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Lecture 4  EE 359: Wireless Communications  Autumn 2011
Statistical Fading Models. Narrowband Models
Lecture Outline
•
Model Parameters from Empirical Data
•
Random Multipath Model.
•
Time Varying Channel Impulse Response.
•
Narrowband Fading Approximation.
•
InPhase and Quad Signal Components under LLN.
•
Mean, Autocorrelation, and Cross Correlation in Narrowband Fading.
1.
Model Parameters from Empirical Data:
•
Constant
K
obtained from measurement at distance
d
0
.
•
Power falloF exponent
γ
obtained by minimizing the MSE of the predicted model
versus the data.
•
The resulting path loss model will include average attenuation, so
μ
ψ
dB
= 0.
•
The shadowing variance
σ
2
ψ
dB
obtained by determining MSE of the data versus the
empirical path loss model with the optimizing
γ
.
2.
Statistical Multipath Model:
•
At each time instant there are a random number
N
(
t
) of multipath signal components.
•
Each component has a random amplitude
α
n
, phase
θ
n
, Doppler shift
f
D
n
=
v
λ
cos
θ
n
,
and path delay
τ
n
= (
d
n

d
)
/c
.
•
Thus, received signal is
r
(
t
) =
R
N
(
t
)
s
n
=0
α
n
(
t
)
e

jφ
n
(
t
)
u
(
t

τ
n
(
t
))
e
j
2
πf
c
t
.
3.
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 Spring '10
 Rejaei
 Electromagnet

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