For example,
let us consider two signals whose frequency separation is varied, and comparisons are made at
the same time interval, for example, .
(3.45)
Aplot of this function is given in Fig. 3.19 for two values of the RMS delay spread (2 sec and 100 nsec).
r(f, 0)
1
1 [2p # f ]2 # tRMS
t 0
r(f, t)
J2
o (2p # fm # t)
1 [2p # f ]2 # tRMS
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(a) Flat Fading Relationship.
(b) Frequency Selective Fading Relationship.
PDP
Arrival Time (seconds) t1 t2
PDP
Arrival Time (seconds) t2 t1
Symbol Time Interval
Symbol Time Interval
FIGURE 3.18 Frequency selective fading example.
Envelope Correlation Function ?? (??†f, 0)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 200 400 600 800 1000 1200
Frequency Separation (??†f )
r
r (2 ?µsec)
r (100 nsec)
FIGURE 3.19 Envelope correlation plot for two signals separated by f Hz.
134 CHAPTER THREE
FIGURE 3.21 Coherence bandwidth comparisons.
This plot shows the envelope correlation decreases as the frequency separation between the two
signals increases. Also the rate of decay for the correlation function increases as the CBWdecreases.
Next consider the example of 2 time samples of a single signal, whose time separation is varied,
and comparisons are made at the same frequency, for example, .
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