts on outgoing path
are wasted or an additional signaling procedure should be carried
out in order to release them. In order to avoid wasted resources
reservation, in [2] we proposed the Preemption Window (PW)
mechanism which enhances the E-OBS for efficient QoS support.
In this paper we evaluate exhaustively the performance of the
resulting architecture showing all its advantageous with respect
to other solutions.
I. I NTRODUCTION
Optical burst switching (OBS) is a promising solution for
reducing the gap between switching and transmission speeds in
future networks [3]. Packets coming from client networks are
aggregated and assembled into optical data bursts in the edge
nodes of an OBS network. A burst control packet (BCP) is
transmitted through a dedicated control channel and delivered
prior to the data burst (the so called offset-time). In this
way the electronic controller of an intermediate (core) node
has enough time both to reserve a wavelength on its output
link, usually for the duration time of the incoming burst,
and to reconfigure dynamically the switching matrix. The
output wavelength is released for other connections when the
burst transmission is finished in the node. Such a temporary
utilization of wavelengths allows for higher resource utilization as well as for better adaptation to highly variable input
traffic in comparison to optical circuit-switching networks.
Moreover the aggregation of data packets helps to overcome
the fast processing and switching requirements of optical
packet switching (OPS) technology. In fact, OBS allows using
state-of-the-art switching elements [4].
There are two distinct signalling architectures considered for
OBS networks. The first one is based on a connection-oriented
signalling protocol which performs end-to-end resources reservation with acknowledgment in so called two-way reservation
mode. The other exploits a connection-less signalling protocol
which allocates the resources on-the-fly, a while before the
burst arrival, in a one-way reservation mode1. Since the problem of the two-way reservation signalling concerns the latency
due to the connection establishment process such architectures
are less interesting for long-haul network applications due to
the large latency and are not addressed in this paper.
The one-way reservation signalling that can operate effectively in large distance OBS networks performs according to
a statistical multiplexing paradigm; hence it encounters the
problem of burst contention inside the network. Indeed, when
a burst control packet enters a node in order to perform the
wavelength reservation for its data burst, it may happen that
the requested resources are not available at the output link and
the burst has to be dropped. The lack of optical random access
memories complicates the resolution of burst contention in
optical networks. To alleviate this problem several mechanisms
based on wavelength conversion, deflection routing and fibre
delay line (FDL) buffering together with dedicated burst
scheduling algorithms have been proposed.
From the very beginning, there were two distinct control
architectures considered for OBS networks [3]. The difference
between them comes from different management of offset
times. A conventional OBS (C-OBS) introduces the offset time
in soft-way by delaying the transmission of burst with respect
to the BCP in the edge node. At each core node, the offset time
decreases by the time the BCP spends in the switch controller.
Another idea for an OBS operation comes from OPS world and
it intends to emulate the offset time by means of an additional
fiber delay unit (FDU) introduced in the data path at the input
port of the core node in the so called offset time emulated
OBS (E-OBS) architecture. FDU delays the arrival of the burst
with respect to the arrival of its BCP and in such hard-way
it introduces the offset-time. Although C-OBS has attracted
lots of attention we highlighted in [1] that problems such
as unfairness in access to the shared transmission resources,
Załącznik 2.3
facility in adopting alternative and backup routing, scheduling
complexity, etc. can be avoided in E-OBS.
In this paper we deal with the problem of Quality of Service
(QoS) provisioning in the E-OBS architecture. Effective QoS
provisioning engages both the definition of specific QoS
classes to be given for higher level applications and dedicated
mechanisms providing such classes in the network. QoS
mechanisms in OBS networks based on one-way signalling
usually utilize a services differentiation approach, which may
be exploited in different ways:
• differentiation of the burst inherent parameters in edge
nodes such as offset times -in so called Offset-Time
Differentiation mechanism [5]- and burst size [6],
• differentiation of reservation and scheduling procedures
in core nodes such as threshold-based, burst preemption
and intentional burst dropping schemes [7], or
• differentiation of signaling procedures and routing strategies [8].
Burst preemption (BP), offset time differentiation (OTD)
and wavelength threshold mechanisms are the most addressed
QoS mechanism in OBS networks. In [9] we showed that
BP outperforms the other mechanisms in terms of overall
throughput while maintaining the same burst loss probability
as for OTD for high priority traffic.
The general drawback of preemptive mechanisms is a need
for an additional signaling protocol to be used to release
resources in case of the successful preemption. Indeed in a COBS architecture (see Section III) even when the preemption
happens, the control packet corresponding to preempted burst
(the so called phantom burst) continues its trip towards the
destination node reserving the resources. In such a case either
the resources reserved for the preempted bursts on outgoing
path are wasted or an additional signaling procedure should
be carried out.
In [2] we proposed the Preemption Window (PW) technique
which enhances the E-OBS architecture for QoS support. We
proved that the problem of phantom bursts is overtaken using
such technique while maintaining the same good performance
as for the classical burst preemption.
In this paper we present a deeper analysis of the benefits of
the PW technique applied in the E-OBS architecture compared
to the burst preemption in C-OBS. The rest of the paper is
organized as follows. In Section II we briefly describe the
E-OBS network architecture and its benefits with respect to
C-OBS one. Section III is dedicated to the presentation of the
Preemption Window technique and its behavior. In Section IV,
an exhaustive analysis of the performance of the PW technique
applied in E-OBS is presented for both single node scenario
and network scenario. Section V draws some conclusions.
II. E-OBS NETWORK ARCHITECTURE
Figure 1 presents the E-OBS network architecture. An EOBS node is a typical OBS node [10] with additional optical
taps to extract the control channels and a pool of fiber
delay units (FDUs) introduced into the data path of the input
interface -each input fiber is connected to one FDU. Note that
(a)
(b)
Fig. 1. a) General E-OBS node architecture and b) example of behavior. ∆
is the 1-hop offset time corresponding to the queuing and processing delay
of one node, δs is the switching delay
in the literature the FDU term is usually replaced by the FDL
term; nevertheless, we use FDU so that to distinguish this
component from more complex FDL buffers.
E-OBS architecture allows a different control operations
than C-OBS. The edge node launches the BCP into the control
channel prior to its data burst and with some small offset time
provided to compensate the switch reconfiguration delay at
the egress node (δs in Fig. 1(b)). At each core node, while
the BCP goes directly to the switch controller, the data burst
is delayed by the FDU for a period ∆ (which depends on
the length of the FDU). During this time, the BCP undergoes
the queueing in an input buffer and the processing in one (or
more) processor unit(s). Before being converted back to optical
form and transmitted through the output control channel to the
output interface, the BCP is buffered in such a way that the
offset time is as it was at the ingress. This operation is repeated
at each core node so that the offset is kept as fixed as possible
from link to link inside the network. Once the burst reaches
the egress node, it is disassembled and the data are delivered
to the client networks.
In [1] and [14] we showed that C-OBS posses several
drawbacks such as the problem of unfairness in access to
transmission resources, constraints in the alternative routing,
a need for complex void filling-based resource reservation
algorithms, some difficulties in QoS provisioning, etc. On the
contrary, thanks to the introduction of one FDU of few km per
input port in the core nodes and to its fixed offset provisioning,
the E-OBS can bring significant facilities to the mentioned
Załącznik 2.3
problems. At the same time, E-OBS performs as well as COBS in terms of burst loss probability and end-to-end delay.
III. P REEMPTION W INDOW
A. The problem of phantom burst in burst preemption
Burst Preemption (BP) can be classified as a contention
resolution based mechanism that in case of contention allows
the processing unit of the switch to overwrite a low priority
(LP) reservation with a later arriving high priority (HP) one.
The preemption may concern either the whole burst [15] (full
preemption) or it allows for a partial preemption when a
burst segmentation technique [16] is applied. Although burst
segmentation offers better performance characteristics it is at
the cost of higher complexity since this technique involves
additional information about the data bursts to be carried and
processed in the core nodes.
As mentioned in Section I, the general drawback of burst
preemptive mechanisms is the possible waste of resources
on the ongoing path due to the phantom bursts. In COBS networks, the burst control packet which belongs to
a preempted LP data burst does not have any knowledge
about the preemption. Thus, it continues its trip towards the
destination node and consumes unnecessarily both the controlplane resources, when being processed in the node controllers,
and data-plane resources, when reserving the wavelengths for
its (preempted) data burst.
In order to assess such an overhead, we develop an approximate estimation of the preemption effect that is produced in a
single node. In particular, we introduce a preemption rate (R)
metric that represents the number of preempted bursts over all
the bursts (successfully) transmitted at the node output link.
If we assume i.e.d. burst inter-arrival times and i.i.d. burst
lengths, the preemption rate of a full burst preemption scheme
can be calculated as (see Appendix A for a derivation):
R=
αHP [Erl (ρ, W ) − Erl (αHP ρ, W )]
1 − Erl (ρ, W )
(1)
where ρ, αHP , W are, respectively, the overall load, HP
class relative load, the number of wavelengths in the link, and
Erl(.) is the Erlang B-loss formula given by (9).
Figure 2 presents the preemption rate of a BP mechanism
in a single node scenario. As we can see, R significantly
increases in the systems with lower number of wavelengths
as well as at higher traffic loads. A small disparity between
analytical and simulation results comes from the fact that the
simulated bursts are stream-like arranged in a data channel
(bursts can not overlap each other) and their arrivals are not
more exponentially distributed.
R corresponds to the percentage of additional signalling
required at each node to release the preempted bursts. If
such signalling procedure is not provided there is a waste of
transmission resources due to these preempted reservations in
all the nodes on the ongoing paths. In large networks of high
number of nodes the problem might be intensified since all
nodes undergo similar effect.
(a)
(b)
Fig. 2. Percentage of additional signalling necessary to release preempted
burst at each node, with HP class load: a) 30%, b) 50%.
B. The principle of Preemption Window
Taking into account the reasons explained in the previous section there is a motivation for adapting the E-OBS
architecture for the burst preemptive mechanism. In such an
architecture there is no offset-time setup by edge nodes. The
offset is artificially introduced by means of additional FDU
inserted in the data path at the input port of core nodes. Control
packet and burst travel simultaneously through the network.
When both reach a core node the control packet goes directly
to the switch control unit, whilst the burst is delayed in the
FDU by period ∆ (the 1-hop offset time). During this time
the control packet is processed.
Starting with this basis, E-OBS can be enhanced with the
QoS support by means of the Preemption Window (PW)
mechanism. In such a mechanism, a control packet is delivered
to the switch controller with some extra offset (∆e ), besides
the 1-hop offset time(∆). This additional offset constitutes a
Załącznik 2.3
all the nodes of the routing path. A disadvantage of this
solution is the increase of variation of offset times, which
may further intensify the unfairness in access to transmission
resources. For this reason we consider the PW mechanism is
more appropriate for E-OBS architectures.
In the PW mechanism, the value of T becomes an important
trade-off between high burst delay (too large preemptive window) and ineffective burst preemption (too short preemptive
window). Period T can be calculated as:
Fig. 3.
T = ∆+ − δp
The length of preemptive window in PW mechanism.
(2)
where ∆+ is the offset introduced by inlet FDU in E-OBS
node, and δp is the effective processing delay of control packet.
Since δp could be variable, period T could vary as well.
In the simplest case, T corresponds to the idle waiting time
period δi after the processing of control packet. In order
to increase this period, the FDU can add some additional
preemptive offset ∆p . In this case T could be also expressed
as:
T = δi + ∆p
(3)
Scope of the following section is to give an overview of the
effect of the value of T to the burst loss probability.
Fig. 4.
Principles of the preemption window mechanism.
preemptive window T during which the controller can preempt
the reservation of lower priority by the one of higher priority.
Preemptive window T begins after the end of processing of
the burst control packet and lasts till the arrival of its payload
(see Figure 3). In further discussion, for simplicity, we assume
that the payload comprises a guard band for the switching
operation.
Figure 4 shows an illustrative example of the PW mechanism. In this example, a preemption of the LP burst 1 can
be performed only by the HP burst 2 since the control packet
of the later arrives in preemptive window T . On the other
hand, the HP burst 3 is not allowed to preempt the LP burst
1 because its control packet arrives out of window T .
An important rule of the PW mechanism is that the BCP,
after its processing, is waiting in the memory of the controller
until T expires and only then it can be sent to the next node
(if the burst has not been preempted) or dropped (in case of
successful preemption). After the BCP is sent the preemption
of its burst is not allowed in the node. Thanks to these rules
any BCP has its corresponding data burst (no phantom bursts
are present) and there is no need for any signaling procedure
to be carried out in order to release the resources on the
outgoing path in case of successful burst preemption. It should
be pointed out that the PW mechanism can work with both
full and partial burst preemption techniques.
The preemption offset can be provided in both C-OBS and
E-OBS architectures. In the former the edge node adds an
additional offset, which accounts the preemption windows in
IV. N UMERICAL RESULTS
In this section, we use event-driven simulation to show that
a full-burst preemptive mechanism in E-OBS architecture with
the PW mechanism applied can achieve easily the performance
of classical burst preemption in the conventional OBS. We
analyze two different scenarios: in the first one we consider a
single node, which can be buffer-less or enhanced with some
FDLs capabilities, whilst in the second one a full network
scenario with bufferless nodes is considered.
In all cases, two classes of services, namely High Priority
(HP) and Low Priority (LP) are available. The metrics that
we study are the burst loss probabilities, both for the HP
(BLPHP ) and the LP (BLPLP ) class as well as overall BLP
(BLPT otal ).
A. Node scenario
We consider a general non-blocking OBS node architecture with full wavelength conversion. The switch has 4×4
input/output ports and W number wavelengths per port, each
one operating at 10 Gbps. A one-way signaling protocol,
the simple Horizon resources reservation, and the LAUC
scheduling are applied. The switching and processing times
are 1 µs and 10 µs, respectively.
The traffic is uniformly distributed between all input and
output ports. Regarding the burst length and the inter-arrival
time (IAT) distributions we apply the ones studied in [17][18].
In particular, the bursts length is Gaussian distributed with a
mean burst length equal to 40kbytes (1µ). Minimum burst
length is setup to 4kbytes while its maximum value is
4Mbytes. The burst IAT, after the assembly process, is also
Gaussian distributed with a mean depending on the traffic
Załącznik 2.3
load. The mean load per input channel (wavelength) is 0.8.
The percentage of HP traffic load is denoted as α and it is
equal to 25% if not specified differently.
It is worth to mention that all simulation results have 99%
level of confidence. It is achieved by means of at least 10
repetition of the same simulation.
1) Bufferless node: For the bufferless case, in Fig. 5 we
can see that the preemption window, which is equal to T , has
a big impact on BLPHP characteristics. In particular, when T
increases performance of the preemption mechanism improves
resulting in lower BLPHP . It is due to the fact that the more
time the LP burst reservation is exposed to be preempted the
higher probability that HP burst preempts it. Other remark is
that all the BLPHP characteristics look alike regardless of
the system parameters. Indeed the characteristics fall quasilinearly from their maximum obtained for T = 0 and they
slow down rapidly at T = 1.3 ∗ 1/µ, to stabilize at about 2/µ.
These results could serve us in order to find an upper bound
on the effective offset introduced by means of the input FDU.
The behavior described above can be explained by Fig. 5(a)
that presents comparative results of BLPHP for 3 resources
reservation mechanisms, namely without preemption (NP), a
classical Burst Preemption (BP) when even the preemption
of LP burst being transmitted is allowed and finally the PW
mechanism. We can see that for T = 0 which results in the lack
of preemption window, the PW offers the same results like the
NP. In such case no preemption can occur and indeed the PW
and NP behaves the same. On the other side, for T above 2/µ
the PW achieves the performance of the BP mechanism. To
go further we have to recall both the considered burst length
distribution that is a Gaussian like with a mean equal to 1/µ
and the principle of operation of the PW mechanism. Namely,
assuming that preemption window is higher than 2/µ, from
the burst length distribution we obtain that almost all bursts
are shorter than this preemption window. For this reason all
those bursts’ reservations are exposed for preemption during
whole their duration and this is just like in the BP. Therefore
the BP mechanism can be easily emulated by the PW when
T is high enough.
From Fig. 5(a) we can also see that the impact of PW
mechanism on BLPLP and BLPT otal is small. The BLPLP
curve slightly deteriorates when increasing T and it stabilizes
soon. With higher T a given LP reservation is exposed for
more time to the preemption and the preemption may occur
even at the moment being close to the end of reservation.
In such case we may waste more resources belonging to
this reservation prior to the moment of preemption what can
impact the BLPT otal . Nevertheless, as the simulation results
show this effect is almost imperceptible since BLPT otal is
very stable in the whole range of T and it is only slightly
deteriorated at higher offset-times in comparison to the NP
case (when T = 0).
Figure 5(b) presents the performance obtained for different
system and traffic parameters. Briefly, we can notice that
increasing the number of wavelength (λs) as well as decreasing
the percentage of HP traffic load (α) improves BLPHP
(a)
(b)
Fig. 5. a) Burst Loss Probabilities for different reservation mechanisms, b)
HP burst loss probability vs. HP traffic ratio and number of wavelengths.
characteristics what seems to be obvious. Moreover, we see
again that all the curves become stable starting from T = 2/µ.
Figure 5 shows also that effective PW guaranteeing low HP
blocking probability (e.g. on the level of 10−6 ) would be
reduced in the systems with more wavelengths.
For the bufferless node, we provided analytical model and
results for the case of single wavelength in [1]. In case of multiple wavelengths, additional simulation results are available
in [14] where also the exponential traffic model is considered.
2) Node with FDL buffering: For the scenario with buffering capabilities we assume the core node enhanced with a
feed-back FDL buffer [19]. Such architecture allows us to
preempting any LP burst by a HP burst even if it is actually
transmitted through the buffer’s FDL. In fact, when preemption
occurs we know that thanks to our control architecture (see
Section III) the LP burst has not reached the output port.
Therefore, we can easily block it by means of the switching
matrix in order to make impossible its propagation towards the
output link. Note that preemption of a burst being transmitted
Załącznik 2.3
(a)
Fig. 6. a) Blocking probabilities in the node with FDL buffers applied
(α=25%).
through the feed-forward FDL buffer might result in the
propagation of a part of optical signal that has not been
blocked by the matrix. Since this useless part of the burst will
reach the next node it can cause false optical signal detections
and therefore additional information such as jam sequence
might need to be added.
In our study we assume that the feed-back buffer emulates
N output feed-forward buffers, each one operating with 8
optical channels, where N is equal to the number of output
ports. The number of delay lines is between 1 and 4 depending
on the simulation. The provided delays are linearly increasing
with a basic delay unit equal to 32µs, which corresponds to
the mean burst duration.
