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

Theoretical Modeling Considerations 11-15
−1
−2
x exp( −x)
I0
( x)
= 0.
39894 + 0.
01328592t
+ 0.
00225319t
−3
−4
−0.
00157565t
+ 0.
00916281t
−5
−6
−0.
02057706t
+ 0.
02635537t
−7
−8
−0.
01747633t
+ 0.
00392377t
+ ε
ε
<
−7
1.
9 ⋅10
, (11-44)
to evaluate exp( − x)
I 0( x)
. Inserting the latter into (11-40) results in the numerically
somewhat more friendly expression
f v
( v)
∞
2Kv
1 ⎡
= ∫ exp⎢−
s π z ⎢⎣
0
( ln(
z)
− m)
2
2s
2
− K
although carrying out the integration still requires care.
Table 11-3: Parameters for Loo's Model
Shadowing Class
Rayleigh Scatter Lognormal Shadowing
⎤
⎥
⎥⎦
K (dB) m s
Infrequent light 6.3 0.115 0.115
Frequent heavy 18.8 -3.91 0.805
Overall 4.0 -0.69 0.23
2 ( v − z)
exp( −2Kvz)
I ( 2Kvz)
dz
The probability that the received voltage is less than or equal to v is
0
, (11-45)
v
Fv
( v)
= ∫ fv
( u)
du
(11-46)
0
from which the cumulative distribution function A in dB is found using
A = 20log( v)
(11-47)
Values of the model parameters were derived by Loo from propagation data measured
over a helicopter to vehicle link with 15° elevation angle in a rural environment with two
classes of shadowing: infrequent light and frequent heavy. The parameters are
summarized in Table 11-3 for environments with infrequent light shadowing, such as a
road with occasional sparse trees and frequent heavy shadowing, i.e., a road with many
large trees with overhanging crowns.