MRN -5 – Radio Planning

Transcription

Politecnico di Milano
Facoltà di Ingegneria dell’Informazione
MRN -5 – Radio Planning
Mobile Radio Networks
Prof. Antonio Capone
What is radio planning?
o  When we have to install a new wireless
network or extend an existing one into a new
area, we need to design the fixed and the
radio parts of the network. This last phase is
called radio planning.
Antonio Capone: Wireless Networks
2
What is radio planning?
o  The basic decisions that must be taken during
the radio planning phase are:
n  Where to install base stations (or access points,
depending on the technology)
n  How to configure base stations (antenna type,
height, sectors orientation, tilt, maximum power,
device capacity, etc.)
X
X
X
X
3
Radio Planning
o  When planning and optimizing a cellular system, a
number of aspects must be considered, including
n 
n 
n 
n 
n 
signal propagation,
traffic estimation,
antenna positioning,
antenna configuration,
interference.
o  Here we’ll focus on the decision problems that give
rise to interesting and challenging mathematical
programming models which must account for the
peculiarities of the specific network technology.
4
Propagation prediction
o  One of the key elements for the radio planning is
propagation prediction that allows to estimate the
area covered by each base station
o  The covered area
is the area where
the received
signal strength is
R
above a threshold
o  Received signal
strength depends
on emitted power
and path loss
5
Traffic estimation
o  Traffic distribution in the service
area is usually hard to predict in
the radio planning phase since it
depends on several issues
including area population,
buildings, market penetration of
the considered service, etc.
o  Traffic distribution is usually
provided using a discrete set of
points I, test points (TP), that
are considered as centroids of
traffic
6
Antenna positioning
o  The selection of possible antenna sites depends on
several technical (traffic density and distribution,
ground morphology, etc.) and non-technical
(electromagnetic pollution, local authority rules,
agreements with building owners, etc.) issues.
o  We denote with S the set of
candidate sites (CS)
o  We can assume that the
channel gain gij between TP
i and CS j is provided by a
propagation prediction tool
7
Antenna configuration
o  Radiation diagram
o  Horizontal (sectors) and
vertical (tilt) angles
o  Maximum emission power
(pilot channel power)
o  Height
o  Base station capacity
o  Etc.
8
Antenna configuration
o  The antenna configuration affects only the signal
level received at TPs
o  For each CS j we can define a set of possible
antenna configurations Kj
o  We can assume that the channel gain gijk between
TP i and CS j depends also on configuration k.
o  Based on signal quality requirement and channel
gain we can evaluate if TP i can be covered by CS
j with an antenna with configuration k,
o  And define coefficients:
⎧1 if TP i can be covered by
aijk = ⎨ CS j with conf. k
⎩0 otherwise
9
Summarizing
S = {1,..., m}set of candidate sites (CS)
for each j ∈ S , K j set of configurations
I = {1,..., n}set of test points (TP)
⎧1 if TP i is covered by CS j with conf. k
aijk = ⎨
⎩0 otherwise
i ∈ I , j ∈ S, k ∈ K j
10
Interference
o  Multiple access techniques are used to define
communication channels on the available
radio spectrum
FDMA
TDMA
CDMA
o  Radio resources for wireless systems are
limited and must be reused in different
areas (cells)
o  Resource reuse generates interference
11
Interference
o  Interference can be tolerated (good communication
quality) if the Signal-to-Interference Ratio (SIR)
is high enough
o  SIR constraint limits the number of simultaneous
communications per cells, i.e. the system capacity
o  Capacity is another key element that must be
considered during radio planning
o  FDMA/TDMA cellular systems adopt a two phases
radio planning
n  Coverage planning
n  Capacity planning (frequency assignment)
o  CDMA cellular systems require a single phase
approach
n  Joint coverage and capacity planning
12
Coverage planning
13
Coverage planning
o  The goal of the coverage planning phase is
to:
n  Select where to install base stations
n  Select antenna configurations
o  In order to guarantee that the signal level
in all TPs is high enough to guarantee a
good communication quality
o  Note that interference is not considered in
this phase
14
Set covering problem (SCP)
o  Let us first consider a simple model
where decisions are only on where to
install base stations
o  Decision variables:
!# 1 if a BS is installed in CS j
yj = "
#$ 0 otherwise
o  Propagation parameters
!# 1 if CS j covers TS i
aij = "
#$ 0 otherwise
15
o  Problem:
Minimize Z = ∑ c j y j
j∈J
s.t.