In Fig. 6 we show the results of BLP for different buffer
size and number of wavelengths as a function of T . We see
that even with one FDL used there is no significant gain
in the performance when increasing T . It is due to the fact
that the buffer itself introduces some variable preemption
window and therefore no additional preemption offset in the
input FDU is necessary. This also explains why, even with
T equal to 0, the results of BLPHP are much lower than
BLPLP and BLPT otal . Therefore the length of the input
FDU and its resulting delay can be reduced. Note that the
control architecture still keeps the control packets in core
nodes waiting for the transmission of the bursts in order to
avoid signaling complexity if a preemption occurs.
Finally, we can observe that application of FDLs decreases
blocking probability of LP bursts, In particular, in the system
with 32 wavelengths and only 1 FDL the BLPLP can be
below 10−4 in a node.
B. Network scenario
In the network scenario, we consider three different topologies (see Figure 7): one regular topology consisting of a 25nodes Manhattan street network (with a nodal degree of 4),
and two real topology consisting of the NSFNet topology of
15 nodes and 22 links, which represents an America backbone
(b)
(c)
Fig. 7.
a) Manhattan topology, b) NSFNet topology, c) EON topology.
network, and the EON (European Optical Network) topology
with 28 nodes and 39 links.
We assume each node is both an edge and a core bufferless
node capable of generating bursts destined to any other nodes.
The traffic is uniformly distributed between nodes. We assume
each edge node offers the same amount of traffic to the network. In this network context, the offered traffic is normalized
to the transmission bitrate and expressed in Erlangs, where
one Erlang corresponds to an amount of traffic that occupies
an entire wavelength. For example 51.2 Erlangs mean that
each edge node generates 512 Gbps, being 10 Gbps the bitrate
of each wavelength. The value of T is set to 16 km which
corresponds to 2.5 times the average burst duration.
The rest of configuration parameters is the same as in
Section IV-A.
Załącznik 2.3
(a)
Fig. 9. Burst loss probability as a function of the number of residual hops
in EON topology.
network topologies. We can see that the fairness in C-OBS is
very poor. In fact, the bursts that begin their trip (i.e., with
high number of residual hops, the right side of the figures)
may undergo much lower losses than the bursts having just the
ultimate hops to reach the destination (i.e., with few number
of residual hops, the left side of the figures). On the other
hand, in the E-OBS architecture each burst has the same time
horizon to make the reservation of resources since the offset
times, which are determined by the length of FDU, are the
same. The results presented in the figure confirm this ability.
V. C ONCLUSION
(b)
Fig. 8.
Burst loss probability for LP and HP traffic comparing Burst
Preemption (BP) and Preemption Window (PW) mechanisms in a) Manhattan
topology, and b) NSFNet topology.
In Figure 8 and Figure 9, we compare the classical Burst
Preemption (BP) applied in the C-OBS architecture and the
Preemption Window (PW) applied in the E-OBS architecture.
In Figure 8, the comparison is in terms of BLPLP and
BLPHP considering Manhattan and NSFNet topologies. We
select few number of wavelengths (W = 8 and W = 16)
in order to have significant results for HP traffic. Although
the considered topologies are very different, Figure 8(a) and
Figure 8(b) present similar behavior. The results show that PW
presents slightly better performance for LP traffic than BP.
This improvement is mainly due to the absence of phantom
bursts, which, as commented in Section III, is a design feature
of the PW mechanism. In terms of BLPHP , the improvement
of the PW is less evident.
In Figure 9, we show another feature of the E-OBS architecture, and, consequently, of the PW mechanism in terms of class
isolation. In this figure, we focus on the fairness goodness,
i.e., the variation of burst loss probabilities with respect to the
residual number of hops to reach the destination for different
In this paper we studied the Preemption Window (PW)
mechanism applied in the offset-time emulated OBS (E-OBS)
architecture for efficient preemption-based QoS support. This
E-OBS architecture applies a fiber delay unit at the input port
of core nodes in order to emulate conventional offset-times.
The essential part of proposed architecture is that PW allows
for preemption of a low priority burst only in specific period
when the burst has not reached the output link. The mechanism
is also responsible for transmitting the control packet and the
burst simultaneously in such a way that there is not separation
between them in a link. Thanks to these rules the well-known
problem of phantom burst is eliminated.
Obtained simulation results show that in a bufferless OBS
node, the performance of the PW mechanism is like of the
conventional burst preemption. Although the study was done
for the full-burst preemption principle, the considered solution
can be used with any other preemption scheme like e.g.
with the burst segmentation. In the buffered node scenario,
the application of FDLs decreases substantially the blocking
probability of LP bursts, while, at the same time, it needs
shorter fiber delay units at the input port of the core nodes.
Finally, in the network scenario, PW in E-OBS architecture
surpasses the performance of the classical burst preemption
applied to conventional OBS architecture. The absence of
phantom bursts reduces the overall network load and thus there
Załącznik 2.3
is more room for low priority traffic. Moreover, considered EOBS architecture does not experience the offsets’ variations
what dismisses related unfairness problem in resources reservation.
where ρ, αHP , W are respectively the overall traffic load, HP
class load ratio and the number of wavelengths in a link and
Erl(·) is given by (9).
A PPENDIX A
The work described in this paper was carried out with the
support of the BONE-project (”Building the Future Optical
Network in Europe”), a Network of Excellence funded by
the European Commission through the 7th ICT-Framework
Programme, and by the Spanish Ministry of Education and
Science under the CATARO project (Ref. TEC2005-08051C03-01).
T HE PREEMPTION RATE IN A BUFFERLESS OBS NODE
Let npreempt be the number of successful preemptions,
(p)
(np)
nlost HP and nlost HP be the number of HP bursts lost
in non-preemptive (without burst preemption) and preemptive
(with full burst preemption) scenarios respectively, nin HP be
the number of incoming HP bursts, nin be the total number
of incoming bursts and nout be the total number of bursts
transmitted in the output in a given period of time.
Since each preemption means the acceptance of a HP burst
instead of a LP burst, npreempt can be also interpreted as a
difference between all the HP bursts lost in the non-preemptive
scenario and the HP bursts lost in the preemptive scenario:
(p)
(np)
npreempt = nlost
HP
− nlost
HP .
(4)
Obviously:
(np)
nlost
(5)
(p)
(6)
= nin
HP
· BHP ,
HP
= nin
HP
· BHP ,
(p)
nlost
(np)
(np)
HP
(p)
where BHP and BHP are the HP burst loss probabilities in
the non-preemptive and the preemptive scenario.
From the previous equations we obtain:
npreempt
= nin
= αHP
(np)
(p)
· BHP − BHP
(np)
(p)
· nin · BHP − BHP ,
HP
(7)
where αHP is the HP class load ratio.
Than the preemption rate is equal to:
R=
npreempt
=
nout
(np)
(p)
αHP · nin · BHP − BHP
nin · (1 − B (p) )
.
(8)
Note, that the overall burst loss probability of the preemptive
scenario (B (p) ) and the HP burst loss probabilities in the non(np)
(p)
preemptive scenario (BHP ) are the same. Moreover, BHP
depends only on the HP class load due to absolute class
isolation.
Finally, assuming exponentially distributed burst arrivals
and the Erlang B-loss formula:
AW
Erl(A, W ) =
W!
"W
#−1
X Ai
i=0
i!
,
(9)
we can obtain the following estimation of the preemption
rate in a node by the proper substitution:
R=
αHP [Erl (ρ, W ) − Erl (αHP ρ, W )]
,
1 − Erl (ρ, W )
(10)
ACKNOWLEDGMENT
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[17] M. Izal, J. Aracil, “On the influence of self-similarity on optical burst
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[19] D.K. Hunter, M.C. Chia, I. Andonovic,, “Buffering in Optical Packet
Switches”, IEEE Journal of Lightwave Technology, vol. 16, no. 12, pp.
2081-2094, Dec. 1998
Załącznik 2.4
An interoperable GMPLS/OBS Control Plane:
RSVP and OSPF extensions proposal
P. Pedroso*, D. Careglio*, R. Casellas**, M. Klinkowski*,***, and J. Solé-Pareta*
*
CCABA, Universitat Politècnica de Catalunya (UPC), Barcelona, Catalunya, Spain
CTTC, Parc Mediterrani de la Tecnologia (PMT), Castelldefels, Catalunya, Spain
*** National Institute of Telecommunications (NIT), Warsaw, Poland
(ppedroso, careglio, mklinkow, pareta)@ac.upc.edu, [email protected]
**
Abstract— The GMPLS/OBS Control Plane is a bold
research topic. Optical Burst Switching (OBS) networks
need to be capable to be rapidly reconfigured with the aim
of achieving an efficient use of bandwidth, low latency and
high degree of transparency. The OBS Control Plane is just
a packet switched network requiring a high control
complexity. The demands are clear but a well-defined
control plane is still an open issue. As one of excellent
candidate control plane for most of network scenarios,
Generalized Multi-Protocol Label Switching (GMPLS) is
being taken as a reference to design such OBS Control
Plane. In this paper we first describe the proposal for the
interoperable GMPLS/OBS Control Plane and then based
on such architecture we propose and analyze some GMPLS
protocol extensions that must be done to integrate it
properly into OBS networks.
Keywords: OBS, Control Plane, GMPLS, extensions.
I.
INTRODUCTION
GMPLS [1] has been regarded as an excellent
candidate control plane for automatically switched
networks: enhances some MPLS issues and handle in a
generalized way multiple switching domains with a single
set of protocols. It is a common control plane that brings
automated end-to-end provisioning of connections,
efficient managing of network resources as well as of the
QoS levels expected in the new and sophisticated
applications, and lower cost of operation by several
orders of magnitude [2].
On the other hand, OBS [3] is the envisioned mid-term
switching solution for next generation optical backbone
networks. At the present time, it is the most feasible
option as a trade-off between current available
technology and performance while Optical Packet
Switching (OPS) still hurdles some shortcomings.
In this paper we propose an architecture model and
some protocol extensions to interoperate GMPLS and
OBS control layers. Such interoperable GMPLS/OBS
control plane would seamlessly enable the coexistence
and easy migration between circuit-switched and
packet/burst-switched networks.
GMPLS is in principle capable of controlling any
technology – to date it is capable to handle multiple
switching domains as packet (IP), cell (ATM), time
(SDH/SONET), wavelength (WDM) and fiber –, is well
studied and standardized, and can be easily extended by
IETF when new requirements arise. Indeed, recent efforts
are being done to extend it into new domains such as
Ethernet switching [4]. Hence, a further step can be
envisaged where GMPLS includes optical packet/burst
switching domains (OPS/OBS).
As further detailed, the interoperability/integration is
achieved by maintaining the GMPLS and OBS control
components operating at different timescales; meaning
that GMPLS can operate variations in order of
minutes/hours/days as in the case of current standards
while OBS requires processing time in order of
microseconds/milliseconds.
The remainder of this paper is organized as follows.
Section 2 presents the proposed GMPLS/OBS
architecture. Section 3 identifies the GMPLS protocols
shortcomings to operate in OBS networks and describes
those needed GMPLS protocol extensions, namely
RSVP-TE and OSPF-TE extensions. The conclusions are
presented in Section 4.
PROPOSAL FOR AN INTEROPERABLE GMPLS/OBS
CONTROL PLANE
The proposed GMPLS/OBS network [5] is depicted in
Fig. 1. It is based on a transparent all-optical data plane
and a hybrid control plane. Such hybrid control plane
(also referred as interoperable control plane) consists of a
specific OBS control layer and a GMPLS control layer.
These control layers use separate networks.
The GMPLS control layer uses out-of-band, out-offiber (but can be also in-fiber) control architecture, which
can be based on whatever technology and topology. On
the contrary, the OBS control layer shares the OBS
architecture with the data plane; it means that if W
wavelengths are available, one wavelength is reserved to
the Burst Control Packets (BCPs) while the rest W-1
wavelengths are for the data bursts. It is worth to mention
that BCP and data burst must have a strict time
relationship while the GMPLS messages can travel freely
in its network.
The details of the principle of operation are described
in [5]. In brief, the GMPLS control layer is in charge of
configuring the virtual topology for the OBS network,
setting up and tearing down GMPLS TE Tunnels [6]. In
our context, a TE tunnel is seen as a group of
wavelengths, with one or multiple parallel LSPs
established in a single signaling session. It is also in
charge of uploading/updating the forwarding tables stored
in the control units of the OBS nodes. It requires RSVP
and OSPF protocols to maintain the TE tunnels and
update the network status.
A client request is done through the UNI signaling
interface to the GMPLS edge node which checks the
availability of TE tunnels that match the client
requirements: if so, the client traffic is put in an existent
TE tunnel (a single LSP or multiple LSPs according to
the tunnel properties); if not, the edge node sends a
II.
Załącznik 2.4
RSVP-TE Path message to setup in a two-way process a
new TE tunnel (soft reservation - group of wavelengths),
according to database updated by OSPF-TE.
Previous research work [5] defines the baseline of
interoperability (mainly at horizontal level) for
GMPLS/OBS networks but does not enter in important
GMPLS RFC details. Therefore, some extensions to
GMPLS signaling and routing protocols are proposed
below to provide GMPLS with additional features to
work properly over OBS without structural changes in its
RFC specifications.
It is important to mention that the following extensions
are the exploitation of what the IETF working groups are
already contemplating for the GMPLS architecture. Thus,
it is observed a convergence between what is offered by
GMPLS and our architecture needs. The following two
sections point out those GMPLS signaling (RSVP-TE)
and routing (OSPF-TE) extensions.
B. Nomenclature
Figure 1. GMPLS-based Control Plane for OBS networks;
GMPLS controller consists in Routing Controller (RC), Protocol
Controller (PC), Optical Connection Controller (OCC), Link Resource
Manager (LRM), Traffic Policy (TP), Network Call Controller (NCC).
Consequently, the OBS approximates the connection
oriented behavior, i.e., the source-destination path is
determined across the network but the burst’s wavelength
can be chosen at each transit node along the path meaning
that the burst is switched from one wavelength to another
according to policies or occupancy ratio. However always
within the same TE tunnel (different LSPs as is going to
be explain further), given the necessary flexibility for TE
purposes; if an OBS ingress node wants to transmit a data
burst to an OBS egress node, it creates a BCP which must
contain a label identifying the (pre-established or
existent) TE tunnel. Such identifier may identify just one
LSP or a set of them and, as we explain later on, can be
associated to a Call or not. Once the BCP is realized and
the offset time is expired, the edge node sends the
associated data burst. Both BCP and data burst follow the
TE tunnel established by GMPLS. At each intermediate
node, the BCP is electrical converted and processed;
according to the label and to the forwarding table, the
output resources are booked on the fly and the data burst,
which is kept optic, is switched correspondingly. This
means that no physical reservation is done by GMPLS, it
is only in charge of establishing the virtual topology and
thus the set of resources available at each node for each
TE tunnel.
To be a viable architecture, some GMPLS signaling
and routing extensions must be performed. The following
section addresses this scope.
III.
For a clearly interpretation of the proposed extensions,
it is worth to first normalize and clarify the nomenclature
and concepts described in this section.
Hence, following the nomenclature of RFC and in line
with ASON architecture [7][8], we reuse the terms call
and connection as follows: we define a GMPLS/OBS
Call as an association between endpoints and possibly
between key transit points (such as network boundaries)
in support of an instance of a OBS service, building a
relationship by which subsequent connections may be
made. In GMPLS RSVP-TE [6], a Connection is
identified with a GMPLS TE tunnel. Commonly, a TE
tunnel is identified with a single LSP but it should be
noted that for protection, load balancing, and many other
functions, a tunnel may be supported by multiple parallel
LSPs.
Fig.2 illustrates such Call/Connection/LSP hierarchy.
The Call (call_ID) is the logic association, an agreement
between endpoints (source, destination), used to facilitate
and manage a set of TE tunnels. Fig. 2 shows the case
with one Call and 2 TE tunnels. However, TE tunnel may
exist without a Call. One TE tunnel (tunnel_ID) may
include multiple LSPs. In Fig.2, the first TE tunnel
comprises 3 LSPs whilst just one LSP is considered in the
second TE tunnel. In LSC context, each LSP (lsp_ID) is a
wavelength (label<->wavelength identification match). A
more detailed description is in [8].
GMPLS EXTENSIONS
A. General Discussion
To make this interoperable control plane scheme
attractive we must guarantee the general purpose of the
GMPLS protocols, i.e., the new extensions for OBS
should not compromise the overall GMPLS applicability
to other switching technology. Such premise should be
taken into account every time those extensions are
proposed to the GMPLS suite of protocols.
Figure 2. Call/Connection/Tunnel/LSP/Wavelength hierarchy
IV.
RSVP-TE SIGNALING EXTENSIONS
The necessary extension in RSVP-TE protocol under
GMPLS framework is explained next in order to
overcome the mismatch situation identified in the
proposed GMPLS/OBS Control Plane architecture.
The GMPLS RSVP-TE [6] protocol says that only one
label
request
can
be
used
per
message
(Generalized_Label_Request object in the Path message),
Załącznik 2.4
i.e., only one single LSP can be requested at a time (and
therefore virtual reserves only one wavelength) per
signaling message. Conversely, in the considered
architecture we have suggested to set up a TE tunnel
using one or more LSPs (wavelengths) according to the
traffic demands and assuming just one Path-Resv
message exchange in both cases. There are three main
solutions namely waveband switching, independent LSPs
setup and tunnel LSP. This work focuses only in the last
one.
In fact, waveband switching is taken into account in [6]
(and in related RFCs such as [1][9]) but it is not widely
deployed and has the constraint that all the wavelengths
of a waveband must be contiguous. The other solution is
to use several independent Path-Resv messages in order
to set up more than one wavelength for the same TE
Tunnel. It does not require any modification but it has
scalability drawbacks (the number of messages exchange
is high and grow exponentially with errors). For all these
reasons the following solution seems the more
appropriate.
A. Connection Setup
In general terms, the aim is to setup a connection, TE
tunnel, between a pair of edge nodes, inside a Call or not,
having a single Path-Resv message exchange with a
unique identifier at the forwarding tables, whether the TE
tunnel is identified with a single LSP or by multiple
LSPs.
The idea is to enhance the goal of the Session object. In
consequence, the function of the extended Session object
(with call_ID) is to create and represent a tunnel between
the source and the destination node which can be useful
in the context of our proposed model.
The Session object represents the TE tunnel between
an OBS-enabled ingress and egress (table 1). Individual
LSPs (wavelengths) can either be established individually
or, as we propose, in single signaling sessions to reduce
overhead.
The Sender_Template object belonging to the Path
message describes a given sender and, in GMPLS, a
particular LSP within a single tunnel thanks to the lsp_ID
and the sender address (table 1). In such a way, by
making use of this, we could extend the number of LSPs
announced inside of one Path message repeating the
Sender Template object as many times as the number of
LSPs inside the TE tunnel. Each LSP would have
different lsp_ID under the same tunnel_ID.
This would reduced the number of setup messages
exchanged to only one and would make it easier to
identify the traffic flow with same QoS requirements
(various LSPs with the same characteristics) between the
same pair of edge nodes. It also makes easier eventually
updates the TE tunnel (increase or reduce its number of
wavelengths).
