(3.46)
A plot of this temporal correlation for various Doppler frequencies is given in Fig. 3.20.
As previously discussed, there can be a few different definitions used for the CBW of the channel.
In Fig. 3.21 we show two of them for sake of comparison.
r(0, t) J2
o (2p # fm # t)
f 0
Coherence Bandwidth
0.0E+0
5.0E+7
1.0E+8
1.5E+8
1.0E??“9 3.0E??“9 5.0E??“9 7.0E??“9 9.0E??“9 1.1E??“8 1.3E??“8 1.5E??“8 1.7E??“8 1.9E??“8
RMS Delay Spread
CBW (Hz)
CBW = 1/5t
CBW = 1/50t
CBW = 1/2tPi
Temporal Correlation of a Faded Signal
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.005 0.01 0.015 0.02 0.025 0.03
Time (seconds)
Correlation Value
fd = 50 Hz, Jo(x)^2
fd = 200 Hz, Jo(x)^2
FIGURE 3.20 Temporal correlation of two time samples.
The plot shows significant deviation between the definitions when the delay spread is very
small.
3.4.3 Coherence Time (CT)
The PDP presented earlier was used to describe the FSF nature of the wireless channel by defining
the CBWin the vicinity of the receiver. The signal envelope statistical variations were also presented
earlier. However, they do not describe the time varying phenomenon of the wireless channel. This will
be accomplished by relating the CT to the Doppler spread.
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