Digital Signal Processing Reference
In-Depth Information
increasing path length (1)
LOS (2)
decreasing path length (3)
power spectrum
The beat frequency between
the doppler shifted components
determines the coherence time
of the channel.
received power
(2)
(1)
(3)
T
coh
-
f
D,max
0
+f
D,max
Doppler shift [Hz]
time
Figure 4.5.
The beat frequency (bf) between the extreme Doppler-shifted fre-
quencies causes an alternating sequence of positive and destructive
fades every half wavelength of the bf. This determines the coher-
ence time of the channel.
view of the receiver, this process is perceived as a change in the wavelength or
a shift in the carrier frequency of the transmitter. This phenomenon is known as
the
Doppler effect
. Of course, in the indoor channel, there are multiple propa-
gation paths from transmitter to receiver, each of them with a different
Doppler
shift
. The maximum deviation from the original center frequency is called the
Doppler spread
(f
d, max
) of the signal. If there is a direct path between transmit-
ter and receiver, the Doppler spread can be obtained directly from the relative
velocity (v
rel
) between both devices. The maximum Doppler shift is then given
by f
d, max
=
v
rel
/λ
. For an indirect nlos propagation path, however, the speed
at which the length of the path changes does not only depend on the incident
angle of the multipath component on the reflecting surface, but also on the
velocity of the object itself (Figure 4.5).
Typical values for the Doppler frequency shift start at a few Hertz and are often
limited to a few hundreds of Hertz, so the frequency offset itself won't be too
much of a headache for most applications. Rather, the underlying cause which
is described by the Doppler spread forms the real problem: the arrival time of
the multipath components changes over time, and so do the amplitude and the
phase of the channel response. The higher the Doppler spread of the channel