The Label_Set object (also in the Path message) is a
plus that helps the source wavelength requests
announcement.
Thus, there would be a unique identifier for that set of
LSPs (TE Tunnel): tunnel_ID, or, within the Call context,
the couple call_ID + tunnel_ID. As in [8] and in order to
not generate any backward compatibility issue, the
call_ID is not used as part of the processing to determine
the session to which an RSVP signaling message applies
but it uniquely identify the source-destination pair.
TABLE I.
SESSION AND SENDER_TEMPLATE OBJECT FORMATS
SESSION object
Size
Name
4
IPv4 tunnel end point address
2
Call ID
2
Tunnel ID
4
Extended Tunnel ID
Description
IPv4 address of the
egress node for the
tunnel
Call identifier -if it
exists- if not, must
be zero.
A tunnel identifier
that remains constant
over the tunnel’s life.
SENDER_TEMPLATE object
4
IPv4 address
IPv4 source address
2
Not used
Not used
2
LSP ID
LSP identifier
The Session object already defines a 16-bit call_ID
parameter [8], 16-bit tunnel_ID parameter, and a 32-bit
Extended_tunnel_ID parameter. For this reason there will
be no limitation in the maximum number of tunnels once
there are 216+232=260x1012 available identifiers.
Consequently, the Resv message would answer with
more than one Label per message, as much as the number
of lsp_ID (or Sender_Template objects). However, it still
uses one label per wavelength.
Resuming, with just one setup message exchange, i.e.,
one Path and Resv message exchange between a pair of
edge nodes, we can establish a TE tunnel supported by
more than one LSP under a unique identifier, tunnel_ID.
Moreover, only one Generalized_Label_Request object
per Path message is still announced because all those
LSPs share the same properties (same QoS, Encoding
Switching and Type of Switching). In addition, the
Label_Set object is almost mandatory to announce the
desired labels (wavelengths). All LSPs are tied together
by means of the Call concept and Session object.
At the other end, the egress node would answer with a
Resv
message
containing
more
than
one
Generalized_Label object. The egress node must answer
within the same proportion of the request (number of
LSPs) with as many FlowDescriptors as Senders, limited
to a Fixed Filter (FF) reservation style. This would
simplify the forwarding tables of each node. The LSP
election inside the TE tunnel is locally decided. A
standard lambda label format that globally identifies a
wavelength is currently under study in [10].
B. Example of Behaviour
In this section we provide a practical example.
Fig. 3 shows a diagram of the exchanged messages.
We consider the case of establishing a new TE Tunnel by
means of the RSVP-TE extended protocol, followed by
the transmission of the bursts in the OBS network.
Załącznik 2.4
The first messages are the signaling messages in the
GMPLS network namely PATH_message and
RESV_message from RSVP-TE protocol to set up the TE
tunnel of LSPs. In this case the edge node requires the set
up of 8 LSPs; meaning a group of 8 wavelengths. The
Optical Connection Controller (OCC) of the GMPLS
node is responsible for this. In the example of Fig. 3, we
assume that the TE tunnel is established successfully;
between each pair of OBS nodes, 8 wavelengths are
assigned: (λ1, λ2, λ5, λ8-12) between the first and the
second OBS node, (λ1-8) between the second and the third
OBS node, and (λ3-8, λ10, λ11) for the final link.
Remember that we are considering Wavelength
Converter Capable OBS nodes. This information is
downloaded from the Routing Controller (RC) to the
forwarding table of the OBS nodes.
Once the TE tunnel is established, the edge nodes can
send the data. Firstly, the BCP is sent by the control
wavelength (λ0) carrying the proper label (belonging to
the desired tunnel), followed, after the proper offset time,
by the data burst. At each core node the BCP is electrical
processed while the correspondent data burst is forwarded
by means of one of the wavelengths assigned to the TE
tunnel. Here, the Control Units of the OBS nodes are in
charge of locally selecting the wavelength (among the
ones assigned to the TE tunnel) based on the current
resource availability. In Fig. 3, the OBS nodes assign to
the first burst λ1, λ4, and λ3 for the first, the second and
the third link, respectively. The OBS nodes assign
different wavelengths to the second burst in the example:
λ5, λ5, and λ10, respectively.
It is worth to notice that the following BCPs and data
bursts related with the same connection (same tunnel_id)
can be sent without another signaling message exchange.
This solution also accommodated traffic peak variations
by splitting the traffic flow among one, two or the whole
set of wavelengths belonging to the tunnel. However,
every time it would be possible it is advisable that the
output wavelength be the same as the input wavelength to
avoid the dispersion issue.
The output label is the correspondent value of the
chosen output wavelength (one label->one wavelength).
As being study in [10], each numerical label as a
correspondent wavelength value (GMPLS LSC).
Figure 3. Diagram of the exchanged messages in an OBS connection.
In Fig. 4 we look better inside the behavior of an OBS
node. It receives a BCP contains a unique identifier (e.g.,
5) that encapsulates the tunnel_ID and the call_ID -if it
exists- and a wavelength label (as in [10]) representing
the incoming burst’s wavelength (e.g., 50 which may
mean λ5 = 1542 nm) among other specific objects (out of
scope for this example). A possible forwarding table for
this node is depicted in Fig. 4. Once the node is awarded
of the tunnel_ID (e.g. 30) -and call_ID (e.g. 2) if it existsthrough the incoming label (e.g. 5), it is able to know the
set of output wavelengths for the next hop belonging to
such TE tunnel. As said before, the wavelength
assignment is now locally and more close to the data
transmission and it is based on contention resolution,
traffic engineering or operator policies (e.g. traffic load, λ
utilization).
Figure 4. GMPLS-based forwarding table for OBS networks
V. OSPF-TE ROUTING EXTENSIONS
The TE-link update messages have crucial importance
at the TE tunnel setup time.
Within the proposed model, each pair of sourcedestination nodes has a set of possible LSPs
(wavelengths) between them (TE tunnel), for which it is
mandatory to have the information about the
wavelength’s state used by each LSP. This is aimed to
provide more flexibility and efficient management of
network resources.
Standard TE-LSAs messages flooded by OSPF-TE
routing protocol determines TE link usage in an
aggregated way through using bandwidth units (bits/s).
However, this is not sufficient within all-optically
networks.
In such scenarios, for a finer control, a better resource
usage, and increased performance (e.g. reduce blocking
probability in circuit-oriented networks with wavelength
continuity constraints) it is preferable to have network
state information on per wavelength channel granularity
[11] rather than to disseminate network state information
on per link bandwidth basis as in the current OSPF-TE
protocol. Also, it is necessary for a finer control in
backup paths, tunnel paths or bidirectional LSPs.
The availability of a specific wavelength on a WDM
link is key dynamic information that is required by the
RWA process. This information needs to be accurate. In
[11] an object is being study to be added in the TE-LSA
message: Wavelength Bitmap. Each bit belonging to this
bitmap represents a particular frequency (wavelength)
with a value of 1/0 indicating whether the frequency is in
the set or not. However, such binomial condition
occupied/not occupied may not be enough.
Załącznik 2.4
In [12] the number of states is augmented to cover
ampler fields. Using two or three bits instead of one, we
increase the number of states from two (21bit) to four
(22bits) or eight (23bits) respectively. This gives the
flexibility to use them according to our needs.
In the context of OBS, characterized by highly
dynamic traffic demands and reservations duration equal
to burst time transmission, the former commented
network state information (i.e., wavelength granularity) is
crucial. There is needed a state that takes into account
those wavelengths that are not occupied neither truly
occupied but are merely assigned to the TE tunnels and
consequently can be shared by other TE tunnels.
This is important in our model in order to decide which
wavelengths can be used by a new TE tunnel when others
are already established.
Our idea is to follow the aforementioned extensions
and also inhere this concept to OBS. A new state called
Shared is defined for those wavelengths that are not being
used neither truly available (i.e. wavelengths that are
assigned to the TE tunnel but are not committed and
whose utilization depends on the OBS switching). Those
wavelengths are shared among different tunnels and are
virtually assigned to them. This allows the OBS principle
of statistical multiplexing namely different flows can
share same resources. For example in Fig. 5, tunnel1 and tunnel2 are already
setup; tunnel1 uses λ1 and λ2 while tunnel2 uses λ2, λ3
and λ4. Therefore they currently shares λ2. If a third
tunnel would be setup it would be convenient that not
used the shared wavelength to avoid congestion situation
in high load periods. As in [11][12], it results useful to
know what wavelengths are already shared. In the
example, λ1, λ4 and λ5 are assigned to tunnel3. At the
same time, this would make more accurate when decide
eventually updates (add or drop LSPs) of the tunnels.
In Fig. 6 we show the state information with the
extended Wavelength Bitmap for the example illustrated
above. VI. CONCLUSIONS
This paper is seen as a continuous work from [5]. After
the shortcomings identification in the proposed
GMPLS/OBS Control Plane architecture, we proposed
and analyzed some mandatory GMPLS protocol
extensions namely in RSVP and OSPF protocols.
These extensions fulfill some RFC gaps in the
GMPLS/OBS interoperability/integration as well as
guarantee that the new extensions for OBS should not
compromise the overall GMPLS applicability to other
switching technology. Such goal is crucial to this model
be successful in the future.
The next step of our work is to design intelligent path
establishment processes (routing + group of wavelengths)
and perform some simulation studies and come out with
numerical results.
ACKNOWLEDGMENT
The work described in this paper was carried out with
the support of the BONE-project ("Building the Future
Optical Network in Europe"), a Network of Excellence
funded by the European Commission through the 7th
ICT-Framework Programme, and with the support of the
CATARO-project (TEC2005-08051-C03-01) funded by
the Spanish Ministry of Education and Science (MEC).
REFERENCES
[1]
Figure 5. Tunnels and shared wavelengths.
Figure 6. Wavelength’s state: new parameter sharable.
E. Mannie et al., “Generalized Multi-Protocol Label Switching
(GMPLS) Architecture”, RFC 3945, Oct. 2004.
[2] GMPLS Tutorial, www.iec.org.
[3] C. Qiao and M. Yoo, "Optical Burst Switching (obs) - a new
paradigm for an optical internet", Journal of High Speed
Networks, vol.8, no. 1, pp. 69-84, March 1999.
[4] D. Fedyk et al., “GMPLS Ethernet Label Switching Architecture
and Framework” work in progress: draft-ietf-ccamp-ethernet-arch01.txt, February 2008
[5] P. Pedroso, J. Solé-Pareta, D. Careglio, M. Klinkowski,
“Integrating GMPLS in the OBS networks control plane”, in
Proceedings of 9th IEEE International Conference on Transparent
Optical Networks (ICTON2007), Rome, Italy, July 2007.
[6] Berger, L., Ed., “GMPLS Signaling RSVP-TE Extensions”, RFC
3473, January 2003.
[7] ITU-T, "Architecture for the Automatically Switched Optical
Network (ASON)," Recommendation G.8080/ Y.1304, November
2001 (and Revision, January 2003).
[8] D. Papadimitriou, A. Farrel, “Generalized MPLS (GMPLS)
RSVP-TE Signaling Extensions in Support of Calls”, RFC 4974,
August 2007.
[9] Berger, L., “GMPLS Signaling Functional Description”, RFC
3471, January 2003.
[10] Otani, T., et al., “Generalized Labels of Lambda-Switching
Capable Label Switching Routers (LSR)”, work in progress: draftotani-ccamp-gmpls-lambda-labels-01.txt, November 2007.
[11] Bernstein, G., Lee, Y., “Routing and Wavelength Assignment
Information for Wavelength Switched Optical Networks”, work in
progress: draft-bernstein-ccamp-wson-info-01.txt, November 2007
[12] R. Martínez, “Experimental GMPLS-based routing for dynamic
lightpath provisioning and recovery in all-optical WDM
networks”, PhD Dissertation, Universitat Politècnica de
Catalunya. April 11, 2007.
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Tu.C3.1
Flexible Simulators for OBS Network Architectures
Oscar Pedrola1, Sébastien Rumley2, Miroslaw Klinkowski1,3
Davide Careglio1, Christian Gaumier2 and Josep Solé-Pareta1*
1
Technical University of Catalonia (UPC), Jordi Girona 3, 08034 Barcelona, Catalunya, Spain
2
Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland
3
National Institute of Telecommunications (NIT), 1 Szachowa Street, 04-894 Warsaw, Poland
* Tel. (+34) 93 4016982, Fax. (+34) 93 4017055, e-mail: [email protected]
ABSTRACT
Since the OBS paradigm has become a potential candidate to cope with the needs of the future all optical
networks, it has really caught the attention from both academia and industry worldwide. In this direction, OBS
networks have been investigated under many different scenarios comprising numerous architectures and
strategies. This heterogeneous context encourages the development of flexible simulation tools. These tools
should permit both an easy integration of any possible new network protocol design and a rapid adaptation to
different performance target goals. In this paper, we present two OBS network simulators, namely, a C-based
simulator (ADOBS) and our novel Java-based simulator (JAVOBS). We compare their performances and we
provide some exemplary results that point out remarkable flexibility that can be achieved with the JAVOBS
simulator.
Keywords: optical burst switching (OBS), simulation tool, flexibility.
1. INTRODUCTION
To move towards IP-over-WDM architectures, various optical switching techniques have been under intensive
research. Among them, three switching paradigms have appeared as potential candidates. Firstly, Optical Circuit
Switching (OCS) [1] pursues a wavelength routed networking architecture with a whole wavelength as its finest
granularity. However, it lacks both the flexibility and efficiency required to cope with the needs of current traffic
patterns. Secondly, in the Optical Packet Switching (OPS) approach [2], each packet is sent into the network
with its own header. This header is going to be either electronically or all-optically processed at each
intermediate node while the packet is optically buffered. Although OPS may be seen as both the natural choice
and conceptually ideal for the future all-optical networks, current optical technology is still immature and not
able to overcome its exigencies. Finally, in order to provide optical switching for next-generation Internet traffic
in a flexible yet feasible way, the Optical Burst Switching (OBS) paradigm was proposed in [3]. In an OBS
network, a burst control packet (BCP) is sent out-of-band both to reserve all resources and to set up the path for
its burst of data, which will be sent optically after an offset time in a cut through manner. In this way, OBS
allows for an efficient use of resources without the need of optical buffering at any intermediate node. Although
it can be seen as an intermediate step of the migration from OCS to OPS, OBS has emerged as a more
competitive choice for the transmission of data traffic in the near future. In essence, OBS combines the best from
both OCS and OPS while avoiding their shortcomings. Consequently, OBS has received an increasing amount of
attention from the optical research community and has become, nowadays, a research field of its own.
OBS networks display a complex structure and the design of their constituent elements offers several degrees
of freedom. So far, much of the research on OBS networks has been conducted through theoretical analysis.
Undeniably, the analytical approach can provide valuable insights in reduced complexity scenarios but might
scarcely cope with the multiple factors that hide behind a complete network schema. Simulation tools have
become essentials to evaluate complex OBS network scenarios. Indeed, simulators solve many difficulties such
as the need to build a real system, but more important, they allow for the reproducibility of results, which is the
basis for scientific advance.
In this paper, we present both a C-based simulator (ADOBS) [4] and our novel Java-based simulator
(JAVOBS). Considering how rapidly new strategies are engineered to improve the performance of OBS
networks, it is our objective to demonstrate how versatile a simulation tool should be in order to be able to
provide reliable results in a relatively fast yet straightforward way. Section 2 gives an insight of the wide variety
of OBS schemes proposed so far. Section 3 gives a review on the OBS simulation tools presents in the literature.
Section 4 presents and compares the ADOBS and JAVOBS simulators. Section 5 provides some exemplary
results achieved by the JAVOBS simulator. We conclude this paper in Section 6.
2. OBS REVIEW
An OBS network is composed by two types of nodes, namely edge and core nodes. Edge nodes are in charge of
assembling input packets coming from different sources (e.g. IP, Ethernet) into bursts. Then, for each burst,
a separate BCP is sent well in advance, to reserve resources (e.g. bandwidth on a desired output channel) along
the way from the ingress node to an egress node. Core nodes in OBS are responsible for switching individual
bursts and for reading, processing, and updating burst control packets. The BCP carries, among other
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information, the offset time at the next hop, and the burst length. Finally, at the egress node, bursts are
disassembled.
2.1 Burst Reservation Protocols
In order to transmit bursts over an OBS network, a resource reservation protocol must be put in place to ensure
the allocation of resources and to properly configure the optical switch before the corresponding data burst
arrives at the node. A wavelength-routed OBS reservation protocol was proposed in [5] as a two-way reservation
scheme (i.e. a burst cannot be sent without the successful reception of an acknowledgement). Nevertheless, much
of the research has been devoted to the one-way reservation scheme aiming to reduce the light-path setup time
and consequently increase the resource utilization in OBS networks. The just-in-time (JIT) [6], Horizon [7] and
just-enough-time (JET) [3] resource reservation protocols are the most well-known one-way reservation
schemes. More recently, JIT+ [8] and E-JIT [9] protocols have also been proposed. The main difference between
the one-way reservation schemes stems from the manner in which output wavelengths are reserved for bursts.
These schemes include: (a) immediate reservation (JIT, E-JIT); (b) delayed reservation with void filling (JET);
(c) delayed reservation without void filling (Horizon); (d) modified immediate reservation (JIT+).
A comparison of the JIT, JIT+, JET and Horizon protocols can be found in [8]. Delayed schemes produce
a more efficient use of resources, especially when void filling is applied, and perform better in terms of burst loss
probability. However, the sophisticated scheduling algorithms that they require increase the processing times of
BCPs at intermediate nodes. Thus, in such scenario, the simplicity of JIT may balance its relative poor
performance [8]. Indeed, in contrast to the other protocols, hardware implementations of the JIT signalling
protocol have already been realized and published [10].
2.2 Burst Scheduling
When a core node receives a BCP, it must decide which channel to reserve to forward the corresponding data
burst. The goal of a scheduling algorithm is to obtain the right switching configuration matrix for efficiently
transferring input traffic to the desired output.
To date, several algorithms have been proposed to solve the wavelength scheduling problem in OBS
networks. There are two categories of algorithms: (a) without void filling; (b) void filling. The idea behind
algorithms belonging to group (a) is to find an available wavelength in a simple way. They are not aimed to
maximize the use of resources but to generate low processing times. A simple scheduling algorithm, Horizon,
which has also been called latest available unused channel (LAUC) [11], was proposed in [7]. Another example
is the first fit unscheduled channel (FFUC) [12]. More advanced scheduling algorithms belong to group (b).
These algorithms are designed both to provide efficient use of resources and to reduce blocking probabilities.
