15)
where v vehicular speed, is the wavelength of the carrier frequency, is the angle of arrival with
respect to the velocity vector traveling in the same direction as the vehicle. Assuming an omni directional
antenna in the receiver, the arriving multipaths have the opportunity to experience a wide range
of angles. This leads to a Doppler spread since each arriving ray will have its own frequency shift
associated with it. However, the aggregate sum of all the multipaths will exhibit a behavior that is
typically called Doppler spread. Assuming a uniformly distributed angle of arrival, the Doppler
frequency response or Doppler spectrum can be written as
(3.16)
where fcthe carrier frequency. Now returning our attention to the LCR, we notice the quantity is proportional
to the max Doppler shift. In other words, as the vehicle speed increases, the average number
S( f )
3s2
2p # fm
# 1 ?…1 af fc
fm b2
l
fD fm # cos(u)
v
l
# cos(u)
r
R
RRMS
NR 22p # fm # r # er2
r .
NR 3
`
0
r .
p(R, r .
) dr
.
WIRELESS MULTIPATH CHANNEL 123
FIGURE 3.6 High-level view of the multipath propagation phenomenon.
of times we encounter a normalized signal fade, R (in dB), increases. That is we encounter the faded signal
more often because the temporal distance between these nulls has decreased due to mobility.
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