∑a y
ij
j
≥1
∀i ∈ I
j∈S
Pj = { i | aij =1}
o  Let
o  Variables yj define a subset
o  Such that
Pj = I

*
S ⊆S
j∈S*
16
SCP with configurations
⎧1 if a base station with configuration k is installed in CS j
y jk = ⎨
⎩ 0 otherwise
o  Installation
costs:
c jk Cost related to the installation of a
base station in CS j with
configuration k
17
SCP with configurations
min
Objective function:
total network cost
∑ ∑ c jk y jk
j∈S k∈K j
∑∑a
ijk
y jk ≥ 1 ∀i ∈ I
Full coverage constraints
j∈S k∈K j
∑y
jk
≤ 1 ∀j ∈ S
One configuration per site
k∈K j
y jk ∈ {0,1}
∀j ∈ S, k ∈ K j
Integrality constraints
18
o  SCP is NP-hard
o  However several efficient algorithms
has been proposed (see [3] for a
survey)
o  Even simple greedy algorithms allow
to obtain high quality solutions
19
Greedy algorithm for SCP
o  Step 0
Note: we don’t consider
configurations here for the sake of
n  set S*=∅
simplicity
o  Step 1
n  if Pj = ∅ for all j then STOP
Pj
o  Otherwise find k ∈ (J-J*) such that:
is maximum
cj
o  Step 2
n  S*:=S*∪{k}
n  Pj:=Pj-Pk ∀j
o  Go to Step 1.
20
Greedy algorithm: Example
(1)
⎡1
⎢1
⎢
V = ⎢1
⎢
⎢1
⎢⎣1
1 0 1 1 0 0 1 0 0 0 0 1 0 1⎤
⎡7⎤
⎡1⎤
⎢5⎥
⎢1⎥
1 1 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
⎢ ⎥
0 0 0 0 0 1 1 1 1 1 0 0 1 1⎥ Π = ⎢8⎥ C = ⎢1⎥
⎥
⎢ ⎥
⎢ ⎥
1 1 1 1 0 1 0 0 0 0 0 0 1 1⎥
8
⎢ ⎥
⎢1⎥
⎢⎣9⎥⎦
⎢⎣1⎥⎦
0 1 0 1 0 1 0 1 0 1 0 1 1 1⎥⎦
o  Step 0: S*=∅
21
(2)
o  Step 1: k=5
⎡1
⎢1
⎢
V = ⎢1
⎢
⎢1
⎢⎣1
1 0 1 1 0 0 1 0 0 0 0 1 0 1⎤
⎡7⎤
⎡1⎤
⎢5⎥
⎢1⎥
1 1 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
⎢ ⎥
0 0 0 0 0 1 1 1 1 1 0 0 1 1⎥ Π = ⎢8⎥ C = ⎢1⎥
⎥
⎢ ⎥
⎢ ⎥
1 1 1 1 0 1 0 0 0 0 0 0 1 1⎥
8
⎢ ⎥
⎢1⎥
⎢⎣9⎥⎦
⎢⎣1⎥⎦
0 1 0 1 0 1 0 1 0 1 0 1 1 1⎥⎦
22
(3)
o  Step 2:
n  S*= {5},
n  ...