However, void filling algorithms are more complex, hence difficult in implementation and time-consuming. Two
void filling algorithms are: (1) latest available unused channel with void filling (LAUC-VF) [11]; (2) first fit
unscheduled channel with void filling (FFUC-VF) [11]. More recently, the minimum starting void (Min-SV) and
the minimum ending void (Min-EV) scheduling algorithms were presented in [13]. Min-SV and Min-EV
algorithms improve significantly the processing time over LAUC-VF. However, Min-SV/EV algorithms involve
time-consuming memory accesses. Therefore, both types of void filling algorithms are still considered too slow
to provide a viable solution to the problem [14]. Table 1 summarizes the comparison between the algorithms
based on the study in [15]. It uses the following notation: (w) number of wavelengths at each output port; (Nb)
number of bursts currently scheduled on every data channel.
Table 1. Performance comparison of different scheduling algorithms.
Scheduling Algorithm
FFUC
Horizon / LAUC
LAUC-VF
FFUC-VF
Min-SV/EV
Time complexity
O(log w)
O(w)
O(w log Nb)
O(w log Nb)
O(log2 Nb)
Bandwidth utilization
Low
Low
High
High
High
3. OBS SIMULATION TOOLS
OBS networks are still in a phase where several options may have their own opportunity. Therefore, to evolve
there is a strong need to mimic the behaviour of real OBS networks. That is precisely the task of simulation
tools. Since OBS is a relatively young field, much of the studies that can be found in the literature use quite
simple simulation models. For instance, the single node approach is used in [8] and [19]. In general, these
simulation models were developed in purpose for a specific situation and are not suitable to study complete OBS
scenarios. On the other hand, some well-known simulators such as the widely known ns-2, have their own
extensions for OBS networks [16]. A comparison of some existent OBS simulator tools can be found in [17]. To
our best knowledge, none of them was specifically developed for the study of OBS networks, and thus do not
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Tu.C3.1
provide support to the full set of OBS representations. Besides, given their divergence of perception of the OBS
scenario it is not possible to compare their results [17].
In consequence, other tools exclusively aimed to analyse OBS networks have been proposed. For example, in
[18] and [19], two new simulation models are presented. Both models exploit the object-oriented approach using
either the C++ in the former case or the Java programming language in the latter. The common goal of these new
models is to reach the flexibility degree that simulation of OBS networks requires. Following a modular
construction process, a high degree of flexibility is exhibited. At the same time, the introduction of further
developments is facilitated.
4. ADOBS AND JAVOBS SIMULATION TOOLS
The ADOBS simulator [4] is completely developed in C++. Since C++ is a low level programming language, the
developer deals with concepts and operations strictly connected with computer hardware. Hence, speed and
efficiency are achieved at the cost of complexity. Formerly, ADOBS served to study routing algorithms in OPS
networks. Lately, it has been modified to become an ad-hoc event-driven simulator for OBS networks. ADOBS
has been basically used to study the performance of the OBS network layer. On the other hand, the JAVOBS
simulator is a Java-based application that has been exclusively built to simulate OBS networks on top of the
JAVANCO framework [20]. It implements the event-driven model together with fixed-increment time
progression [21]. Thus, we consider that JAVOBS implements a hybrid discrete event simulation model. By its
nature, Java is an interpreted language. This means that user code is temporarily compiled into "Java byte code",
and does not become executable code until the program is actually run. Consequently, C++ runtime performance
is better than that of Java. Nevertheless, we selected Java for our simulator because of both the complexity of
building a simulator from scratch using C++ and the fact that Java is a really flexible and dynamic language. In
addition, Java is a garbage-collected language (i.e. memory handling procedures are automatically
implemented).
Both simulators provide support to both the conventional OBS control architecture (C-OBS) and the
emulated offset time control architecture (E-OBS) [4]. Table 2 presents some features of both simulators.
Table 2. ADOBS / JAVOBS features.
ADOBS
JAVOBS
OBS Protocols
JET, Horizon
JET, JIT, Horizon, E-JIT, JIT+
Scheduling Algorithms
LAUC, FFUC, FFUC-VF, LAUC-VF
LAUC, FFUC, FFUC-VF, LAUC-VF
OBS Architectures
C-OBS, E-OBS
C-OBS, E-OBS
Model Building
Predefined input file
Graphical, script or xml input file.
Programming Language
C++
Java
In order to give credibility to results obtained, both simulators have been analytically validated. The analytical
results are based on a reduced link load model for OBS networks presented in [22]. Figure 1.a presents the
results obtained by both simulators. We used a network topology called SIMPLE [4] with 6 nodes and 8 links
and the shortest-path routing algorithm. Each node is an edge node generating 25.6 Erlangs (0.8, when
normalised to the link capacity) and each link has 32 wavelengths at 10 Gbit/s. Bursts have exponential
distributed arrival time and length (mean 1 Mb). In obtaining the simulation results, we have estimated 99%
confidence intervals. Since the confidence intervals found are very narrow, we do not plot them in order to
improve readability. As can be seen, both simulators match the analytical results. Hence, in this case, we
consider both simulators validated.
A test measuring the running time of both simulators has also been performed. Simulations were run
according to the number of bursts generated and prompted more than one hundred hours of simulation (on an
Intel Core 2 Quad 2.4 GHz desktop computer). In this case we consider two network topologies: (1) NSFNET
(US network); (2) EON (a pan-European network defined in European COST 266 action) with 15 and 28 nodes,
and 23 and 39 links, respectively. JET signalling and LAUC-VF scheduling are used. The mean length of bursts
generated is 40 kB for this experiment. Figure 1.b presents the results obtained.
As expected, ADOBS performs better at low values due to the fact that uses C++ programming. However, it
starts to change at 1 million bursts. From this point on, the ADOBS curves exhibit an exponential increase which
finally creates gaps of up to 96 hours between both simulators. These results may be due to a non-optimized
implementation of the ADOBS simulator. Although JAVOBS is outperformed in short simulations, we observe
a constant growth of the running times for all time scales which exhibits its robustness. Thus, in this case,
become clear the advantages of using a garbage-collected language.
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Analytic al Validation
1.00E +00
AD /JAV OBS Performance
1.00E+06
S im ulation J AVOB S
S im ulation ADOB S
R educed L ink L oad Aproximation
R u n n n in g t im e ( s e c o n d s )
1.00E+04
1.00E -02
B u r s t L o s s P ro b a b i l i ty
ADOBS-EON
ADOBS-NSFNET
JAVOBS-NSFNET
JAVOBS-EON
1.00E+05
1.00E -01
1.00E+03
1.00E -03
1.00E+02
1.00E+01
1.00E -04
1.00E+00
1.00E -05
1.00E-01
1.00E -06
1.00E-02
1.00E+04
1.00E -07
0.4
0.5
0.6
0.7
0.8
0.9
a)
1.00E+05
1.00E+06
1
L oa d
1.00E+07
1.00E+08
Bursts Simulated
b)
Figure 1. a) ADOBS / JAVOBS analytical validation. b) ADOBS / JAVOBS runtime test.
5. JAVOBS IMPLEMENTATIONS / RESULTS
The objective of this paper is to present the flexibility of the JAVOBS simulation tool. To do this, in this section,
we present three different case-studies: (1) Performance comparison of reservation protocols under both the
C-OBS and the E-OBS control architectures supported in JAVOBS; (2) Comparison of the Horizon and the
Constant Time Burst Resequencing (CTBR) [14] schedulers under the single node topology; (3) Analysis of the
network topology flexibility using different degrees of meshed-rings.
5.1 Comparison of the E-OBS and C-OBS control architectures
Considering that fiber delay lines (FDLs) buffers are not used, it has been proved in [23] that the best worst-case
performance of an online best-effort scheduling algorithm is achieved when all bursts have the same offset time
and the same length. One of the benefits of E-OBS comes from the fact that offset times are introduced at each
core node by means of additional fiber delay coils inserted in the data path at the input port of the node, thus,
E-OBS does not experience offset variation inside the network. In such scenario, scheduling algorithms do not
need to implement any void filling technique. Therefore, in an E-OBS network, JIT and Horizon reservation
mechanisms seem to be the most appropriate ones due to its low complexity compared to JET. Indeed, the overprovisioning of resources that characterizes JIT is substantially reduced using E-OBS due to smaller offset times.
Figure 3 presents the comparison between both architectures under the different signalling protocols obtained by
JAVOBS. We consider the EON network topology and a mean burst length of 40 kB. The processing and
switching times are estimated according to [8] and [4]. We observe that using E-OBS, the performance of the
5 different signalling protocols is quite similar, thus, the possibility of reducing the network complexity by using
low complexity techniques such as JIT is not unfounded. On the contrary, in C-OBS becomes clearer the
advantage of using complex reservation mechanisms due to the variable offsets.
E - OB S RE S E RVAT ION P ROT OC OL S C OMP ARIS ON
1.00E +00
1.00E +00
1.00E -01
1.00E -01
B u r s t L o s s P r o b a b ility
B u r s t L o s s P r o b a b ility
C - OB S RE S E RVAT ION P ROT OC OL S C OMP ARIS ON
1.00E -02
JET
J IT
1.00E -03
Horizon
J IT+
1.00E -04
1.00E -02
JET
J IT
1.00E -03
Horizon
J IT+
1.00E -04
E -J IT
E -J IT
1.00E -05
1.00E -05
0.1
a)
0.15
0.2
0.25
0.3
L oad
0.35
0.4
0.45
0.5
0.1
b)
0.15
0.2
0.25
0.3
0.35
0.4
L oa d
Figure 3. Burst loss probability vs. load, in a) conventional and b) emulated offset time OBS.
0.45
0.5
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5.2 Constant Time Burst Resequencing (CTBR) implementation
Since OBS has ultra high speed requirements, the bandwidth efficient scheduling algorithms proposed so far are
not considered a viable solution to the problem due to its large processing times. Recently, in [14], a hardware
implementation of an optimal wavelength scheduler that can produce burst schedules in a time complexity of
O(1) was presented. The idea consists of producing schedules by bursts arrivals rather than BCPs arrivals. The
optimal wavelength scheduler consists of two components: (a) the CTBR block; (b) the horizon scheduler. It is
important to notice that the driving force behind this technique is the simplicity of horizon and its ability to
operate at high speed.
In order to test, once more, the flexibility of our simulator, we have developed a set of classes to study the
CTBR mechanism. To perform the simulation, we have used the parameters specified in [14] with the aim of
comparing the results obtained. Since the topology utilised for the simulation is not mentioned, we assumed the
single node implementation. The performance of both the Horizon and CTBR scheduler is compared. The offset
times of all bursts are generated according to a lognormal distribution with mean 100 µs. Figure 4 shows the
results obtained. We observe a clear match with the results presented. The burst loss probability of the horizon
scheduler increases when the ratio between the offset time standard deviation and the burst length increases.
On the other hand, in the CTBR scheduler, the curves remain flat regardless of the ratio variation.
Figure 4. Performance of the CTBR scheduler
5.3 Flexible topology simulations
Eventually, the flexibility of JAVOBS has been tested regarding the network topology side. The study consists
of a set of simulations over a variable ring topology. Indeed, when designing a network there is a trade-off
between the costs of the deployment of resources and the performance achieved. In order to reach an optimal
solution to the problem (if a solution exists), it is very helpful to have a tool permitting “what-if” studies.
JAVOBS also allows topological modifications in a straightforward way. To prove it, we present a very simple
case in an 8 node ring topology. The study consists of a simulation that starts with 8 links and 32 wavelengths
per link and ends with 28 links (full-mesh) and 9 wavelengths per link. At each step, keeping intact the last
topology, new links are added. In order to keep constant the network capacity, the number of wavelengths per
link is recomputed at each step. Figure 5 shows the results obtained together with the topologies generated.
A shortest-path routing algorithm has been used. The arrival rate λ of BCPs is such that λ/µ = 51.2 for all
scenarios. As expected using the shortest-path routing algorithm, the blocking probability is clearly reduced as
more direct links between each source-destination pair become available.
Figure 5. Ring topology study.
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6. CONCLUSIONS
We have presented our novel Java-based simulation tool JAVOBS, which has been exclusively developed for the
study of OBS networks. We have also given a recent overview of the existent simulation tools for OBS
networks. We have verified that comparisons between simulators were impossible due to their heterogeneity.
The ADOBS and JAVOBS simulators have been described, validated and compared. Finally, we have shown the
flexibility of our simulator through a series of experiments that exhibit its performance. From the results of these
experiments, it is concluded that: (1) as OBS networks are still undergoing intense research and development, its
study requires simulation tools that facilitate the introduction of enhancements and new techniques, (2) as long
as the simulation model is valid, flexible simulation tools such as JAVOBS can save time and computational
resources.
ACKNOWLEDGEMENTS
The work described in this paper was carried out with the support of the CATARO-project (TEC2005-08051C03-01) funded by the Spanish Ministry of Education and Science (MEC) and within the COST Action 291,
supported by Swiss National Science Foundation.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
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C. Qiao, M. Yoo: Optical burst switching (OBS)-A new paradigm for an optical Internet, J. High Speed Networks,
vol. 8, no. 1, pp. 69-84, Jan. 1999.
M. Klinkowski: Offset time-emulated architecture for optical burst switching - modelling and performance evaluation,
Phd’s Thesis, DAC department, Technical University of Catalonia (UPC), Feb. 2008.
M. Duser, P. Bayvel: Analysis of a dynamically wavelength-routed, optical burst switched network architecture,
IEEE/OSA J. Lightwave Technol, vol. 20, no. 4, pp. 574-585, April 2002.
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networks, in Proc ISCC 2007, Aveiro, Portugal, July 2007.
I. Baldine, M. Cassada, A. Bragg, G. Karmous-Edwards, D. Stevenson: Just-in-time optical burst switching
implementation in the ATDnet all-optical networking testbed, in Proc. Globecom 2003, San Francisco, CA, Dec. 2003.
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vol. 25, no. 8, August 2007.
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M.Casoni, et al.: M_OBS_SIM: A powerful modular optical burst switched (OBS) network simulator, Simulation
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S. Rumley, C. Gaumier, et al.: Software tools and methods for research and education on optical network, in COST
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C. Phillips: A review of high performance simulation tools and modeling concepts, Recent Advances in Modeling and
Simulation Tools for Communication Networks and Services, pp. 29-48, Springer, 2008.
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Etap 3:
Badania warunków integracji zróżnicowanych formatów
modulacji, usług czasu rzeczywistego i transmisji
danych w konwergentnej przezroczystej sieci optycznej
Etap 4:
Studium uniwersalnej optycznej sieci do transmisji cyfrowej
i analogowej Radio-over-Fibre gwarantującej
optymalną jakość usługi
Praca nr 14310028
Etap 3:Badania warunków integracji zróżnicowanych formatów modulacji, usług czasu
rzeczywistego i transmisji danych w konwergentnej przezroczystej sieci optycznej
Etap 4:Studium uniwersalnej optycznej sieci do transmisji cyfrowej i analogowej
Radio-over-Fibre gwarantującej optymalną jakość usługi
Praca nr 14310028
Kierownik pracy:
doc. dr hab. Marian Marciniak
Wykonawca pracy:
doc. dr hab. Marian Marciniak
W ramach etapu 3
Przeprowadzono badania konwergentnej sieci przezroczystej optycznej do transmisji usług
czasu rzeczywistego sieci z komutacją obwodów, usług sieci pakietowej i sieci transmisji
danych, w tym ultraszybkich sieci Ethernet 100GbE/1000GbE.
Badania prowadzono w ramach COST 291 Towards Digital Optical Networks oraz
COST 293 Graphs and Algorithms for Telecommunication Networks we współpracy
z międzynarodowymi organizacjami normalizacyjnymi ITU Study Group 15 Optical
Transport Networks dla optycznej sieci transportowej OTN oraz IEEE High Speed Study
Group dla sieci transmisji danych Ethernet.
Wykazano, że przezroczysta sieć optyczna z gęstym zwielokrotnieniem w dziedzinie
długości fali DWDM może z powodzeniem zapewniać wymogi związane z ruchem usług
czasu rzeczywistego, usług pakietowych i sieci transmisji danych. W szczególności wykazano
celowość i możliwość połączenia optycznej sieci transportowej SHD/SONET 10 Gbit/s,
40 Gbit/s, 160 Gbit/s oraz sieci transmisji danych Ethernet 10GbE, 100GbE, 1000GbE
w ramach wspólnego standardu ITU i IEEE.
W ramach etapu 4
Analizowano możliwość transmisji radiowego sygnału analogowego w technologii Radioover-Fibre w przezroczystym łączu światłowodowym obok sygnałów cyfrowych
telekomunikacji oraz transmisji danych.
Wskazano na ograniczenia dla transmisji sygnału radiowego o wysokiej częstotliwości
60 GHz i powyżej wynikające z parametrów transmisyjnych światłowodu. W szczególności
wykazano, że zjawisko dyspersji polaryzacyjnej jest głównym ograniczeniem pojemności
transmisyjnej (szybkość modulacji × odległość transmisji) istniejących łączy opartych na
światłowodach jednomodowych. Wskazano na kierunki dalszych badań zmierzających do
powszechnego wykorzystania technologii Radio-over-Fibre.
Rezultaty włączono do raportu końcowego COST oraz opublikowano w wydawnictwach
międzynarodowych.
Szczegółowe wyniki zawierają załączone publikacje:
[1]
[2]
[3]
[4]
[5]
[6]
M. Marciniak: 100 Gb Ethernet and beyond, in COST 291 Workshop "The Role of Optical
Networking in The Future Internet", Villanova, Spain, March 11, 2008. (Załącznik 3.1)
M. Marciniak: Emerging standards for 100 Gbit Ethernet access and beyond, in COST 291 Final
Report, Chapter 4 Section 3, to be published by Springer Science-Business Media.
(Załącznik 3.2)
M. Marciniak: Future networks – beyond next generation networking, in Proc. of ICTON 2008,
paper Mo.B1.5, vol. 1, pp. 25-28, Athens, June 2008. (Załącznik 3.3)
M. Marciniak: Sub-wavelength information photonics: materials, phenomena, and functional
devices, in Proc. of ICTON-MW 2008, paper Sa2.1, pp.1-3, Marrakech, Morocco, Dec. 2008.
(Załącznik 3.4)
Goncharenko A. Esman, V. Kuleshov, M .Marciniak: Matrix infrared-visible image converter
based on waveguide microring resonators, in Proc. of ICTON 2008, paper Tu.C2.4, vol. 2,
pp. 96-99, Athens, June 2008. (Załącznik 3.5)
H.V. Baghdasaryan, T.M. Knyazyan, A.S. Berberyan, T.T. Hovhannisyan, M. Marciniak: An
optical model of a transmission-type vertical-cavity electro-absorption modulator on Si/SiO2 for
high-speed intra/inter-chip interconnects, in Proc. of ICTON 2008, paper We.C2.6, vol. 2,
pp. 174-177, Athens, June 2008. (Załącznik 3.6)
3
Załącznik 3.1
100 Gb ETHERNET AND BEYOND
Marian Marciniak, National Institute of Telecommunications, Warsaw, Poland
Abstract- 100 Gb Ethernet is coming. This contribution discusses the feasibility of optical networking to accommodate 100
Gb Ethernet requirements.
WHY HIGHER SPEED ETHERNET?
