W03.1_Propagation.pdf
5
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Transcript of W03.1_Propagation.pdf
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03-1
-140
-120
-100
-80
-60
-40
0 200 400 600 800 1000
Distance from BS
S
i g n a l s t r e n g t h i n d
B
03-2
Received carrier power ∝∝∝∝ d −−−−γ γγ γ
where d = distance from transmitter to receiver
typically, γ γγ γ is in the range 2 to 4
γ γγ γ = 2 (open rural environment)
γ γγ γ ~ 4 (typical dense urban environment).
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03-3
Free Space Propagation
2
4
=
d GGPP RT T R
π
λ
2
−∝d P R
Received power
Transmitted power
Gain of transmitting antenna
Gain of receiving antenna
separation between antennas
wavelength
Friis equation:
variation with d:
03-4
Two rays
Transmitter Receiver
d
hT h R
2
2
=
d
hhGGPP
RT
T RT R (Plane Earth propagation Equation)
variation with d : 4−∝d P R
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03-5
Slow fading is due to terrain contour, clutter (buildings, trees)
•different paths at the same distance
from the transmitter experience different clutter,
hence different path loss => shadowing
Slow fading is usually modelled as having a
log-normal distribution
Local mean follows a log-normal distribution
i.e. signal in dB follows a Normal (Gaussian) distribution.
- variance normally around 8 dB.
03-6
0
0.1
0.2
0.3
0.4
0.5
-3 -2 -1 0 1 2 3
Signal Level Variation (dB)
P r o b a b i l i t y
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03-7
Fast fading due to multipath non-line-of-sight transmission
Fast fading (Rayleigh fading) typically has Rayleigh distribution.
Rayleigh:
{ }22 / 1AstrengthsignalPr σ A
e−
−=≤ (Rayleigh distribution)
{ } L
L
e−
−=≤ 1LpowersignalPr (Negative exponential distribution)
03-8
Rayleigh, pdf =)2 /(
2
22 σ
σ
r e
r −
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5 6
Signal Level Variation
P r o b a b i l i t y
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03-9
Suzuki distribution:
Signal level is determined by:
•Path Loss
•with shadowing about this value
•with Rayleigh fading about this value
( )
σ π σα σ
α
µ σ
σ d ee x
xP
x
s
22
2
2
log
20 2 2
1.)(
−−−
∞
=
needs to be computed numerically, but shown to be quite accurate.
Log-normalRayleigh
