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

11-28
11.5.2.2 Three-Dimensional Model
Propagation Effects for Vehicular and Personal Mobile Satellite Systems
An extension to the single scatterer multipath model of Vogel and Hong [1988] allows a
vehicle to be driven through a region with many randomly distributed, point-source
multipath scatterers [Vishakantaiah and Vogel, 1989]. The output of the drive simulator
yields time series of signal amplitude and phase as well as Doppler spectra, all for userspecified
conditions. These outputs, in turn, can be used to calculate system performance
parameters. The simulator does not consider shadowing, and this limits its application to
very low fade margin systems, where multipath-fading effects determine system
performance most of the time.
In order to obtain the total field at the receiver due to many scatterers, the vector
sum of the constant incident field and all the scattered fields e is formed similarly to
(11-66) and the relative total power and phase are calculated from
and
total
( ) ( ) 2
2
1 + ∑ ereal
+ ∑ e
Power (11-70)
Phase
total
= imag
∑
⎛ e ⎞ imag
= arctan ⎜ ⎟ ,
⎜ ⎟
(11-71)
⎝1
+ ∑ ereal
⎠
where the summation includes the real or imaginary parts of each scatterer's response e to
the incident wave.
The model was validated by comparing the predicted power and phase assuming a single
scatterer to the results from measurements, both with similar parameters as well as by
comparing the calculated power spectral density to the one expected [Clarke, 1968].
Figure 11-7 demonstrates that the model produces the correct Doppler spectrum, centered
on the received carrier frequency. The shape shows the typical signature of mobile
multipath propagation, a sharply band-limited spectrum with maximum power at the
edges. The frequency deviation of the scattered wave (±120 Hz) agrees with the value
expected from the geometry. The signal level output of the model shows a peak-to-peak
variation of less than 1.5 dB assuming 1000 scatterers located in an annular region with
radii of 400 and 2000 m, a drooping dipole antenna, and the height of the scatterers
randomly distributed between 0 and 10 m. This peak-to-peak variation is in agreement
with measurements made in locations where no scatterers are in the immediate vicinity of
the vehicle.