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

774 INTRODUCTION TO INFORMATION THEORY
Figure 13. 10
Ideal behavior of
SNR vs. y for
various ratios of
Br to B.
60
t
50
so
No , dB 40
BT = oo 16
B
8 5 3
2
30
20
10
0
- 1 0 0
10
20 30
'/, dB --
Equations (13.70) and (13.71) give the ideal law of exchange between the SNR and the bandwidth.
The output SNR S0/N0 is plotted in Fig. 13.10 as a function of y for various values of
Br/B.
The output SNR increases exponentially with the bandwidth expansion factor Br /B. This
means that to maintain a given output SNR, the transmitted signal power can be reduced
exponentially with the bandwidth expansion factor. Thus, for a small increase in bandwidth,
we can cut the transmitted power considerably. On the other hand, for a small reduction in
bandwidth, we need to increase the transmitted power considerably.
Let us now investigate how two digital systems fare in comparison to the ideal system.
PCM
As seen earlier, M-ary PCM shows a saturation effect unless we go to higher values of M as
y increases. If the message signal is quantized in L levels, then each sample can be encoded
by logM L number of M-ary pulses. If B is the bandwidth of the message signal, we need to
transmit 2B samples per second. Consequently, R M , the number of M-ary pulses per second, is
Also, the transmission bandwidth Br is half the number of (M -ary) pulses per second. Hence,
(13.72a)
From Eq. (10.98a), the power Si is found as
(13.72b)
Also,
(13.73)