⎡1
⎢1
⎢
V = ⎢1
⎢
⎢1
⎢⎣1
1 0 1 1 0 0 1 0 0 0 0 1 0 1⎤
⎡7⎤
⎡1⎤
⎢5⎥
⎢1⎥
1 1 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
⎢ ⎥
0 0 0 0 0 1 1 1 1 1 0 0 1 1⎥ Π = ⎢8⎥ C = ⎢1⎥
⎥
⎢ ⎥
⎢ ⎥
1 1 1 1 0 1 0 0 0 0 0 0 1 1⎥
8
⎢ ⎥
⎢1⎥
⎢⎣9⎥⎦
⎢⎣1⎥⎦
0 1 0 1 0 1 0 1 0 1 0 1 1 1⎥⎦
23
(4)
o  Step 2:
n  … ricalculate V e Π
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
1 0 1 0 0 0 1 0 0 0 0 0 0 0⎤
⎡3⎤
⎢3⎥
1 0 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 1 0 1 0 0 0 0 0⎥ Π = ⎢2⎥
⎥
⎢ ⎥
1 0 1 0 0 0 0 0 0 0 0 0 0 0⎥
⎢2⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
24
(5)
o  Step 1:
n  k=1
o  Step 2:
n  S*= {5,1},
n  ricalculate V e Π
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
1 0 1 0 0 0 1 0 0 0 0 0 0 0⎤
⎡3⎤
⎢3⎥
1 0 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 1 0 1 0 0 0 0 0⎥ Π = ⎢2⎥
⎥
⎢ ⎥
1 0 1 0 0 0 0 0 0 0 0 0 0 0⎥
⎢2⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
25
(6)
o  … ricalculate V e Π
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎤
⎡0⎤
⎢2⎥
0 0 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 0 0 1 0 0 0 0 0⎥ Π = ⎢1⎥
⎥
⎢ ⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥
⎢0⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
26
(7)
o  Step 1:
n  k=2
o  Step 2:
n  J*= {5,1,2},
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎤
⎡0⎤
⎢2⎥
0 0 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 0 0 1 0 0 0 0 0⎥ Π = ⎢1⎥
⎥
⎢ ⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥
⎢0⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
27
(8)
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎤
⎡0⎤
⎢0⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 0 0 1 0 0 0 0 0⎥ Π = ⎢1⎥
⎥
⎢ ⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥
⎢0⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
28
(9)
o  Step 1:
n  k=3
o  Step 2:
n  J*= {5,1,2,3},
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎤
⎡0⎤
⎢0⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 0 0 1 0 0 0 0 0⎥ Π = ⎢1⎥
⎥
⎢ ⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥
⎢0⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
29
(10)
o  STOP
⎡0
⎢0
⎢
V = ⎢0
⎢
⎢0
⎢⎣0
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎤
⎡0⎤
⎢0⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎥
⎢ ⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥ Π = ⎢0⎥
⎥
⎢ ⎥
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥
⎢0⎥
⎢⎣0⎥⎦
0 0 0 0 0 0 0 0 0 0 0 0 0 0⎥⎦
30
(11)
o  In this simple example it’s easy to
observe that the solution J*=
{5,1,2,3} is sub-optimal
o  In fact this solution has a lower cost:
⎡1
⎢1
⎢
V = ⎢1
⎢
⎢1
⎢⎣1
1 0 1 1 0 0 1 0 0 0 0 1 0 1⎤
⎡7⎤
⎡1⎤
⎢5⎥
⎢1⎥
1 1 0 0 1 0 0 0 0 0 1 0 0 0⎥⎥
⎢ ⎥
⎢ ⎥
0 0 0 0 0 1 1 1 1 1 0 0 1 1⎥ Π = ⎢8⎥ C = ⎢1⎥
⎥
⎢ ⎥
⎢ ⎥
1 1 1 1 0 1 0 0 0 0 0 0 1 1⎥
8
⎢ ⎥
⎢1⎥
⎢⎣9⎥⎦
⎢⎣1⎥⎦
0 1 0 1 0 1 0 1 0 1 0 1 1 1⎥⎦
31
Maximum coverage problem
(MCP)
o  In practice the coverage requirement is often a
“soft constraints” and the problem actually
involves a tradeoff between coverage and
installation costs
max λ ∑ zi − ∑ ∑ c jk y jk
i∈I
Objective function: trade-off
between cost and coverage
j∈S k∈K j
∑∑a
ijk
y jk ≥ zi
∀i ∈ I
Definition of variables z
j∈S k∈K j
∑y
jk
≤ 1 ∀j ∈ S
One configuration per site
k∈K j
y jk ∈ {0,1}
zi ∈ {0,1}
∀j ∈ S, k ∈ K j
Integrality constraints
∀i ∈ I
32
Assigning test points to base
stations
o  When a TP is covered by more than
one base station:
∑∑a
ijk
y jk # of base stations covering TP i
j∈S k∈K j
the serving base station is not
defined
o  We can define new assignment
variables:
!# 1 if TP i is assigned to CS j
xij = "
#$ 0 otherwise
33
Set covering with
assignment (SCA)
min
∑∑c
jk
y jk
j∈S k∈K j
∑x
ij
= 1 ∀i ∈ I
Coverage constraints
j∈S
∑y
jk
≤ 1 ∀j ∈ S
k∈K j
xij ≤
∑a
ijk
y jk
Definition of variables x
k∈K j
y jk ∈ {0,1}
∀j ∈ S, k ∈ K j
xij ∈ {0,1}
∀i ∈ I, ∀j ∈ S
34
Capacity constraints
o  Obviously, without additional constraints SCA
provides the same solution as SCP
o  Using x variables we can add constraints on
cell capacity:
∑d x
i ij
≤
i∈I
∑v
jk
y jk
∀j ∈ S
k∈K j
where di is the traffic demand associate to TP
i and vjk is the capacity of a base station in
CS j with configuration k
o  Other constraints related to cell ‘shape’ can
be added
35
Assignment to the ‘nearest’
base station
o  One of these rules is the requirement of assigning a TP
to the “closest” (in terms of signal strength) activated
BS.
