B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

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INTRODUCTION TO INFORMATION THEORY
Figure 13. 1 1
Comparison of
ideal system
behavior to that
of PCM.
8
7
r
6
Rb 5
Br
4
Ideal
PCM
I
9 dB
M = 8
M = 7
M = 6
M= 5
M=4
3
2
I
I
I
I
M = 3
M = 2 ( binary)
20 10 0 10 20 30 40
S-
N' dB- '
or
(13.79)
This is clearly seen in Fig. 13. 11 (solid horizontal lines).
Orthogonal Signaling
We have already shown that fEq. (10.122)] for M -ary orthogonal signaling, the error-free
communication rate is
bit/s (13.80)
We showed in Eq. (13.64) that this is precisely the rate of error-free communication over
an ideal channel with infinite bandwidth. Therefore, as M - oo, the bandwidth of an M -ary
scheme also approaches infinity, and its rate of communication approaches that of an ideal
channel.
13.7 FREQUENCY-SELECTIVE CHANNEL CAPACITY
Thus far, we have limited the discussion of capacity to distortionless channels of finite bandwidth
under white Gaussian noise. Such a channel model is suitable for application when
channels are either flat or flat fading. In reality, we often face many types of complex channels.
In particular, we have shown, in Chapter 12, that most wireless communication channels in
the presence of significant multipath tend to be frequency-selective channels. We now take a
look at the capacity of frequency-selective channels that do not exhibit a distortionless (flat)
spectrum.
First, consider a band-limited AWGN channel whose random output is
y =H• x+n