The technical feasibility of 100 GbE has been already proven, as well as its confidence in reliability. The principle of scaling
the IEEE 802.3 MAC to higher speeds has been already established within IEEE 802.3. Systems with an aggregate bandwidth
of greater than or equal to 100 Gb/s have been demonstrated and deployed in operational environment. The 100 GbE project
will build on the array of Ethernet component and system design experience, and the broad knowledge base of Ethernet
network operation. Moreover, the experience gained in the deployment of 10 Gb/s Ethernet might be exploited. For instance,
parallel transmission techniques allow reuse of 10 Gb/s technology and testing.
100 Gb ETHERNET CHALLENGES
Ethernet is now widely adopted for communications in local area networks and in metropolitan area networks. The Ethernet
is facing the next evolutionary step towards 100 Gbit/s Ethernet, or 100GbE [1]. As Ethernet becomes more prevalent, the
issues related to the software, electronics, and optoelectronics need to be addressed. This becomes more provident for
100GbE as a technology does not simply refer to high bit rate transmission at 100 Gbit/s, but also relates to switching, packet
processing, and queuing and traffic management at 100G line rate. 10 Gb/s and recently 40 Gb/s have become commercially
deployed standards in optical networking. Dense Wavelength Division Multiplexing technology allows to accommodate the
100 Gb Ethernet traffic with classical voice and emerging packet networks in a single infrastructure, therefore reducing the
costs of the 100GbE introduction.
As system throughput doubles roughly every 2 years, this implies the following network throughput roadmap [2]: 10Gbps in
2007, 40Gbps in 2011, 100Gbps in 2014, 160Gbps in 2015?, 640Gbps in 2019? Industry experts claim a standard describing
1 Tb/s Ethernet will be need by 2012 [3]!
IEEE HSSG (Higher Speed Study Group) experiences indicate:
– 40 Gb/s Ethernet will provide the same cost balance between the LAN and the attached stations as 10 Gb/s Ethernet.
– The cost distribution between routers, switches, and the infrastructure remains acceptably balanced for 100 Gb/s Ethernet.
Given the topologies of the networks and intended applications, early deployment will be driven by key aggregation & highbandwidth interconnect points. This is unlike the higher volume end system application typical for 10/100/1000 Mb/s
Ethernet, and as such, the initial volumes for 100 Gb/s Ethernet are anticipated to be more modest than the lower speeds. This
does not imply a reduction in the need or value of 100 Gb/s Ethernet to address the stated applications.
CONCLUSIONS AND FUTURE DIRECTIONS
Optical networks consisting of standard single mode fibres are in principle suitable for transportation of data rates up to 100
Gbit/s and more. But physical limitations given by the fibres themselves require new technologies to overcome these
limitations. Noise accumulation, chromatic dispersion, polarisation mode dispersion and nonlinear effects limit data rate and
maximum transmission distance. Highly stable 100 Gbit/s Ethernet transmission over different distances through the network
would require pushing state of the art in the limits towards optimisation and development of new technologies and
components for transmitters and receivers.
Therefore it is necessary to provide a solution for applications that have been demonstrated to need bandwidth beyond the
existing capabilities. These include data centres, internet exchanges, high performance computing and video-on-demand
delivery. Network aggregation and end-station bandwidth requirements are increasing at different rates, and is recognized by
the definition of two distinct speeds to serve the appropriate applications.
Core networking applications have demonstrated the need for bandwidth beyond existing capabilities and the projected
bandwidth requirements for computing applications. Switching, routing, and aggregation in data centres, internet exchanges
and service provider peering points, and high bandwidth applications, such as video on demand and high performance
computing environments, have demonstrated the need for a 100 Gb/s Ethernet interface.
Bandwidth requirements for computing and core networking applications are growing at different rates, which necessitates
the definition of two distinct data rates for the next generation of Ethernet networks in order to address these applications:
Servers, high performance computing clusters, storage area networks and network attached storage all currently make use of
1G and 10G Ethernet, with significant growth of 10G projected in ’07 and ’08. I/O bandwidth projections for server and
computing applications indicate that there will be a significant market potential for a 40 Gb/s Ethernet interface.
ACKNOWLEDGMENT
The author acknowledges cooperation with the European COST (European Co-operation in the field of Scientific and
Technical Research) projects: COST Action 291 Towards Digital Optical Networks (TDON) consortium, and COST Action
293 Graphs and Algorithms for Telecommunications (GRAAL).
REFERENCES
[1] IEEE 802.3 Higher Speed Study Group tutorial: “An Overview: The Next Generation of Ethernet”, IEEE 802 Plenary, Atlanta, GA, November 12, 2007
[2] Shimon Muller, Andy Bechtolsheim, Ariel Hendel, HSSG Speeds and Feeds Reality Check, January 2007,
http://www.ieee802.org/3/hssg/public/jan07/muller_01_0107.pdf
[3] J. McDonough, “Moving Standards to 100 GbE and Beyond”, IEEE Applications § Practise, Online Magazine, Vol 45 Suppl. 3, pp. 6-9, November 2007
Załącznik 3.2
4. Evolution of Optical Access Networks
Giorgio Maria Tosi Beleffi, Italian Communication Ministry, Italy
Silvia Di Bartolo, Tor Vergata University, Italy
Antonio Luis Jesus Teixeira, Mário Lima, Carlos Almeida, Natasa Pavlovic, Insituto de Telecomunicacoes,
Portugal
Y. Shachaf, C.-H. Chang, P. Kourtessis, University of Hertfordshire, UK
Marian Marciniak, National Institute of Telecommunications, Poland
E. Leitgeb, M. Löschnigg, P. Fasser, Graz University of Technology, Austria
Maurice Gagnaire, Telecom ParisTech, France
Lena Wosinska, Jiajia Chen, The Royal Institute of Technology, Sweden
Abstract. This chapter reviews the current developments in access network architectures and protocols to
communicate dynamically the emerging broadband services to end-users at low cost. Following a summary
of Gigabit Ethernet and Passive Optical Network (PON) standards and deployment issues with reference to
Ethernet (EPON) and Gigabit-capable PON (GPON) infrastructures, an original transparent network
architecture is presented to allow interoperability of time division multiplexing (TDM) and wavelength
division multiplexing (WDM) PONs, by means of coarse routing. To provide flexible connectivity at
extended service reach hybrid wireless and free space optic technologies have been investigated to terminate
mobile end users to high bandwidth PON terminals. To demonstrate independent bandwidth management of
the constituent sectors of such architectures developed dynamic bandwidth allocation (DBA) algorithms are
summarised followed by an original control plane to coordinate the various mandatory access control (MAC)
protocols. Finally, to provide reliable service delivery several protection schemes have been analysed.
Keywords: Fibre-to-the-home (FTTH), passive optical network (PON), Gigabit Ethernet (GE), Radio over
fibre (RoF), Dynamic bandwidth allocation (DBA), Protection.
Załącznik 3.2
4.3 Emerging Standards for 100 Gbit Ethernet Access and Beyond
4.3.1 Introduction - Why Higher Speed Ethernet?
Ethernet, being originally a computer networking protocol, nowadays is able to unify long distance, metro and
access networking into a single network of the future [1]. The deployment of Fibre-To-The-Home in access
observed in Japan, Korea, US and Europe will assure a broad bandwidth for the user at an affordable cost [2].
Computing speed and system throughput doubles approximately every two years. Consequently, fundamental
bottlenecks are happening everywhere. Increased number of users together with increased access rates and
methods and increased services results in explosion of bandwidth demand. Networking is driven by the
aggregation of data from multiple computing platforms. As the number of computing platforms grows fast, this
results in a multiplicative effect on networking [3].
Therefore it is necessary to provide a solution for applications that have been demonstrated to need bandwidth
beyond the existing capabilities. These include IPTV, downloading/uploading of large files at short time, internet
exchanges, high performance computing and video-on-demand delivery. High bandwidth applications, such as
video on demand and high performance computing justify the need for a 100 Gb/s Ethernet in metro and access
networks. Indeed, even a personal computer will surpass 10 GHz computation speed in few years.
4.3.2 100 Gbit Ethernet Challenges
Ethernet is now widely adopted for communications in local area networks and in metropolitan area networks.
The Ethernet is facing the next evolutionary step towards 100 Gbit/s Ethernet, or 100GbE [4, 5]. As Ethernet
becomes more prevalent, the issues related to the software, electronics, and optoelectronics need to be addressed.
This becomes more evident for 100GbE, since that technology does not simply refer to high bit rate transmission
at 100 Gbit/s, but also relates to switching, packet processing, and queuing and traffic management at 100 Gbit/s
line rate. This is in parallel with a remarkable progress in transmission as 10 Gb/s and recently 40 Gb/s systems
have become commercially deployed standards in optical networking, and multiplying the total aggregate
capacity by an use of DWDM technology and transmitting simultaneously several wavelength channels. This has
faced problems in view of fibre impairments, one of the most serious ones being fibre Polarisation Mode
Dispersion (PMD). In particular, care has to be taken to minimise PMD coefficient when manufacturing the
fibres and cables.
The IEEE HSSG (Higher Speed Study Group) objectives are:
• Support full-duplex operation only
• Preserve the 802.3 / Ethernet frame format utilizing the 802.3 Media Access Control (MAC)
• Support a Bit Error Rate (BER) better than or equal to 10-12 at the MAC/PLS (Physical Layer Signalling)
service interface
• Support a MAC data rate of 100 Gb/s
• Provide Physical Layer specifications which support 100 Gb/s operation over:
• At least 40km on SMF (Single Mode Fibre)
• At least 10km on SMF
• At least 100m on OM3 MMF (850nm Laser Optimized Multi-Mode Fibre)
• At least 10m over a copper cable assembly
As an amendment to IEEE Std 802.3, the proposed project will follow the existing format and structure of
IEEE 802.3 MIB definitions providing a protocol independent specification of managed objects (IEEE Std
802.1F). As was the case in previous IEEE 802.3 amendments, new physical layers specific to either 40 Gb/s or
100 Gb/s operation will be defined.
4.3.3 Transparent Optical Transmission for100 Gbit Ethernet
The technical feasibility of 100 GbE has been already proven, as well as its confidence in reliability. The
principle of scaling the IEEE 802.3 MAC to higher speeds has been already established within IEEE 802.3.
Systems with an aggregate bandwidth of greater than or equal to 100 Gb/s have been demonstrated and deployed
in operational environment. The 100 GbE project will build on the array of Ethernet component and system
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design experience, and the broad knowledge base of Ethernet network operation. Moreover, the experience
gained in the deployment of 10 Gb/s Ethernet might be exploited. For instance, parallel transmission techniques
allow reuse of 10 Gb/s technology and testing.
An alternative approach to avoid the development of ultra-fast electronic circuits is to use advanced
modulation formats that achieve 100 Gbit/s information rate while allowing lower transmission rates. In such a
case, the implementation will require components operating around 50 GHz and since electronic circuitry for 40
Gbit/s is already commercially available, there will be an easier migration to the development of say 50 Gbit/s
capable silicon components.
Finally, for short reach interfaces there have been a number of implementations that provide 10 or 12 parallel
10 Gbit/s lanes for a total aggregate bit rate of 100 Gbit/s or 120 Gbit/s. Such solutions are being currently under
discussion in the IEEE HSSG [6].
The next step in order to increase data rates and speed of the services is the introduction of services based on
100 Gb Ethernet. But 100 Gbit/s transmission is standing on the very beginning and the worldwide level of
knowledge and know-how in the field of 100 Gbit/s is still low. A lot of research activities have to be done until
the first test links can be prepared for commercial and field exploitation. First of all integrated circuits are
necessary which enable transmission equipment, like e.g. transceivers, to provide this high speed data signal with
an adapted modulation technique. To make the technology suitable for exploitation basic physical effects must
be investigated in order to use them for a future technology or to minimise or overcome them if they contribute
impairments. Only then all the processes for the production of necessary components can be controlled with the
desired and necessary reliability. Other challenges like the cost reduction of the components, the reduction of the
operational expenses of the network operators and the minimisation of the energy consumptions are also a big
challenge and subject of research.
The existing 802.3 protocol has to be extended to the operating speed of 40 Gb/s and 100 Gb/s in order to
provide a significant increase in bandwidth while maintaining maximum compatibility with the installed base of
802.3 interfaces, previous investment in research and development, and principles of network operation and
management.
4.3.4 Future Directions
Optical networks consisting of standard single mode fibres are in principle suitable for transportation of data
rates up to 100 Gbit/s and more, are to be widely deployed both in long distance and in metro/access. Physical
limitations laid by the fibres themselves require new technologies to overcome these constraints. Noise
accumulation, chromatic dispersion, polarisation mode dispersion and nonlinear effects limit data rate and
maximum transmission distance. Highly stable 100 Gbit/s Ethernet transmission over different distances through
the network would require pushing state of the art in the limits towards optimisation and development of new
technologies and components for transmitters and receivers.
A possible solution for 100GbE modulation format can be a pure multi-level amplitude modulation, offering the
advantage of lower clock frequency and required signal bandwidth of critical components, e.g. modulators. On
the other hand, the robustness of multi-level modulation scheme against such common impairments in the
transmission path as optical amplifier noise and fibre dispersion must be carefully analyzed.
Bandwidth requirements for computing and networking applications are growing at different rates. These
applications have different cost / performance requirements, which necessitates two distinct data rates, 40 Gb/s
and 100 Gb/s.
4.3.5 References
[1] M. Marciniak, Future Networks – beyond Next Generation Networking, 10th Anniversary International Conference on
Transparent Optical Networks, Conference Proceedings Vol. 1, pp. 25-28, Athens, Greece, June 22-26, 2008.
[2] P. Cochrane, “Fibre-to-the-home (FTTH) Costs Are Now In!”, Proceedings of the IEEE, Vol. 96 No.2, pp. 195-197,
February 2008
[3] IEEE 802.3 Higher Speed Study Group tutorial: “An Overview: The Next Generation of Ethernet”, IEEE 802 Plenary,
Atlanta, GA, November 12, 2007
[4] J. McDonough, “Moving Standards to 100 GbE and Beyond”, IEEE Applications & Practise, Online Magazine, Vol 45
Suppl. 3, pp. 6-9, November 2007
[5] M. Marciniak, 100 Gb Ethernet over Fibre Networks– Reality and Challenges, ICTON - 'Mediterranean Winter' 2007,
Sousse, Tunisia, December 6-8, 2007.
[6] Shimon Muller, Andy Bechtolsheim, Ariel Hendel, HSSG Speeds and Feeds Reality Check, January 2007,
http://www.ieee802.org/3/hssg/public/jan07/muller_01_0107.pdf
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Mo.B1.5
Future Networks – beyond Next Generation Networking
Marian Marciniak, Senior Member, IEEE
National Institute of Telecommunications, Department of Transmission and Optical Technologies
1 Szachowa Street, 04-894 Warsaw, Poland
ABSTRACT
Transparent optical networking enables mankind to share and interchange huge amounts of data at local, regional
and global distances in real time. It is clear now that the Next Generation Networking is not a goal but an
intermediate step rather towards the Future Networking.
1. INTRODUCTION
The previous decade has upgraded optical fibre transmission with the transparency of the links resulting in
a potential of long distance DWDM transmission with hundreds or thousands of independent transmission
channels within a single fibre, enabling the aggregate transmission rate of terabit per second and beyond.
Fixed and mobile communications will continue to converge coming years. Consequently, Next Generation
Networks (NGN) have been deployed widely starting with the International Telecommunication Union (ITU)
Study Period 2005-2008, and they will evolve towards The Network of The Future (i.e. other than NGN) under
the next Study Period 2009-2012 as an activity lead by ITU-T Study Group 13.
Ethernet, being originally a computer networking protocol, nowadays is able to unify long distance, metro
and access networking into a single Network Of The Future [1]. The deployment of Fibre-To-The-Home in
access observed in Japan, Korea, US and Europe will assure a broad bandwidth for the user at an affordable
cost [2].
The expansion of Internet traffic worldwide forces the global communication community to shift from
classical circuit switched, connection oriented networks to packet switched, connectionless transmission of data,
with a strong interest in guarantees of the network reliability and availability as well as the security of the
information and of the infrastructure, generalized mobility etc.
It is generally but apparently erroneously accepted that the packet traffic should replace the circuit-switched
traffic everywhere, provided the Quality of Service and security issues are resolved satisfactorily. In fact the
Internet as being based on a ‘best-effort’ principle and carrying a traffic of a statistic nature is inherently
vulnerable as Quality of Service and security are concerned. The rationale to keep circuit-switched connections
at least for some real-time applications has been promoted by ourselves [3], and it is being recognised more
widely recently [4].
2. WHY FUTURE NETWORKS?
New areas have emerged, e.g. IPTV, sensor networks, home networks, a need for interoperability of satellite
with NGN and/or Future Networks, including full integration of the satellite transmission in public networks,
taking account of emerging technologies and services.
There are growing concerns with respect to: scalability/ubiquity, security/robustness, mobility, heterogeneity,
Quality of Service (QoS), re-configurability, context-awareness, manageability, data-centric, network
virtualization, economics, etc. A Future Network able to provide futuristic functionalities beyond the limitation
of the current network including Internet, is getting a global attention.
Three-dimensional approach
Three dimensions of the Future Network objectives are: Scope, Depth, and Packaging.
Dimension 1 – Scope includes: future Ubiquitous Networking environments (e.g. Ad-hoc networks including
RFIDs and Sensors), use of IPv6, Home Network and service technology, new and converged transport
technology.
Dimension 2 – Depth aims to develop a technology capable to support control protocols (both service and
transport control), service and application support platforms to enable convergence with relevant protocols
aspects, media processing including codec(s), and other related issues.
Dimension 3 – Packaging foresees various packages offered to the customer such as: service scenarios (e.g.
Voice/Multimedia/Video/IPTV over NGN), Web based services using NGN, 3rd party (i.e. other than network
operation and service provider) applications , U-health (U stands for ubiquitous), e-learning, etc.
Network aspects - layered approach
This approach is based on three layers, those are:
− transport (access and core) layer,
− transport control, service control layer,
− and service/application support layer.
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The approach is based on NGN principles, but it is not just limited to NGNs, rather directed to networks in
general.
3. FUTURE NETWORK REQUIREMENTS
A number of issues have to be resolved when introducing Future Networks. Those concern: Emerging services
and capabilities in an evolving NGN, QoS enablement in the NGN, Convergence of third-Generation
International Mobile Telecommunications (IMT-2000) and fixed networks, Impact of IPv6 to NGN, Public data
networks, Packet forwarding and deep packet inspection for multiple services in packet-based networks and
NGN environment, Security and identity management, Enabling COTS (Commercial Off-The-Shelf)
components in an open environment, and Distributed Services Networking (DSN).
Considerations for Ubiquitous Networking should include Web-based networking as personalized IPTV service,
Mobile Web, ID registration, location tracking and dynamic mobility control including security. This should
include a reliable and secure sensor networking with novel devices such as RFIDs and sensors [5].
