Two-ray model - UTH e

Transcription

Two-ray model - UTH e
Wireless signal propagation
(two ray model)
Thanasis Korakis
University of Thessaly
[email protected]
Two-ray model
●
Used when a single ground reflection
dominates the multipath effect
●
The received signal consists of
○ the LOS ray (the transmitted signal) and
○ a reflected ray, which is reflected off the ground, and
may interfere constructively or destructively
Why is this model so
important?
Free-space path loss model does not
consider interference.
Consider the problem of delivering wireless
coverage to an island using a wireless
backhaul from mainland
(this problem is based on a real scenario)
Low tide
Constructive interference
High-quality signal
High tide
Destructive interference
Very poor signal
Two-ray interference model
● Explains deep fades caused by multipath
interference
○ where they will occur, and how deep they will be
● Validated by measurements on many
different wireless systems
Two ray interference model
Two ray interference model
Distance traveled by direct ray:
Distance traveled by reflected ray:
Two ray interference model
Phase difference between rays:
Reflection coefficient at ground (depends on
material):
Two ray interference model
The received signal is the superposition of the
two rays. Using the free space path loss model:
the power of the two rays adds to:
Two ray interference model
Assume that delay spread is small compared to
signal bandwidth (narrowband assumption):
Then we can express the received power as:
What does the power look
like over distance?
Example on next slide based on real
measurements
Two ray model, large d
If we assume
d becomes
large, equal
gains, perfect
reflection:
Two ray model, large d
Then the phase difference becomes (using
Taylor expansion):
Two ray model, large d
and the expression for received power can be
simplified as:
Two ray model, as multi-slope model
● We saw that for large d received power Pr
decays according to
Pr = K P t / d 4
● For small d, two-ray model decays like freespace model, according to
Pr = K P t / d 2
(but two-ray model also include multipath)
Two ray model, as multi-slope model
Two ray model, as multi-slope model
What is considered large d?
● Power decays with d-4 when d > dc
dc = 4πhthr / λ
this is known as the critical distance, and
comes from the expression for phase difference
● Power decays with d-2 if d < dc
Simplified path loss models
● More generally: the main characteristics of
path loss (without multipath interference)
are captured by the expression:
Pr = K Pt [d0 / d]n
2≤n≤6
Includes free-space, two-ray, log-distance models
K factor (in detail)
● In free space & two ray models respectively:
K(free space) = Gt Gr λ2 / (4π)2 L
K(two ray) = Gt Gr ht2 hr2 / L
● Where
○
○
○
○
Gt and Gr are the Tx and Rx antenna gains
ht and hr are the Tx and Rx antenna heights
λ is the wavelength
L >=1 is the system loss factor (if not specified, L=1)
Log-distance PL model
PL = PL0 + 10nlog10( d / d0 )
Where:
○ PL0 is the Path loss in an indicative distance d0
○ n varies with propagation environments
Example 1
● Calculate free space & two ray path loss, given L=1, if :
○ frequency of signal is 2GHz
○ Tx and Rx antenna gains are 9dBi and 30dBi
○ Tx and Rx antenna heights are 15m and 1.5m
○ the distance Tx - Rx is 21Km
● 9dBi → 7.94 and 30dBi → 1000
○ since G(dBi)= 10 log10(G) (further details later)
● λ = c / f = 3x108 / 2x109 m = 0.15m
Example 1 (K factors)
● K(free space) = Gt Gr λ2 / (4π)2 L =
7.94 x 1000 x (0.15m)2 / (4π)2 x 1 = 1.13m2
● K(two ray) = Gt Gr ht2 hr2 / L =
7.94 x 1000 x (15m)2 x (1.5m)2 / 1 = 4019625m4
Example 1 (Path losses PL and dc)
● PL(free space) = 10log10(d2/K(free space) ) = 10log10((21x103)
2
/1.13) = 10log10(345.4x106) = 85.38dB
● PL(two ray) = 10log10(d4/K(two ray))=
10log10((21x103)4/4019625) = 10log10(0.048x1012) = 106.85
dB
● dc = 4π ht hr / λ = 4π x 15m x 1.5m / 0.15m = 1884m
○ d > d , so the two ray model predicts better
Multipath reception
● The received signal contains:
○ the direct LOS radio wave, but also
○ a large number of reflected radio waves (not only
one like in two ray reflection model)
● In urban centers, LOS is often blocked by
obstacles and a collection of differently
delayed waves is all what is received
Rayleigh Fading
Assumes that a received multipath signal
consists of a (theoretically infinitely) large
number of reflected waves
This model has played a major role in our
understanding of mobile propagation, first
proposed by Lord Rayleigh in 1889
○ describing the resulting signal if many violinists
in an orchestra play in unison...
References
1. T. S. Rappaport, Wireless Communications:
Principle and Practice, 2nd ed. Singapore:
Pearson Education, Inc., 2002.
2. S. Haykin and M. Moher, Modern Wireless
Communications. Singapore: Pearson
Education, Inc., 2002.

Similar documents

Find Homes for Sale in Columbia, SC at Ray Covington

Find Homes for Sale in Columbia, SC at Ray Covington Looking for homes for sale in Columbia, SC? At Ray Covington, we have a top team of experienced Real estate Agent and Realtor in Columbia, SC who are expertise in selling & purchasing of homes. Feel free to contact us at (803) 331-8833 at any time! Visit Us: http://raycovington.com/

More information