o  One way to express this constraint for a given TP i is to
consider all the pairs of BSs and configurations that
would allow connection with i and sort them in
decreasing order of signal strength.
o  Let {( j1, k1 ), ( j2 , k2 ),..., ( jL , kL )}
be the ordered set of BS-configuration pairs
o  The constraints enforcing the assignment on the
‘nearest’ BS are:
L
y jl kl + ∑ xijh ≤ 1
1 ≤ l ≤ L −1
h=l+1
36
Politecnico di Milano
Facoltà di Ingegneria dell’Informazione
CDMA planning
Approaches to the radio
planning
2nd Generation Systems
(GSM, D-AMPS, ...)
o  two-phases approach
n  1) Radio coverage
o  minimum signal
level in all the
service area
n  2) Frequency
assignment
o  meet traffic
constraints
o  meet quality (SIR)
constraints
3rd Generation Systems based
on W-CDMA
o  two-phases approach not
suitable because:
n 
n 
no frequency planning for
CDMA
power control determines
the cell breathing effect
Planning must also consider
⇒  traffic demand
⇒ 
distribution
SIR constraints
38
Covering traffic in W-CDMA
systems
o  Traffic generated can be considered
covered (served) by the system if the
QUALITY of the connection is good
o  Quality measure: Signal-toInterference Ratio (SIR)
SIRdownlink
SIRuplink
Prec
= SF
αI out + I in + η
Prec
= SF
I out + I in + η
39
Power Control (PC)
mechanism
o  Dynamic adjustment of the transmitted power to
minimize interference
o  Two PC mechanisms:
n  Power-based PC
o emission powers are adjusted so that
received powers are equal to a given Ptar
n  SIR-based PC
o emission powers are adjusted so that all
SIR are equal to a given estimated SIRtar
40
Cell breathing effect
o  Due to the power limitations the area actually
covered by a BS depends on interference (traffic)
level
o  When traffic (interference) increases
the SIR constraint cannot be met for
terminals far from the BS due to
higher channel attenuation
o  Since only terminals close to the BS
can be actually served it is as if the
actual cell area reduces
o  Since this phenomenon affects
coverage, traffic levels must be
carefully considered during radio
planning
41
Joint coverage and capacity
planning
o  set of candidate sites where to install BSs:
S={1,…,m}
n  installation costs: cj, j∈S
o  set of test points (TPs): I={1,…,n}
n  traffic demand: ai, i∈I
n  equivalent users: ui=φ(ai)
o  propagation gain matrix: G=[gij], i∈I, j∈S
Problem:
Select a subset of candidate sites where to
install BSs, and assign TPs to BSs so that
quality constraints are satisfied and the
total cost is minimized
42
planning
⎧1 if a BS is installed in j ∈ S
yi = ⎨
⎩0 otherwise
⎧1 if test point i ∈ I is assigned to BS j ∈ S
xij = ⎨
⎩0 otherwise
o  Basic constraints:
∑x
ij
≤1
∀i ∈ I
assignment
∀i ∈ I,∀j ∈ S
coherence
j∈S
xij ≤ y j
xij , y j ∈ {0,1} ∀i ∈ I,∀j ∈ S
integrality
43
planning
o  Objective function:
max ∑∑ ui xij − λ ∑ c j y j
i∈I j∈S
j∈S
maximize
covered traffic
minimize
installation costs
o  We assume a power-based Power Control
(received power = Ptar)
o  variables xij are defined only for pairs such that:
Ptar
≤ Pmax
gij
power limit
44
planning
o  SIR constraints:
Ptar
≥ SIRmin y j
Ptar
uh g hj ∑
xht − Ptar
∑
h∈I
t∈S g ht
∀j ∈ S
signal power
total interference
o  bilinear constraints which can be easily
linearized:
%
(
ghj
1+ M (1− y j ) ≥ SIRmin ' ∑ ∑ uh xht −1*
& h∈I t∈S ght
)
∀j ∈ S
with a value of M large enough
45
planning
o  Solution approach:
n  State-of-the-art ILP solvers can provide
the exact solution only for very small
instances
n  Heuristics have been proposed
n  Promising approach based on Tabu
Search
46

MRN -5 – Radio Planning

Transcription

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