The best way to describe this phenomenon is to transmit a Quaternary Phase Shift Keying (QPSK) signal
and emphasize the received signal??™s constellation diagram at different points in time. Here the emphasis
is on both the amplitude variations and their associated phase shifts. This is described in Fig. 3.10.
WIRELESS MULTIPATH CHANNEL 125
Normalized Average Fade Time
Duration (AFTD)
0.001
0.01
0.1
1
??“40 ??“30 ??“20 ??“10 0 10
20*LOG(R) [dB]
Normalized AFTD
R
RRMS
Time
tj+1
??“ tj
??“
FIGURE 3.9 Rayleigh fading temporal variations to emphasize the AFTD.
FIGURE 3.8 Average fade time duration plot.
I
R(t)
Time
I I
Q
Q Q
A
B
C
FIGURE 3.10 QPSK example to demonstrate the Rayleigh fading phenomenon.
Figure 3.10 shows the received signal constellation diagram for QPSK after encountering the multipath
faded channel. The point worthy of mention is that as the signal encounters a fade not only does
the signal amplitude decrease significantly, but also the phase changes abruptly. The reduced signal
level or equivalently reduction in signal to noise ratio (SNR), makes estimating this abrupt phase
change challenging (see Fig. 3.11).
126 CHAPTER THREE
Rayleigh Fading Signal for fd = 200 Hz
??“35
??“30
??“25
??“20
??“15
??“10
??“5
0
5
0 0.
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