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

Optical Methods for Assessing Fade Margins 10-5
10.4 Clear, Shadowed and Blocked Propagation States
Fading for mobile satellite communications can be modeled by assuming that distinct
signal level statistics pertain to three major propagation states, i.e., when the line-of-sight
is clear with multipath contributions, shadowing by foliage, and blocked by buildings.
Karasawa et al. [1994] fitted L-Band satellite fade data obtained in urban Japan at 32°
elevation to a cumulative probability distribution consisting of a weighted linear
combination of fading density functions developed by Rice, Loo, and Rayleigh. This
linear combination is expressed by
fν ( v) = C f Rice( v) + S f Loo( v) + B f Rayleigh(
v)
, (10-2)
where C, S, B are probabilities of clear, shadowed, and blocked states, and fv denotes the
probability density function (PDF) for the signal envelope. The Ricean density
distribution is given by
2 [ ] ( )
f ( v) = 2Kv exp − K( v + 1) I 2Kv
, (10-3)
Rice o
Loo’s density function [Loo, 1985] is given by
f Loo
( 20log(
z)
− m)
2
2 Kv 1
2 2
( v)
8.
686 exp
K(
v z ) I0
( 2Kvz
)dz
2
z
0
2
⎥ ⎥ ∞ ⎡
⎤
= ∫ ⎢−
− +
, (10-4)
π σ ⎢⎣
σ
⎦
and the Rayleigh density function is given by
2
f Rayleigh( v) = 2Kv
exp( −Kv
) , (10-5)
where ν is the received voltage relative to the clear path voltage, K is the ratio of the
direct power received to the multipath power, I 0( ν ) is the modified Bessel function with
argumentν , m is the mean of log(ν ) , and σ is the standard deviation of log(ν ) . It
should be noted that (10-2) does not account for any specular reflection or any building
diffracted power for blocked conditions.
Satellite beacon and photogrammetrically measured values of K for the three fade
states are tabulated in Table 10-3. Employing earth-satellite measurements at 1.5 GHz
and 32° elevation for urban Tokyo, Karasawa et al. [1994] estimated values of C, S, B of
0.55, 0.1, 0.35, respectively. The “path-state mixture vector” for this case is defined as
M =< 055 . , 01 . , 0. 35 > . (10-6)
For the fit using (10-6), the RMS fade prediction error over the 5% to 95% interval is 1.3
dB (3 rd column, last row in Table 10-3). The measured ( Δ ) and modeled (short dashed)
cumulative fade distributions (CDF) of Karasawa et al. [1994] are plotted in Figure 10-4.
Shown to the right of the distribution are error curves defined as the difference between
the measured and modeled dB values. A peak error of approximately 3 dB occurs at a