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

Attenuation Due to Roadside Trees: Mobile Case 3-7
Table 3-1: Listing of parameter values of α( P), β( P), γ(
P ) in Equation (3-7).
Percentage, P α( P) β( P) γ( P)
1 34.7600 -0.4430 0.0
2 32.3756 -0.5106 1.3863X10 -3
5 29.2235 -0.5999 3.2189X10 -3
10 26.8391 -0.6675 4.6052X10 -3
20 24.4547 -0.7351 5.9915X10 -3
30 17.3022 -0.5201 4.2391X10 -3
40 12.2273 -0.36754 2.9957X10 -3
50 8.2910 -0.2492 2.0313X10 -3
60 5.0748 -0.1525 1.2433X10 -3
70 2.3556 -7.0805X10 -2
80 0.0 0.0 0.0
5.7711X10 -4
For the case in which 20° > θ ≥ 7°
, the distribution derived using the formulations () or
(3-7) is first calculated at θ = 20 ° . This distribution for θ = 20 ° is subsequently assumed
to be invariant at the smaller elevation angles. That is,
for 80% ≥ P ≥ 1% and 20° > θ ≥ 7°
A ( P,
θ , f ) = A(
P,
20°
, f ) . (3-8)
Equation (3-8) implies that the probability distributions at elevation angles smaller than
20° are the same as those at 20°. Extending the model to elevation angles smaller than
20° is a complex task for the following reasons: (1) The EERS model tacitly assumes
that the canopies of single trees shadow the Earth-satellite path. At lower angles, there
may be a greater likelihood that the path cuts the canopies of multiple trees or multiple
tree trunks. (2) At smaller angles, there may also be a greater likelihood that the terrain
itself blocks the Earth-satellite path creating high attenuation. (3) Ground multipath may
also influence the distribution considerably. Based upon empirical experience for cases
where the above caveats did not arise, it has been found that with good approximation the
EERS model at 20° elevation is representative of results at 7° or 8°. The rationale for this
assumption is characterized in Figure 3-4. At 20° elevation, the Earth-satellite path is
already passing through the lower part of the tree canopies. Reducing the path elevation
angle is likely to result in attenuation caused by tree trunks that may tend to mitigate the
signal degradation. On the other hand, attenuation effects may increase because of fading
from those tree canopies that are further offset from the road (as was the case in Alaska).
The combination of these two effects generally results in the median fade statistics to be
relatively invariant to angles below 20°, although larger deviations about the median are
expected because of the breakdown of the aforementioned underlying assumptions.