Handbook of Propagation Effects for Vehicular and ... - Courses

Theoretical Modeling Considerations 11-19
scattered multipath echoes. The resulting signal amplitude has a Ricean probability
density characterized by a constant ratio of direct to scattered power. In the shadowed
state, the amplitude of the line-of-sight signal is assumed to have lognormal statistics.
When combined with constant level diffuse multipath, the probability density (11-40)
derived by Loo applies.
The overall probability density of the received voltage is developed analogously to the
derivation of (11-57) as
f v
2
( v)
= ( 1 − S)
2Kv
exp[
− K(
v + 1)
) ] I ( 2Kv)
×
∞
∫
0
1 ⎡
exp⎢−
z ⎣
2
( 20log(
z)
− m)
2 2 ⎤
K ( v z ) I ( Kv
z)
dz
2s
2
0
−
8.
686
+ S
s
+
⎥
⎦
0
2
2Kv
π
(11-58)
where S, K, K , m, and s are the five model parameters already described in the previous
section.
Table 11-5: Parameter Values for the Lognormal Shadowing Model
Parameter Range of Values Remarks
K 22 to 13 dB Low to high multipath, unshadowed
K 21 to 18 dB Low to high multipath, shadowed
m -1 to -10 dB Light to heavy shadowing
s 0.5 to 3.5 dB Light to heavy shadowing
S 0.0 to 1.0 No shadowing to frequent shadowing
The parameters given in Table 11-5 were determined by a least square error fit of the
statistical model to propagation data collected using a helicopter as the source platform.
11.4.4.1 Discussion
As was the case for the other statistical models, the lognormal shadowing model has been
fit to measured cumulative fade distributions quite well. One would expect an increased
multipath power level to go hand-in-hand with shadowing conditions. The small range
and low level found for K seem to indicate that the model does not adequately uncouple
shadowing and scattering. The range of applicability of the model vis-à-vis elevation
angle has also not been specified.
Because of the complexities in evaluating (11-58), a much simpler empirical model (in
the next section) was derived from the statistical results by curve fitting procedures.
11.4.5 Simplified Lognormal Shadowing Model
This model [Barts and Stutzman, 1991; Barts et al., 1987] has the inputs S, K, K , m, and
s, which have been defined in the previous two sections and assume the values