Packet based ubiquitous networks request for rules for a variety of connection types:
− connection-oriented circuit-switched,
− connection-oriented packet-switched,
− and connectionless packet switched networks.
Requirements for QoS enablement
This issue involves a variety of transport technologies (Ethernet, IP and MPLS in the core; DSL, UMTS, WiFi,
and WiMAX in the access) and terminal devices (phone, laptop, i-pod), and multiple administrative domains
(e.g. home network and provider network), and finally mobility (moving) and nomadicity (changing location) of
the user.
Evolution towards integrated multi-service networks
This concerns especially interworking of IP Television (IPTV) and Home Networks. The specific requirements
are to efficiently carry narrow-band and broadband services of a fully integrated IP-based network across non-IP
based networks (e.g. FR and ATM); to enable interworking between the NGN and the legacy networks, and to
incorporate efficiently home networks (including their ability to support IPTV).
Public Data Networks (PDN)
Those should efficiently support packet based services over the transport network that provides connectivity
using technologies such as Ethernet, T-MPLS mapping over SDH/OTN. The question to solve is how can the
various aspects of the NGN services including IPTV, etc. (such as QoS, reliability, addressing, routing, naming,
security/privacy) be accommodated in the PDN?
Packet forwarding and Deep Packet Inspection (DPI)
This is essential for multi-service delivery in packet-based networks. It is especially important for real-time
multi-service (e.g. IPTV/VoIP) traffic as those applications are jitter, delay and packet loss sensitive.
Identity Management (IdM)
There is a need for:
− Efficient support of subscriber services using common IdM infrastructure to support multiple applications
including inter-network communications,
− Ease of use and single sign-on / sign-off, Public Safety Services, International Emergency and Priority
Services, Electronic Government (eGovernment) Services, Privacy/User Control of Personal Information
(i.e. Protection of Personal Identifiable Information (PPII)).
Security
Public switched telephone networks (PSTNs) that use circuit based technology are relatively secure.
Unfortunately, it is not so with Internet, and with packet networks in general. While there are several regional
and global organizations working on various aspects of security, still their coordination and cooperation is
difficult and challenging. Consequently, the efforts to secure packet infrastructures have been somewhat
fragmented and event-driven. Till now there is not much success towards achieve the desired level of protection
against threats. As the threats multiply, the countermeasure have to be undertaken at a global scale.
Security of the Future Network involves protection of NGN infrastructure and resources (services and
applications) including National Security and critical infrastructure protection, but also confidence of
transactions and protection from Identity Theft. The specific questions are:
− What are the security requirements of NGNs to effectively counter these threats?
− How to define security architecture of Identity Management in NGN?
− What are security requirements to Identity Management in NGN?
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− What new Recommendations are needed for supporting secure interoperability among different Circles
of Trusts (CoT) in NGN?
− What are security requirements of IPTV as its study evolves?
COTS components
A special requirements for enabling COTS (Commercial Off-the-Shelf) components in an open environment are
driven by:
- technology trends towards the use of open source operating systems (such as Linux),
- availability of COTS components.
NGN holds the promise of mix and match (plug and play) components and enabling services to be developed by
third parties. It is necessary to elaborate a common approach that helps the customer to navigate through the
appropriate interfaces and options to deliver an open and integrated communications platform using appropriate
standards.
Mobility management
A number of issues have to be considered in order to:
− determine what is needed to support global roaming and seamless mobility and delivery of services within
or across networks for both IMT and NGN?
− identify or define the user and operator’s perspective of mobility management capabilities for both IMT
and NGN,
− develop the architecture (interrelationship) and definition of the functional entities required to provide
mobility management capabilities for both IMT and NGN,
− allocate the functional entities to physical entities in order to determine which interfaces can use existing
protocols or enhancements to existing protocols and which interfaces need protocol development for
mobility management capabilities for both IMT and NGN.
Service Scenarios are necessary for:
− NGN based IPTV that converges traditional broadcasting services and telecommunication services over the
NGN environment,
− 3rd party services for ubiquitous environments,
− Converged Number Portability (NP) Service, Converged Private Numbering Plan Service and Multimedia
Conference (MultiCONF).
100/1000 Gb Ethernet
Ethernet is now widely adopted for communications in local area networks and in metropolitan area networks.
The Ethernet is facing the next evolutionary step towards 100 Gbit/s Ethernet, or 100GbE [6].
As communication system throughput doubles roughly every 2 years, this implies the following network
throughput roadmap [7] 10 Gbps in 2007, 40 Gbps in 2011, 100 Gbps in 2014, 160 Gbps in 2015?, 640 Gbps in
2019? Some experts claim a standard for 1 Tb/s Ethernet will be need by 2012 [8]!
As Ethernet becomes more prevalent, the issues related to the software, electronics, and optoelectronics need
to be addressed. This becomes more evident for 100GbE, since that technology does not simply refer to high bit
rate transmission at 100 Gbit/s, but also relates to switching, packet processing, and queuing and traffic
management at 100 Gbit/s line rate. This is in parallel with a remarkable progress in transmission as 10 Gb/s and
recently 40 Gb/s systems have become commercially deployed standards in optical networking, and multiplying
the total aggregate capacity by an use of DWDM technology and transmitting simultaneously several wavelength
channels. This has faced problems in view of fibre impairments, one of the most serious ones being fibre
Polarisation Mode Dispersion, PMD. In particular, care has to be taken to minimise PMD coefficient when
manufacturing the fibres and cables.
4. CONCLUSIONS & FINAL REMARKS
It is obvious now the Network of the Future is at the door. It will be truly ubiquitous, bringing novel applications
as IPTV, and Home Networks. Next Generation Networks are an intermediate step leading to the Future
Network.
It is necessary to provide a solution for applications requiring bandwidth beyond the existing capabilities.
These include IPTV, downloading/uploading of large files at short time, internet exchanges, high performance
computing and video-on-demand delivery. High bandwidth applications, such as video on demand and high
performance computing justify the need for a 100/1000 Gb/s Ethernet. Indeed, even a personal computer will
surpass 10 GHz computation speed in few years.
Finally, we have to abandon the usual question ‘What in the hell will people do with omnipresent IP and
terabit networking?’. Twenty years ago, when the optical fibres were revolutionising long distance
communications, conservative people asked ‘Do we really need millions of phone calls at the same time?’. In
1829 equally conservative people asked looking at George Stephenson’s ‘Rocket’: ‘Do we really need 13 tons of
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coal travelling with a speed of 13 miles per hour?’ One can multiply such sort of questions: ‘Do we really need
to fly at a 36,000 feet attitude?’, ‘What we have to do in the space?’. COST 291 success story advises the
opening of new doors results in novel opportunities [9].
5. ACKNOWLEDGEMENTS
The author acknowledges cooperation with COST 291 Towards Digital Optical Networks (TDON) consortium,
COST Action 293 Graphs and Algorithms in Telecommunications, (GRAAL), and with The International
Telecommunication Union – Study Groups 13 and 15. Interactions with The International Electrotechnical
Commission – Technical Committee 86 ‘Fibre Optics’, and The International Union of Radio Science –
Commission D ‘Electronics and Photonics’ are acknowledged. This research has been partially supported by the
State Committee for Scientific Research under COST/51/2006 national grant.
REFERENCES
[1] M. Marciniak, “100 Gb Ethernet over Fibre Networks– Reality and Challenges”, ICTON - 'Mediterranean
Winter' 2007, Conference CD-Proceedings IEEE Catalog Number: CFP0733D-CDR, paper Sa1.3, 6 pages,
Sousse, Tunisia, December 6-8, 2007.
[2] P. Cochrane, “Fiber-to-the-home (FTTH) Costs Are Now In!”, Proceedings of the IEEE, vol. 96 no.2,
pp. 195-197, February 2008.
[3] M. Marciniak, “From circuit- to packet-switched or to hybrid network?”, 5th International Conference on
Transparent Optical Networks ICTON 2003, Workshop on All-Optical Routing, Invited Paper Mo.B2.5,
Conference Proceedings, vol. 1, pp. 47-50, Warsaw, Poland, June 29 - July 3, 2003.
[4] N.S. Rao, W.R. Wing, and J. Verrant, “Research networks revive interest in circuit switching”, Lightwave
www.lightwaveonline.com, pp. 25-27, December 2007.
[5] M. Marciniak, “Reliability for future ubiquitous network societies – challenges and opportunities”,
Proceedings of the 8th International Conference on Transparent Optical Networks ICTON 2006, vol. 3
pp. 130-131, Nottingham, United Kingdom, June 18-22, 2006.
[6] IEEE 802.3 Higher Speed Study Group tutorial: “An Overview: The Next Generation of Ethernet”, IEEE
802 Plenary, Atlanta, GA, November 12, 2007.
[7] S. Muller, A. Bechtolsheim, A. Hendel, “HSSG Speeds and Feeds Reality Check”, January 2007,
http://www.ieee802.org/3/hssg/public/jan07/muller_01_0107.pdf .
[8] J. McDonough, “Moving Standards to 100 GbE and Beyond”, IEEE Applications & Practice, Online
Magazine, VOL. 45 suppl. 3, pp. 6-9, November 2007.
[9] M. Marciniak, “Emerging standards for 100 Gbit Ethernet access and beyond”, in: COST 291 Final Report,
Editor: Ioannis Tomkos, Springer - LNCS series, accepted for publication.
Załącznik 3.4
ICTON-MW'08
Sa2.1
Sub-Wavelength Information Photonics:
Materials, Phenomena, and Functional Devices
Marian Marciniak, Senior Member, IEEE
National Institute of Telecommunications
Department of Transmission and Optical Technologies
1 Szachowa Street, 04-894 Warsaw, Poland
ABSTRACT
The emerging area of sub-wavelength photonics aims at integrating photonics with nanotechnology and
achieving functionalities of a substantial novelty. Nevertheless, our understanding of the interplay between light
and nanostructured matter is still incomplete, and full integration of light with nanoscale devices and processes,
as well as dynamic and all-optical control of such structures, requires fundamental advances.
1. INTRODUCTION
Functional sub-wavelength photonic structures fabricated from various materials with present-day
nanotechnology offer previously unavailable possibilities. Metal/dielectric interfaces between bulk media and in
double- multi-layer structures offer novel, previously unexplored dispersion and light-guiding properties. The
power of light is driving the photonic revolution – and information technologies that were formerly entirely
electronic are increasingly exploiting light to communicate and provide intelligent control functionalities.
Consequently, the new emerging area of sub-wavelength photonics is aimed at integrating photonics with
nanotechnology and developing novel photonic devices and functionalities.
Sub-wavelength photonics opens up both potentially novel devices and new physics associated with small
structure dimensions. It allows for functional devices that are compact, lightweight, portable, low-powered,
wearable, environmentally compatible, remotely controllable – and densely integrated [1].
The physics and technology of sub-wavelength structured optical materials offer novel phenomena and
applications over and above classical integrated optics because of their unique dispersion characteristics, which
include photonic band-gap behaviour and slow propagation of light. The associated strong optical confinement
has already led to much more compact devices and enhanced non-linear effects, implying the possible
replacement of electronic functionality by ultra-fast all-optical operation.
Sub-wavelength structured materials guide light in novel ways, and enable for a construction of devices with
strong light confinement. The examples are photonic wires and photonic crystal channel waveguides, providing
both compactness and enhanced functionality. They allow for miniaturization and the possibility of tailoring the
properties of the material structure/device to obtain novel or enhanced functionalities as a wide tuneability, low
switching power, exotic dispersion properties, as well as sensitivity to environmental conditions what enables for
sensing in sensor networks. Photonics that uses surface plasmon-polaritons (plasmonics) may solve the intrinsic
electronics-photonics size-scale mismatch problem. However, the realisation of efficient coupling to and from
plasmonic device structures, non-linear effects – in particular the trade-off between strong localization and
propagation losses all require study.
Miniaturization and interconnection of photonic devices can be addressed in a variety of media that includes
photonic crystal fibres, light sources, detectors, couplers, connectors, switches, logic devices, amplifiers,
sensors- and integrated photonic sub-systems. In fact, the approaches used range from micro- to nano-scale,
since the mechanisms change substantially, as do the experimental aspects (fabrication and characterization)
along with them. Integration of electronic and photonic devices on the same chip will enable the systems
urgently demanded by the ubiquitous information society – e.g. ultra-fast computers with optical intra-chip
connections and photonic diagnostic instruments for single molecule and early cancer detection.
Several European and worldwide research initiatives are active in different aspects of sub-wavelength
photonics. Those are COST Actions as COST 299 FIDES, COST 288 on Ultrafast Nanophotonics, Networks of
Excellence as PHOREMOST, METAMORPHOSE, NEMO, industrial organisations and networks, International
Standard Bodies, and other parties. An excellent progress in this field of research has been achieved within
COST Action P11: Physics of linear, nonlinear and active photonic crystals (2003-2007) [2]. Based on the
achievements of COST P11, a further research in this field has been recently initiated in the framework of the
starting COST Action MP0702: Towards Functional Sub-Wavelength Photonic Structures [3]. This contribution
reports on the research agenda of COST Action MP0702.
2. RESEARCH DIRECTIONS
The objective of the COST Action MP0702 is to establish active links between European laboratories working in
the field of artificial materials for photonics applications, where the structural dimensions are at or below the
wavelength of light. The goal is to increase knowledge about the basic mechanisms of the interaction of light
with matter on a sub-wavelength scale. The scientific innovation concerns: the basic mechanisms of light-matter
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interaction in micro- and nanostructured materials – including metals (plasmonics), the trade-off between strong
localization and propagation losses, photonic diagnostic instruments, and non-linear effects. The technological
impact of the Action will lead to the implementation of advanced optical equipment and devices with high
performance and low cost.
Plasmonics
The use of surface plasmonic fields will lead to a novel generation of photonic devices that are much more
compact than those available with current optical technologies, as well as it will bridge the gap between the
photonic and electronic technologies.
3D metal/dielectric nanostructures, e.g. metal nanoparticles of different shapes (spheres, rods, stars) capped
with proper organic adsorbates, have a strong potential as biosensors or biomedicine. In this sense, direct laser
ablation methods can provide an interesting approach as far as the purity and biocompatibility of the final
products are concerned. The stability of such systems also deserves careful investigation. Among these
structures, those including capping fluorophores are of great interest for biosensing or bioimaging. However, the
interaction of metals and fluorophores still represents an open problem, resulting in an enhancement or
a quenching of the fluorescent emission, depending on different factors, ranging from the geometry of the system
to the physico-chemical properties of the interacting materials.
Intense subwavelength 'superfocusing' of light
This can be achieved by using noble-metal nanoparticles, which interact strongly with light at the frequency of
a coherent electron oscillation, or localized surface plasmon (SP) in the particle. Existence of "hot spots" on
nanoparticles, where local fields are highly concentrated, makes possible gigantic enhancement of both linear
and nonlinear optical responses of molecules and atoms placed in this spots, and thus shows promise for
realization of efficient lab-on-a-chip sensing platforms and super-resolution imaging devices and also for
modification (e.g. strong enhancement) of spontaneous emission of atoms or quantum dots that are in resonance
with SP modes. However, localized SP resonances on nanoparticles have low Q-factors.
Metamaterials
Negative-index enable new ways of imaging and sensing. In particular, the possibility to reduce the speed of
light is essential for the creation of a compact photonic chip for all-optical signal processing. Flexible and
dynamic manipulation of slow light opens up new possibilities for parallel switching of pulses, all-optical
sensing and monitoring, and optical computing.
Nonreciprocity
Magnetophotonic crystals have recently become the subject of worldwide intense research activities. The
enhancement of the non-reciprocity in MOPhC devices opens up the possibility of a whole new scale of
miniaturized and improved non-reciprocal devices, such as non-reciprocal directional PhC couplers, nonreciprocal Mach-Zehnder PhC interferometers, non-reciprocal circulating PhC cavities etc.
Hybrid sub-wavelength scale materials and components
Dielectric and semiconductor microcavities trap light in compact volumes by mechanisms of total internal
reflection or distributed Bragg reflection, which results in optical modes with extremely high Q-factors. That
enables ultrafast nano-scale optical components as semiconductor microlasers, wavelength-selective filters,
coupled-cavity optical waveguides, etc. High-Q optical cavities may allow for novel functionalities in Dense
Wavelength-Division-Multiplexed fibre communication networks owing to tight field confinement and long
photon lifetimes and the enhancement of cavity refractive index change on spectral characteristics.
For nanophotonic interconnection at high data rates, compact photonic crystal or micro-disc lasers, operating
electrically with close to ideal quantum efficiency and 100 µW cw output power levels, will be required. Use of
high index semiconductor substrates is unavoidable and must be built into the device design. Hybrid integration
techniques are also likely to be required here – and also for non-reciprocal or non-linear functionality.
Hybrid photonic-plasmonic structures for light focusing, near-field enhancement and biosensing
Optical microcavities have demonstrated potential in the development of inexpensive, ultra-compact, highly
sensitive and robust biochemical sensors for both mass and fluorescence sensing. Such sensors may detect
resonant frequency shifts caused by the changes in their environment through the interaction of the evanescent
field of the ‘whispering gallery’ mode (WG mode) outside the microcavity with analyte or with nanoparticles
and macromolecules. High value of the Q-factor of the WG modes used for detection is crucial for efficient and
robust detection, as the resonance linewidth and the fluorescence enhancement effect are directly related to this
value. However, only the evanescent portion of the WG-mode field extends to the outer medium, whereas high
intensity of local electromagnetic field is essential for many important applications in biotechnology and
biosensing. High field intensity translates into extraordinary amplification of the Raman scattering and increased
sensitivity of fluorescent detection.
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As one of possible applications of hybrid photonic-plasmonic structures, clusters of SP nanoparticles as opticalmicrocavity-coupled end-structures for focusing optical energy to sub-wavelength spots will be investigated.
Such end-structures can potentially find use for focusing and channelling optical energy to nanoscale detectors
such as single atoms, molecules or quantum dots. This research direction may result in novel classes of photonic
devices as well as biosensing for both mass and fluorescence detection.
Nonlinear dynamics of photonic systems
Most of the current applications of active photonic systems, in particular of light sources, rely on our
understanding of how the output of such systems evolves in time and how these rich dynamical behaviours can
in turn be made useful. Mode locked sharp intensity pulses, all-optical generation of fast intensity dynamics
beyond the GHz, mode switching dynamics, are examples of current activities in this field that have significant
impact in terms of industrial applications. Interesting innovative light sources in the context of nonlinear
dynamics and control of laser properties include the lasers based on quantum dot active regions, microcavities
and photonic crystal lasers. That research enable for the development of novel concepts for light sources and
ultrafast and ultrashort light pulses.
