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Performance of Communication Systems Corrupted by Noise Chap. 7
7–9 COMPARISON OF ANALOG SIGNALING SYSTEMS
Table 7–2 compares the analog systems that were analyzed in the previous sections. It is seen
that the nonlinear modulation systems provide significant improvement in the noise performance,
provided that the input signal is above the threshold. Of course, the improvement in
the noise performance is obtained at the expense of having to use a wider transmission bandwidth.
If the input SNR is very low, the linear systems outperform the nonlinear systems.
SSB is best in terms of small bandwidth, and it has one of the best noise characteristics at
low input SNR.
The selection of a particular system depends on the transmission bandwidth that is
allowed and the available receiver input SNR. A comparison of the noise performance of
these systems is given in Fig. 7–27, with V p = 1 and For the nonlinear systems a
bandwidth spreading ratio of B T /B = 12 is chosen for system comparisons. This corresponds
to a b f = 5 for the FM systems cited in the figure and corresponds to commercial
FM broadcasting.
Note that, except for the “wasted” carrier power in AM, all of the linear modulation
methods have the same SNR performance as that for the baseband system. (SSB has the same
performance as DSB, because the coherence of the two sidebands in DSB compensates for the
half noise power in SSB due to bandwidth reduction.) These comparisons are made on the
basis of signals with equal average powers. If comparisons are made on equal peak powers
(i.e., equal peak values for the signals), then SSB has a (S/N) out that is 3 dB better than DSB
and 9 dB better than AM with 100% modulation (as demonstrated by Prob. 7–34). Of course,
when operating above the threshold, all of the nonlinear modulation systems have better SNR
performance than linear modulation systems, because the nonlinear systems have larger transmission
bandwidths.
Ideal System Performance
What is the best noise performance that is theoretically possible? How can wide transmission
bandwidth be used to gain improved noise performance? The answer is given by Shannon’s
channel capacity theorem. The ideal system is defined as one that does not lose channel
capacity in the detection process. Thus,
C in = C out
m 2 = 1 2
(7–142)
where C in is the bandpass channel capacity and C out is the channel capacity after detection.
Using Eq. (1–10) in Eq. (7–142), we have
B T log 2 [1 + (S>N) in ] = B log 2 [1 + (S>N) out ]
(7–143)
where B T is the transmission bandwidth of the bandpass signal at the receiver input and B is
the bandwidth of the baseband signal at the receiver output. Solving for (S/N) out , we get
a S N b out
= c1 + a S B T >B
N b d - 1
in
(7–144)