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

Theoretical Modeling Considerations 11-17
11.4.3 Total Shadowing Model
Another statistical model characterizing the fade distribution applicable to LMSS
propagation has been devised by Lutz et al. [1986]. As in Loo's model, Ricean, Rayleigh,
and lognormal probability densities are combined and model parameters are derived from
least-square error fits to measured data. However, there are significant differences in the
way the three distributions are assigned to the two major propagation phenomena,
scattering and shadowing. As described in the previous section, Loo combines a constant
intensity Rayleigh distributed scattering voltage with a lognormally shadowed line-ofsight
signal voltage. Lutz et al., on the other hand, consider two distinct propagation link
states; shadowing, and no shadowing. In the unshadowed state, the envelope statistics are
assumed to be Ricean with constant K-factor due to the superposition of the direct wave
with constant intensity multipath echoes. When the propagation link is shadowed by
roadside trees, the line-of-sight is assumed to be totally obscured and most of its power
converted into scattered waves, leaving only multipath signals with Rayleigh statistics,
but their average strength is modeled as lognormally distributed. Loo modulates the
Ricean K-factor by shadowing the line-of-sight component. Lutz, in the shadowed state,
varies the intensity of the Rayleigh scattering process, or the K -factor, in the absence of
any line-of-sight signal. In Lutz's model, the probability density of the received voltage
for the unshadowed fraction (1-S) of the driving distance is Ricean. When expressed in
terms of the received power P’, it has the form
[ − K(
P′
+ 1)
] I ( 2K
P′
)
′ P′
, ( ) = K exp
0 , (11-51)
f P Rice
where unity line-of-sight power is assumed and K is the ratio of line-of-sight to average
multipath power. That is
K =
P′
1 . (11-52)
mp
For the shadowed fraction S of the total distance, the power is Rayleigh distributed and
has the following form when expressed in terms of the received power, P'
( − KP′
)
′ , ( P′
) = K exp , (11-53)
f P Rayleigh
where K is the reciprocal of the average multipath power as given by (11-32). Lutz et
al. postulate this multipath power Rayleigh intensity 1 K to be lognormally distributed.
The density can be expressed in terms of the K -factor, the mean m, and the standard
10 log K as
deviation s of ( )
where
f K
( K )
( 10log(
K ) m)
4.
343 ⎡ −
exp⎢−
Ks
2π
⎢⎣
2s
= 2
2
⎤
⎥ , (11-54)
⎥⎦