Nonlinear light propagation phenomena
There has been a strong interest recently towards the theoretical and experimental study of light localization,
spatial solitons, soliton interactions, pattern formation, filamentation and subdiffractive propagation, and
nonlinear parametric processes in extended photonic structures. Examples include cavity nonlinear optics and the
works related to dissipative solitons and localized structures, photonic crystal waveguides and bandgap solitons,
the inclusion of photonic crystals and metamaterials into optical cavities for the control of the diffraction and the
modulational instabilities leading to patterns, photonic lattices and their use for pattern control and parametric
photon generation enhancement. The easily reconfigurable waveguides with controllable properties in photonic
systems are of a great interest for optical interconnections and optical routing applications.
Photonic-crystal fibres
With an appropriate design of the fibre cross section, single-mode waveguiding can be provided even in largemode-area PCFs. Large-mode-area PCF components allow for high-power fibre lasers, amplification of a shortpulse fibre laser output, compression of submegawatt, subpicosecond laser pulses, as well as for supercontinuum
generation for high-energy laser pulses. An accurate design of a PCF dispersion profile for precise dispersion
compensation through fibre structure engineering is the key to optimizing the performance of fibre laser sources
of ultrashort light pulses. There are potential application areas in such fields as laser spectroscopy, optical
diagnostics, frequency conversion of ultrashort low-energy light pulses, optical data transmission and processing,
biomedical applications, gas- and condensed-phase sensing including biosensing.
Slow-light structures and devices
Periodic refractive index modulation introduces unique features in the dispersion dependencies, such as the
appearance of distinct spectral bands and gaps. The light is slowed down at the band edges, and becomes
localized inside the gaps, allowing for new ways to manage the flow of light. The goal is, in particular, to
investigate and design photonic structures that change the behaviour of light waves, opening novel possibilities
for control of slow light. A specific goal is, by profiting from nonlinear optical effects, to exceed the
performance offered by other, essentially linear geometries with the aim of generating delays many times the
length of the optical pulse.
The slow-light regime is associated with the appearance of critical points in the dispersion dependencies and
accordingly strong chromatic aberrations. To overcome this restriction, we will design structures for realization
of the required velocity reduction, but operating sufficiently far from the critical resonance to achieve full control
over the wave dispersion. For example, chromatic aberration can be suppressed in a waveguide array with phaseshifted gratings, whereas we find that in the previously considered geometries the aberrations are very strong.
3. CHALLENGES AND FUTURE RESEARCH
Our understanding of the interplay between light and nanostructures is far from being complete. Full integration
of light with nanoscale devices and processes, as well as dynamic and all-optical control of such structures, will
require fundamental advances in this research area.
Integration of electronic and photonic devices on the same chip will enable the systems urgently demanded
by the ubiquitous information society – e.g. ultrafast computers with optical intrachip connections – and
photonic diagnostic instruments for single molecule and early cancer detection. Photonics that uses surface
plasmon-polaritons (plasmonics) may solve the intrinsic electronics-photonics size-scale mismatch problem –
and new self-organized electromagnetic materials may bring low cost solutions for industrial applications.
Achievement of efficient coupling to and from plasmonic device structures, nonlinear effects – and the trade-off
between strong localization and propagation losses all require study.
3
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Although it is clear that some of the major problems related to novel artificial materials are still technological in
nature, the physics of photonic structures at sub wavelength is still an open problem. The aim is to shed light on
several fundamental questions that remain open presently regarding the physics of the optical interaction caused
by the dimensions of the structures being studied, and by the combination of different materials (hybrid
structures) that modify critical properties such as the spatio-temporal response, the nonlinear response and other
effects. The Action research agenda will therefore be at the forefront of modern optics, and it aims to combine
the fundamental concepts of nonlinear photonics and plasmonics with nanotechnology, thereby developing novel
photonic devices for manipulating light on the nano-scale, including sensing and imaging – and processing of
information with unparalleled operating speeds. The main topics for further study are:
•
•
•
•
•
•
•
physics of nanostructured materials, taking into account different methods of realizing structured materials
and their characterization,
artificial optical materials, including metals and hybrid materials for the manipulation and detection of light,
including biosensing and superresolution behaviour,
nonlinear optical interactions in artificial materials, taking into account both quadratic and cubic nonlinear
effects, the spatio-temporal response and saturation effects, and nonlinear dynamics,
pulse propagation, taking account of cubic nonlinear effects, and spatio-temporal effects in nanophotonic
structures, including photonic crystal fibres,
quantum aspects of propagation – and the interaction of optical fields in artificial materials for the
generation of non-classical optical states and light sources,
new methods of diagnosis at the nano-scale to be applied in various areas,
innovative concepts of nonlinear nanoscale photonics for applications in all-optical communication and
information technologies.
ACKNOWLEDGMENT
The author acknowledges very profitable and enjoyable interactions with COST (European Co-operation in the
field of Scientific and Technical Research) Action MP0702 Towards Functional Sub-Wavelength Photonic
Structures community. Special thanks go to Concita Sibilia, Trevor Benson, Richard De La Rue, and Bouchta
Sahraoui – all partners in COST MP0702.
REFERENCES
[1] Y. Fainman, Ultrafast optics and nanophotonics in information systems, in International Topical Meeting
on Information Photonics 2008, Technical Digest, pp. 118-119, Nov. 16-20, 2008, Awaji Yumebutai,
Hyogo, Japan
[2] C. Sibilia, T. M Benson, M. Marciniak, T. Szoplik (Eds.), Photonic crystals: physics and technology,
Springer, Optics & Lasers series, 2009.
[3] COST Action MP0702: Towards Functional Sub-Wavelength Photonic Structures (2008-2012),
Memorandum of Understanding – Technical Annex, http://cost-mp0702.nit.eu/cost-mp0702 .
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Matrix Infrared-Visible Image Converter Based on Waveguide
Microring Resonators
Igor Goncharenko1, Alexander Esman2, Vladimir Kuleshov2, Marian Marciniak3
1
Institute for Command Engineers of the Ministry of Emergencies, Minsk, Belarus
2
Institute of Physics, National Academy of Sciences, Minsk, Belarus
3
National Institute of Telecommunications, Warsaw, Poland
Tel: (375 17) 341 7411, e-mail: [email protected]
ABSTRACT
We propose a novel concept of image converter from an infrared range into a visible range of electromagnetic
waves by the use of waveguide resonator structures of a micron size as a sensitive element. The method is based
on the modulation of the resonator proper equidistant spectrum under the influence of the external
electromagnetic radiation of the infrared spectral range, which changes the optical properties of the sensitive
element material. The structure and principles of operation of the matrix converter of infrared images into visible
ones on the base of a matrix of the waveguide microring resonators are investigated. It is shown that sensitivity
of such converter to the variation of infrared radiation power can be as low as 2.6·10−12 W.
Keywords: infrared converter, waveguide microring resonator, infrared radiation, thermal image, resonance
wavelength, heat transfer.
1. INTRODUCTION
Thermal imaging translates a long-wavelength infrared energy produced in the 8- to 14-µm waveband into
digital data that can be used to produce a visible image or be fed into a computer for interpretation. However an
excess cost, unsatisfactory weight and size parameters, insufficient reliability of infrared sensors constrain from
the wide practical use of thermal imaging devices. At present, two forms (cooled and uncooled) and five types
(on the base of indium-stibium composites, cadmium-mercury-tellurium composites, Schottky barrier,
microbolometers, quantum well structures) of IR photodetector devices are commercially available.
In the last years the investigations on development of matrix IR receivers of a new type (uncooled bolometric
and pyroelectric and thermoelectric) have been extensively carried out [1,2]. Uncooled receivers are the most
preferable from the point of view of cost and weight and size parameters due to the absence of cooling systems
and optomechanical scanning. At that point uncooled bolometer matrices are challenging. However a number of
unsettled by now problems connected with high contact noise, low temperature coefficient of resistance, etc. do
not allow to reach the required sensitivity of IR devices that restrains their application for solution of a wide
range both military and civil tasks.
The most common form of thermal imaging technology available today is the microbolometer sensor [3].
Although microbolometers have greatly reduced the price of thermal imaging (compare with older “cooled”
technology), microbolometer-based cameras still range from $8 000 to $20 000, depending on resolution,
performance and features. In addition, their manufacturing requires a highly complex multimask step design,
which makes them expensive to produce. Microbolometers also are limited in their power consumption, needing
~2 W for normal operations and even higher for large array size. The image quality is somewhat limited, too.
Recently, the methods of converting the information transferred by IR range wave into the visible range
wave followed by detecting and processing by conventional means have been intensively investigated. The
optical IR-radiation reading technologies rely on temperature-dependent changes in optical properties. Such
changes are optically read out using standard digital camera electronics. This conversion can be produced by the
use of passive optical Fabry-Perot resonators [3] or semiconductor laser resonators [4]. However such resonators
don’t possess the waveguiding properties and an optical radiation propagating through them partially leaks
resulting in additional losses. The use of semiconductor laser resonators for converting the IR-images into
visible ones can be accomplished by deteriorating the threshold characteristics defined by laser pump power and
noisiness.
In the present paper we propose to use matrix of waveguide resonators for IR-to-visible image conversion.
2. PRINCIPLE OF OPERATION AND OPTIMIZING THE PARAMETERS OF MATRIX IR
CONVERTER
Single matrix element constitutes a closed optical waveguide with the bending radius of the order of tens of
microns (see Fig.1). The waveguide is disposed on a dielectric substrate. In order to obtain the total internal
reflection condition the buffer layer with reflective index lower than the waveguide index is positioned between
the waveguide and substrate. On the top of the waveguide the film from a high thermal radiation absorbing
material is deposited. It could be, for instance, platinum or golden sponge usually used in bolometers [5]. Under
978-1-4244-2625-6/08/$25.00 ©2008 IEEE
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the buffer layer the reflecting film may be disposed for concentrating the IR radiation on the waveguide and
preventing an undesirable substrate heating. Straight optical waveguides coupled with the ring resonator
waveguide are used for input and output of optical signals. Input signal on the wavelength coinciding with one
of the resonance wavelengths of the resonator couples into the ring waveguide. Signals on the wavelengths
different from the resonance wavelength do not couple to the ring and travel straight through on input
waveguide. The signal coupled into the ring waveguide passes from it to the output waveguide. Any variation of
the resonator optical length Ln, where L is the geometric resonator length, n is waveguide material index, leads
to shifting its resonance wavelength. As a result the intensity of the output signal on the carrier wavelength
coinciding with the resonance wavelength of the unperturbed resonator changes.
Figure 1. Structural diagram of the single element of the matrix converter of IR images into visible images.
The material of waveguide microring resonator designed for measuring temperature changes has to be both
transparent to a given radiation spectral range and possessing negligible thermoemission. Increasing the free
carrier density under the influence of the temperature (thermal electron emission) reduces the material refractive
index [6]. Therefore, the thermal electron emission and thermal expansion exert opposite influence on resonator
optical length that reduces the sensitivity of IR-conversion. The most suitable material for near infrared
wavelength region mostly used in optical communication and information processing is fused or crystalline
silica. In that case the microresonator ring waveguide and input and output waveguides can be manufactured
using well-established technology of doping impurity diffusion into the silica substrate.
The intensity of the signal E12 passing through the resonator in a steady-state condition to the output
waveguide is defined by [7,8]:
(E1
(
)(
)
(
)(
)
E0 )2 = k12 k 22 ⎡1 − 2 1 − k12 1 − k 22 (1 − α )cos φ + 1 − k12 1 − k 22 (1 − α )2 ⎤ ,
⎢⎣
⎥⎦
(1)
where E02 is the intensity of the signal at a wavelength λ entering through the input waveguide, k1,2 are coupling
coefficients between microresonator and input and output waveguides, respectively, α is the resonator round-trip
loss coefficient,
φ = 2π L n/λ
(2)
is the resonator round-trip phase. Temperature variation changes the resonator radius as a result of thermal
broadening:
dR = αТ R dT,
(3)
where αТ is the linear coefficient of thermal expansion. At the same time, the refractive index of the resonator
waveguide also changes due to both the material thermal expansion and temperature variation of energy gap of
the electronics absorption peak [9,10]:
(4)
2n(dn/dT) = K 2[−3αТ S − (2/Eg)(dEg /dT) S 2] = GS + HS 2,
where n and dn/dT are the room temperature refractive index and its variation with temperature, K 2 = n 2 – 1;
S = λ2 λ2 − λ2g is a normalized wavelength, Eg is the energy gap with central wavelength λg. Constants G and
(
)
H related respectively to the thermal expansion coefficient (αТ) and temperature coefficient of the energy gap
(dEg /dT) are experimentally determined for a variety of glasses [9].
The optical signal at a wavelength λ correlated with the one of resonance wavelengths of the resonator is
supplied at the input. This radiation couples into microresonator and comes through it to the output waveguide.
Therefore, in the absence of temperature variation the output optical signal has maximum intensity. Temperature
variation changes the resonator optical length what implies shifting its resonance wavelengths. Now the signal
wavelength doesn’t correlate with resonance wavelength and output signal intensity decreases proportionally to
the temperature change.
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Thus the IR radiation modulates the radiation of a visible spectrum range, i.e. optical resonator transfers the
information transmitted by IR radiation into the visible wave. The set (matrix) of such resonators converts the IR
images entirely into the visible images.
Fig. 2 shows the calculated output signal intensity at wavelength 1.563216 µm as a function of temperature
variation for resonators with radii 64, 256 and 512 µm and coupling coefficients 0.5 (Fig. 2a) and 0.75 (Fig. 2b).
For silica glasses the coefficients used in equation (4) are G = –1.6548, H = 31.7794 [9]. As one can see, the
output signal intensity for the resonators of smaller size and larger coupling coefficient varies smoothly with the
temperature change. In contrary, the intensity of the signal at the output of the resonators with larger radius and
smaller coupling coefficient sharply varies with the temperature change. Therefore, such resonators are
preferable for the registration of minor temperature variation with high accuracy.
Figure 2. Dependence of output signal intensity on temperature change for the resonators with coupling
coefficients 0.5 (a) and 0.75 (b). Solid, dashed and dash-dot curves show the output signals of the resonators
with radii 64, 256 and 512 µm respectively.
It should be noted that we carried out the calculations for wavelength 1.563216 µm, which belongs to near
IR spectral range rather than to visible one. For effective coupling the resonator waveguide and input/output
waveguides have to operate in a single-mode regime. The size of single-mode waveguides for visible spectral
range is very small and technologically inconvenient. The use of a wavelength around 1,56 µm allows
increasing the waveguide size. On the other hand, photodetectors for that wavelength region are well-developed.
Thus the conversion of information of far and middle infrared into that wavelength entirely corresponds to the
object of the research.
The set of microresonators of different size can be used to increase the temperature measurement region without
loss of accuracy. In that case the microresonator with smaller radius is applied for reading tens of degrees (solid
curves in Fig.2) and resonators with larger radius read units and fractions of degree (dashed and dash-dot curves).
Figure 3. Temperature dependence of the intensity of output signals on different wavelength for resonator with
radius 64 µm and coupling coefficient 0.5. Curve 1 presents the signal at 1.5632 µm wavelength, curves 2-6
show the signals at wavelengths that differ by 0.6 µm from each other.
The extension of the temperature measurement region can also be obtained with one microresonator by using
input optical signals on several wavelengths. The difference between wavelengths has to be chosen so that
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output signal on the following wavelength reaches maximal value when the signal on previous wavelength
decreases to a definite level. By analogy with communications systems the level of 10% of the maximal one can
be used. Fig. 3 shows the change of the intensity of output signals on different wavelengths with temperature
variation for resonators with radius 64 µm and coupling coefficient 0.5. The difference between wavelengths is
of about 0.6 nm. The solid lines show the parts of the curves for different wavelengths used for temperature
measurement. As one can see, the temperature variation up to approximately 50 degrees is measured according
to the change of the signal intensity at the first wavelength. The change of the signal intensity at the second
wavelength represents the temperature variation on the next 50 degrees and so on. The region of temperature
measurement is defined by the number of the used wavelengths and the heat resistance of the resonator material.
Spatial separation of the signals at different wavelengths can also be produced by optical filters based on the
similar ring resonators [11-13]. Each filter is tuned at a defined wavelength.
The dynamic range of modern photodetectors for visible light is up to 50 dB without amplifier and
30 ÷ 40 dB with using an amplifier. In actual operating conditions the IR converter operates at the temperature
from −40 to +40 °C, i.e. the temperature variation range is 80 ÷ 100 °C. Such temperature range can be
measured by IR converter on the base of microring resonator with bending radius 64 µm and coupling
coefficient 0.5 (see Fig. 2a). Thus the sensitivity of this IR converter is of the order of 0.01 °C when using the
photodetector with amplifier. The region of temperature measurement of the IR converter with microresonator
radius 512 µm is approximately 10 °C and its sensibility can reach 0.001 °C. However, the sensor element of
such converter must be temperature-controlled.
Detectability of the proposed converter can be estimated by limiting value of the IR radiation power resulting in
temperature changes of the sensor element that can be registered. Presence of the object with the temperature
exceeding the background temperature on ∆T causes the increasing IR radiation power Φ, which falls on receiving
area S of a single element of the matrix converter, on the value [4]:
∆Φ = (S/4)(d/f) 2(∆M/∆T)Φ ∆T,
(5)
where (∆M/∆T)Φ is temperature gradient, d/f is input lens aperture defined as the ratio of entrance aperture d to focal
length f. The absorbed part of this power increased the temperature of the microresonator sensor element by
∆Тr = ε ∆Φ /G,
where G = kSr is heat-transfer between the resonator and substrate, k is the heat transfer coefficient, Sr is the area of
contact of the resonator and substrate, ε is IR radiation absorption coefficient. The absorption coefficient can reach
90% when using the absorbing films from platinum or golden sponge [5]. The silica heat transmission coefficient
equals to 5.7 W m–2 K–1 [15]. For microresonator with radius 64 µm and waveguide width 1 µm the heat-transfer of
the contact microresonator/substrate is equal to G ≈ 2.3·10−9 W K–1. Therefore, the minimal power of IR radiation
changing the microresonator temperature ∆Тr to 0.01 °C is ∆Φ = 2.6·10−11 W.
For spectral region 8 ÷ 12 µm the temperature gradient (∆M/∆T)Φ equals 2.0 W m–2 K–1 at the background
temperature 300 K. Then in accordance with expression (5) for lens aperture d/f = 1 the minimal change of the
radiating object temperature, which can be registered by sensor element, is ∆T = 0.004 °C. Such small value of the
estimated registered temperature change can be explained by the fact that IR radiation is received by the absorbing
film covering the whole area occupied by the resonator, i.e. the receiving area equals S = πR 2, where R is the
resonator radius. Taking into consideration the possible heat loss at the transferring from the absorbing coating to
resonator the minimal temperature change of the radiating object, which is possible to register by sensor element,
can be accepted equal ∆T = 0.01 °C.
Speed of the converter response is defined by the time of steady output signal establishing in the resonator
and the response time of the sensor element to the change of IR signal. The calculation shows that the time of
steady-state establishing in the microresonators with radii 8 ÷ 128 µm is of the order of tens of picoseconds [14].
The time constant of the converter sensor element is τ = C/G, where С is the microresonator heating capacity.
