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

3-8
Propagation Effects for Vehicular and Personal Mobile Satellite Systems
20 o
P(θ) = P(20 ο ) 20 o > θ > 7 o
Figure 3-4: Cartoon depicting the mechanism by which the fades are statistically
invariant at angles smaller than 20° (down to 7°). At angles smaller than 20°, Earthsatellite
paths tend to fall below the canopy of nearby trees but intersect more distant tree
canopies.
3.3.3 Step by Step Implementation of the EERS Model
We presume that it is desired to determine the percentage P of distance traveled over
which a fade is exceeded for a LMSS tree-shadowing scenario at frequency f (in GHz)
and elevation angle to the satellite θ (in degrees). We present here the step-by-step
approach of determining this distribution using the EERS model given by () through
(3-8). Initially, consider the angular interval 60°≥ θ ≥ 20°
. We will return to the
extension of the formulation outside these angle bounds shortly.
Step 1: Calculate the fade distribution at fL = 1.
5 GHz , valid for percentages of distance
traveled of 20% ≥ P ≥ 1% , at the desired path elevation angle, 60°≥ θ ≥ 20°
:
where
A( P,
θ, fL
) = −M
( θ ) ln( P)
+ N ( θ )
(3-9)
2
M ( θ ) = 3.
44 + 0.
0975θ
− 0.
002θ
(3-10)
N ( θ ) = −0.
443θ
+ 34.
76
(3-11)
Step 2: Convert the fade distribution at fL = 1.
5 GHz , valid for 20% ≥ P ≥ 1% , to the
desired frequency, f (GHz), where 0. 8 GHz ≤ f ≤ 20 GHz .
0.
5
⎪
⎧
0.
5
⎡⎛
1 ⎞ ⎛ 1 ⎞ ⎤⎪
⎫
A(
P,
θ , f ) = A(
P,
θ , f L ) exp⎨1.
5⋅
⎢ ⎜
⎟ − ⎜ ⎟ ⎥⎬
(3-12)
⎪⎩
⎢⎣
⎝ f L ⎠ ⎝ f ⎠ ⎥⎦
⎪⎭
Step 3: Scale the fade distribution to percentages of distance traveled 80% ≥ P > 20% :
θ