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

Theoretical Modeling Considerations 11-25
⎧
× ⎨T
⎩
( ΘT
) exp(
jω
t − β )
+
2
σ D(
ΘS
)
π R(
t)
D(
Θ )
Er
( t)
= E0
D
0
where β is the phase shift given by
T
⎡ 2π
exp
⎢
j
⎣ λ
( ( ) ( ) ) ⎬
⎭ ⎫ ⎤
a t − p − R t
⎥
⎦
, (11-66)
2π
β = vt sin(
ΘT
) cos(
ΦT
) . (11-67)
λ
Alos, a(t) is the path length from the wave through the origin to the antenna given by
( t)
= t ( Θ ) cos(
)
a sin Φ , (11-68)
T
T
p is the path length from the wave plane through the origin to the scatterer given by
and where
S
( Θ ) cos(
Φ ) + y sin(
Θ ) ( )
p = x sin sin Φ , (11-69)
E0 line-of-sight field strength, V/m
( )
T
T
D Θ antenna voltage directivity versus elevation Θ T ,
ω0 transmitter frequency, Hz
T transmission of direct wave:
1 = no shadowing, 0 = complete blockage,
σ bistatic cross section of scatterer, m 2
R(t) path length between antenna and scatterer, m
λ wavelength, m.
T
S
T
This model has been shown to produce time series of received data that closely match
those observed, if appropriate parameters are used. One such example is shown in Figure
11-5 and Figure 11-6, which respectively show experimentally received and calculated
signal level and phase for an L-Band receiver using a crossed drooping dipole antenna
and moving at 24 m/s. The transmitter azimuth and elevation angles are 150° and 35°,
respectively. The scattering object is a wooden utility pole about 3 m to the right of and
4 m above the vehicle with a 32 m 2 radar cross section. The model predicts higher
fluctuations before and after passing the pole, an indication that the scattering in reality is
not isotropic.
T