The heating capacity of silica microresonator with bending radius 64 µm, waveguide width and thickness 1 µm
and 0.5 µm respectively is equal to Cr ≈ 0.36·10−9 J K–1. The heating capacity of the unit area of absorbing
coating (golden sponge with absorption coefficient 90%) equals 2·10−6 cal cm–2 K–1 [16]. The heating capacity
of the film with the area S equals Cf ≈ 1.08·10−9 J K–1. Thus the total heating capacity is C ≈ 1.44·10−9 J K–1, and
time constant defined the time of the photodetector response on the change of IR signal power is equal to
τ = 0.626 s.
3. CONCLUSIONS
We propose using the ring waveguide microresonators for conversion of IR images into images of visible range.
Such converters can be manufactured by well-proven technology in integrated form. The accuracy of
temperature change measurement (sensibility of the converter) is set by the selection of resonator optical length
and coupling coefficient between ring waveguide and input/output waveguides. For registration of small
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temperature differences one can use resonators with large size and small coupling coefficients. However, in that
case the temperature measurement range is limited to tens of degrees. In order to measure wider temperature
changes it is necessary to use microresonators with smaller radii and larger coupling coefficients. However, the
resolution of such converter is reduced. The temperature variation in wide region and with high resolution can
be measured by using several microresonators with different radii or supplying optical signal at several
wavelengths into one resonator with small size. Furthermore, the accuracy and temperature measurement region
depend substantially on the material of waveguide microresonator.
Expected parameters of the proposed IR converter are
• measurement range 100 °C;
• temperature sensitivity 0.01 °C;
• power sensitivity 2.6·10−11 W.
When using radiation on 6 wavelengths
• measurement range 60 °C (600 °C);
• temperature sensitivity 0.001°C (0.01 °C);
• power sensitivity 2.6·10−12 (2.6·10−11) W.
Response time of the converter on the change of IR signal power is 0.626 s. Enhancing the heat-transfer
between the resonator and substrate, for instance, due to increasing contact area can reduce the converter response
time. However, that also decreases the sensibility of the converter.
The aim of the paper is describing the new method of conversion of the IR signals into visible radiation.
Therefore, here we present only approximate evaluation of the limiting values of the threshold sensitivity and
response time of the IR converter. So, for instance, we calculated the heat-transfer in simplified version without
taking the convective and radiative components of the heat-exchange into account. Accurate estimates of the
threshold values of these parameters taking into account the analysis of noise components of the converter element
will be stated in separate paper. This also concerns the selection of the most suitable material for microresonator.
REFERENCES
[1] V.G. Malyarov, I.A. Chrebtov, Yu.V. Kulikov, et al.: Comparative studies of the bolometric properties of
the thin film structures based on vanadium dioxide and amorphous hydrogenate silica, Applied Physics.
1999, no .2, pp. 2-13.
[2] S.Ya. Andryushin, N.V. Kravchenko, A.V. Kulymanov, et al.: State of development of microbolometric
matrices in State Research Center of Russian Federation «Scientific Production Association «Orion»»,
Applied Physics, 2000, no. 5, pp. 5-17.
[3] D. Ostrower: Novel technology could increase thermal imaging use, Photonics Spectra, 2006, no. 10,
pp. 66-70.
[4] N.I. Lipatov, A.S. Biryukov: Matrix laser IR-visible image converter, Quantum Electronics, 2006, vol. 36,
no. 4, pp. 389-391.
[5] V.N. Sintsov. Absorbing coatings for thermal image converters, in Proc. 1st USSR Symposium on Thermal
Radiation Detectors. 21-25 October 1966. Kiev: Navukova Dumka, 1967, pp.164-170.
[6] L.N. Dobretsov, M.V. Gomoyunova: Emission electronics. Moscow: Nauka, 1996. 546 p.
[7] T.A. Ibrahim, V. Van, P.-T. Ho: All-optical time-division demultiplexing and spatial pulse routing with
GaAs/AlGaAs microring resonator, Optics Letters, 2002, vol. 27, pp. 803-805.
[8] T.A. Ibrahim, W. Cao, Y. Kim: Lightwave switching in semiconductor microring devices by free carrier
injection, J. Lightwave Technol., 2003, vol. 21, pp. 2997-3002.
[9] H.J. Hoffmann, W.W. Jochs, G. Westenberger: Dispersion formula for the thermo-optic coefficient of
optical glasses, Proceedings SPIE, 1990, vol. 1327, pp. 219-228.
[10] G. Ghosh: Temperature dispersion of refractive indexes in some silicate fiber glasses, IEEE Photon.
Technol. Lett., 1994, vol.6, no. 2, pp. 431-433.
[11] B.E. Little, J.S. Foresi, G. Steinmeyer, et al.: Ultra-compact Si–SiO microring resonator optical channel
dropping filters, IEEE Photon. Technol. Lett., 1998, vol. 10, pp. 549-551.
[12] A. Melloni: Synthesis of a parallel-coupled ring-resonator filter, Opt. Lett., 2001, vol.26, pp.917-919.
[13] S.J. Choi, K. Djordjev, Z. Peng, et al.: Microring resonators vertically coupled to buried heterostructure
bus waveguide, IEEE Photon. Technol. Lett., 2004, vol.16, pp. 2266-2268.
[14] I.A. Goncharenko, A.K. Esman, V.K. Kuleshov, V.A. Pilipovich: Optical broadband analog-digital
conversion on the base of microring resonator, Optics Communications, 2006, vol.257, no.1, pp. 54-61.
[15] V.K. Leko, O.V. Mazurin: Properties of silica glasses. Leningrad: Nauka, 1985, p.165.
[16] V.S. Lysenko, A.F. Mal’nev: Obtaining and properties of absorbing coatings, in Proc. 1st USSR
Symposium on Thermal Radiation Detectors. 21-25 October 1966. Kiev: Navukova Dumka, 1967,
pp. 146-163.
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An Optical Model of a Transmission-Type Vertical-Cavity
Electro-Absorption Modulator on Si/SiO2 for High-Speed
Intra/Inter-Chip Interconnects
Hovik V. Baghdasaryan, Tamara M. Knyazyan, Ara S. Berberyan, Tamara T. Hovhannisyan
and Marian Marciniak*
Fiber Optics Communication Laboratory, State Engineering University of Armenia
105, Terian str., Yerevan 0009, Armenia
Phone: (+37410) 524 934, Fax: (+37410) 545 843, e-mail: [email protected]
* National Institute of Telecommunications, Department of Transmission and
Optical Technologies, 1 Szachowa Street, 04-894 Warsaw, Poland
ABSTRACT
An optical model of a transmission-type vertical-cavity electro-absorption modulator (EA) on Si/SiO2 for highspeed intra/inter-chip interconnects is developed and analysed by the method of single expression (MSE). As an
external radiation source a wideband light source is suggested for avoiding the problem of usage of Si emitter.
Transmission properties of symmetrical structure of a modulator consisting of Si p-n junction embedded between
Si/SiO2 DBRs are analysed versus the values of imaginary part of p-n junction permittivity. Corresponding
distributions of electric field amplitude and power flow density along the structure and surrounding half-spaces
are presented for high and low transmission state. The transparency of the structure permits to have a cascade of
modulators which can be installed in special trunks on chips for connection between different layers of an
integrated circuit.
Keywords: electro-absorption modulator, optical model, method of single expression, numerical modelling,
intra/inter-chip interconnect.
1. INTRODUCTION
Requirements of today’s fiber-optic networks and interconnects in providing high data rates and large capacity at
low cost require both the invention of new technologies, and the development of compact and efficient devices
as well [1, 2]. Electro-absorption (EA) modulators are one of the promising key components of contemporary
optical networks and optical interconnects due to their high-speed operation ability [1, 3-5].
An electro-absorption modulator is a semiconductor device permitting modulation of laser beam intensity via
an electric voltage applied to corresponding electrodes. Its operation principle is based on a change of the
absorption spectrum caused by an applied electric field via change of the bandgap energy. To enhance the
modulation efficiency and achieve a high extinction ratio of contemporary electro-absorption modulators
multiple-quantum-well (MQW) structures are used, where quantum-confined Stark effect takes place [6, 7]. The
advantages of EA modulators over other types of modulators are improved modulation efficiency, high
extinction ratio, high operation speed, low driving voltage, zero biasing voltage, wide bandwidth, small size and
the possibility of monolithic integration with other semiconductor components. All these advantages make EA
modulator as a very useful device for high-speed free-space and fiber-optics communication.
EA modulators are traditionally fabricated using GaAs, AlGaAs, InGaAsP or LiNbO3 material base, however
Si-based EA modulators have been recently considered as solutions to the problem of chip-to-chip and on-chip
interconnects [7-9]. They offer significant benefits over traditional EA modulators, such as lower cost, ease of
fabrication, higher integration of components used in optical networks and high-speed chip-to-chip interconnects
for systems using Si-based circuits.
EA modulators can be realized as edge-operating and vertical-cavity devices as well. Vertical-cavity devices
are preferable over edge-operating ones and are better candidates for mass production; it is possible to fabricate
chips with high degree of integration and to test non-packaged devices [3, 10]. All this keeps the costs of them
down. Moreover, vertical-cavity EA modulators can be integrated efficiently with corresponding radiation
sources, which are vertical-cavity surface-emitting lasers (VCSELs) and resonant-cavity light-emitting diodes
(RCLEDs). Integration of VCSELs or RCLEDs with vertical-cavity EA modulators permits to couple efficiently
modulated radiation into an optical fiber and interconnect structure.
Vertical-cavity EA modulators can be designed as non-resonant and resonant structures as well. Embedding
an absorbing medium into a resonator increases an extinction ratio and modulation efficiency of the modulator
[4, 5]. Mirrors of resonator can be made of either metallic layers and distributed Bragg reflectors (DBRs) as well.
Thus, contemporary EA modulators are wavelength-scale multilayer optical structures. It is evident that small
fluctuations of constituting layers thicknesses will bring to impermissible change of modulator’s characteristics.
Consequently, in order to have a reliable and good operating device a correct computer modelling of its optical
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
This work was supported by the Swiss National Science Foundation JRP IB7320-111057/1, Armenian National Educational
Fund grant EN-elec-1150 and partly by the Armenian State Budget project No. 230.
978-1-4244-2625-6/08/$25.00 ©2008 IEEE
Załącznik 3.6
ICTON 2008
175
We.C2.6
characteristics is a necessary step before costly fabrication process. It will permit to reveal optimal
configurations of EA modulators for high-speed applications. Existing vertical-cavity EA modulators are
reflective-type structures, i.e. they are developed as asymmetric resonant structures. However some needs of
interconnects applications may require development of transmission-type modulators.
The present work is devoted to the analysis of an optical model of transmission-type vertical-cavity electroabsorption modulator on Si/SiO2 by the method of single expression (MSE). The MSE has been actively used in
simulation of different 1D multilayer and modulated media [11-14]. Brief concept of the MSE is described
below along with the numerical results.
2. MAIN PRINCIPLES OF THE METHOD OF SINGLE EXPRESSION
The essence of the MSE is the presentation of the general solution of Helmholtz’s equation for electric field
component Ex ( z ) in the special form of a single expression:
Ex ( z ) = U ( z ) ⋅ exp(−iS ( z )) ,
(1)
where U(z) and S(z) are the real quantities describing the resulting electric field amplitude and phase,
respectively. Time dependence exp ( iω t ) is assumed but suppressed throughout the analysis.
The expression (1) is a steady-state solution of Helmholtz’s equation, which is the settled down result of
wave interaction with a medium. No separation on counter-propagating waves is implied in the MSE, which
gives advantages for investigation of any non-uniform linear and intensity dependent nonlinear media with the
same ease and exactness. In the MSE there is not any necessity in preliminary knowledge of the form of
Helmholtz’s equation solution in traditional form, i.e. the form of traveling, counter-propagating, exponentially
increasing or decreasing waves, or others caused by nonlinearity.
The backbone of the MSE is the following:
• presentation of Helmholtz’s equation solution in the form of a single expression (1);
• reformulation of Helmholtz’s equation in the terms of the variables U(z) and S(z) by taking into account
complex permittivity of medium;
• matching of the boundary conditions of electrodynamics in the terms of the variables U(z) and S(z);
• backward numerical calculation algorithm (initial value problem solution).
The backward direction of boundary problem solution used in the MSE provides the uniqueness through a
single process of integration of Helmholtz’s equation without any iterations while the problem solution from the
illuminated side of the structure unavoidably needs iterations [15].
3. NUMERICAL ANALYSIS OF TRANSMISSION-TYPE EA MODULATOR
In the present paper an optical model of a planar micro-resonant EA modulator with external source of optical
radiation at λ0=850 nm is analysed. Usage of a wideband external source of optical wave will not bring to the
necessity of frequency tuning of a modulator, which is very important for its practical realisation. The model of
Si/SiO2 based EA modulator consisting of p-n hetero-junction surrounded by distributed Bragg reflectors
(DBRs) is suggested (Fig.1).
DBR (Si/SiO2)
Einc
p-n junction
Si
p-layer
Eref
0
DBR (Si/SiO2)
Si
p-layer
Etrans
L
Z
Figure 1. Structure of a micro-resonant modulator with Si p-n junction imbedded within Si/SiO2 DBR mirrors.
In such micro-resonant structure it is possible to get high localisation of optical wave amplitude in active
region of p-n junction. For that it is necessary to have highly reflecting DBRs and p- and n-layers of specific
thickness at fixed thickness of p-n junction. At equal numbers of alternating quarter-wavelength layers of DBRs
the greatest reflectance is provided by the DBR structure starting and ending by a layer of high permittivity
ε = εH [16]. Due to high contrast of permittivities of quarter-wavelength layers of Si ( ε Si′ = 13.4 , ε Si′′ = −0.037 )
′ 2 = 2.38 ) at the wavelength 850 nm [17] the high enough reflectance (R = 0.9878) can be reached
and SiO2 ( ε SiO
by only 2 bilayers plus one layer. The symmetrical structure of p-n junction surrounded by these DBRs is
Załącznik 3.6
We.C2.6
176
ICTON 2008
analysed. The analysis has been carried out for different thicknesses of active layer Lp-n and gain of active layer
ε ′′p − n at different thicknesses of p- and n-layers (Lp and Ln). The typical dependence of the structure
transmittance on the thickness Lp = Ln of p- and n-layers is presented in Fig. 2.
T
1
Figure 2. Transmittance T of EA modulator structure on
normalised thickness of p- and n-layers. L p / λ p = Ln / λn ,
0.8
0.6
λ p = λn = λ0 / ε p , ε p = εn = 13.6 − i0.037 at λ0=850 nm.
0.4
L p − n / λ p − n = 0.8 , λ p − n = λ0 /
0.2
0
Ln/λn
0
0.1
0.2
0.3
ε p − n , ε p − n = 13.8 + i0.0305 .
DBRs are 2 Si/SiO2 bilayers plus one layer.
0.4
There are two sharp peaks of transmittance at Ln/λn=0.099 and Ln/λn=0.351 at the same gain in the p-n
junction equal to ε ′′p − n = 0.0305 . Let’s take as an operating model of EA modulator the structure with
Ln/λn=0.099 where gain in p-n junction is enough to compensate for losses in the structure (T ≈ 1). By changing
the bias on p-n junction it is possible to smoothly decrease transmittance through the whole structure (Fig. 3).
Positive and negative values of ε ′′p − n correspond to forward and reverse bias, respectively. At a positive value of
ε ′′p − n amplification of optical wave takes place while negative value corresponds to absorption of light [18].
T1
0.8
Figure 3. Transmittance T of EA modulator
structure with Ln/λn=0.099 on imaginary part
of permittivity of p-n junction ε ′′p − n .
0.6
0.2
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
′ n
ε ′p−
0
0.05
The operation of EA modulator will be characterised by applying forward and reverse bias to p- and n- layers.
To understand the influence of forward and reverse biases on transmission properties of the modulator it is
necessary to analyse the behaviour of electric field component and power flow density of optical wave within the
modulator structure and surrounding half-spaces. The corresponding distributions of electric field amplitude and
power flow density along the structure and in surrounding half-spaces are presented in Fig. 4a, 4b for forward
and reverse bias, correspondingly.
R=0.1079
T=0.9994
14
ε ′p−n
ε ′p
′
ε Si
14
Ê
12
10
6
4
2
0
-4
-2
0
2
4
6
8
ε n′
′
P
12
10
P
8
ε ′p−n
R=0.6414
T=0.0387
Ê
8
′ 2
ε SiO
6
k0z
2
10
4
0
-4
k0z
-2
0
2
4
6
8
10
(a)
(b)
Figure 4. Permittivity profile ε ′ , distributions of electric field amplitude Ê = U and resulting power flow
density P within and outside of the structure. The thicknesses of DBR layers LSi = 58.1 nm , LSiO2 = 137.7 nm .
The thickness of p-n junction L p − n = 183 nm ( L p − n / λ p − n = 0.8 ), L p = Ln = 22.8 nm ( L p / λ p = Ln / λn = 0.099 ),
ε ′′p − n = 0.0305 (a) and ε ′′p − n = −0.3 (b)
Załącznik 3.6
ICTON 2008
177
We.C2.6
As it is seen from the distributions of electric field amplitude in the structure the strong localisation of field is
observed in the middle of the structure (Fig. 4a). The modest positive value of gain ε ′′p − n = 0.0305 in the p-n
junction makes possible to compensate for total losses in all Si layers. The transparency of a modulator at
forward bias will permit to have a cascade of them for connection between different layers of an integrated
circuit. Such transmitting EA modulators can be installed in special trunks on chips and will be able to send
signals as on the specified level of the same chip or from chip to chip. For negative value of ε ′′p − n = −0.3 low
transmittance of the structure is observed due to essential loss in the p-n junction (Fig. 4b). The modulation
efficiency of the considered structure is higher in transmission regime rather than in reflection one. At fixed
reverse bias the considered structure can operate also as a resonant photodetector. The realisation of the
suggested structure on Si and SiO2 will permit to develop EA micro-resonant transmission-type modulator
highly integrated with CMOS technology.
4. CONCLUSION
The suggested structure of a transparent at modest forward bias EA modulator is prospective in the cascaded
realisation of inter- and intra-chip optical links. The distinguishing feature of the suggested modulator is its
efficient operation in transmission regime. The small thickness of a modulator will permit to reach high
operation speed necessary for next generation of inter- and intra-chip optical interconnects. The possibility of
modulator operation also in the regime of photodetector will permit to develop multifunctional cascades of
optical interconnects. Usage of Si and SiO2 as material base of the modulator structure will be useful for its easy
integration with existing CMOS technology. The application of external wideband light source at λ0=850 nm
will help to avoid the problem of usage of an emitter on Si.
ACKNOWLEDGEMENTS
This work was supported by the Swiss National Science Foundation JRP IB7320-111057/1, Armenian National
Educational Fund grant EN-elec-1150 and partly by the Armenian State Budget project No. 230.
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