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Performance of Communication Systems Corrupted by Noise Chap. 7
Example 7–9 IMPROVEMENT FACTOR FOR AN FM SYSTEM
Using Eq. (7–29), evaluate and plot the FM system improvement factor, I = (SN) out /(S/N) in ,
in dB units as a function of b f for the case of sinusoidal modulation. See Example7_09.m for
the solution.
The output SNR can be expressed in terms of the equivalent baseband SNR by substituting
Eq. (7–84) into Eq. (7–127), where P s = A 2 c >2,
(S>N) out
(S>N) baseband
= 3b f 2 a m V p
b 2
(7–130)
For the case of sinusoidal modulation, (m>V p ) 2 = 1 2 ,
and Eq. (7–130) becomes
(S>N) out
(S>N) baseband
= 3 2 b f 2 (sinusoidal modulation)
(7–131)
At first glance, these results seem to indicate that the performance of FM systems can be
increased without limit simply by increasing the FM index b f . However, as b f is increased, the
transmission bandwidth increases, and, consequently, (SN) in decreases. These equations for
(SN) out are valid only when (SN) in 1 (i.e., when the input signal power is above the
threshold), so (SN) out does not increase to an excessively large value simply by increasing
the FM index b f . Plots of Eq. (7–131) are given by the dashed lines in Fig. 7–24.
The threshold effect was first analyzed in 1948 [Rice, 1948; Stumpers, 1948]. An
excellent tutorial treatment has been given by Taub and Schilling [1986]. They have shown
that Eq. (7–131) can be generalized to describe (S/N) out near the threshold. For the case of
sinusoidal modulation, the output SNR for a FM discriminator is shown to be
a S N b out
=
1 + a 12 p b fb a S N b baseband
3
2 b f 2 (S>N) baseband
1
ee- c
2(b f + 1) a S N b df
baseband
(7–132)
(No deemphasis is used in obtaining the result.) This output SNR characteristic showing the
threshold effect of an FM discriminator is plotted by the solid lines in Fig. 7–24. This figure
illustrates that the FM noise performance can be substantially better than baseband performance.
For example, for b f = 5 and (S/N) baseband = 25 dB, the FM performance is 15.7 dB
better than the baseband performance. The performance can be improved even further by the
use of deemphasis, as we will demonstrate in a later section.
Example 7–10 NOISE PERFORMANCE FOR AN FM SYSTEM
Using Eq. (7–132), evaluate and plot (S/N) out as a function of (S/N) baseband in dB units for sinusoidal
modulation. Plot for two cases: b f = 10 and b f = 2. See Example7_10.m for the solution.
Compare these results with those shown in Fig. 7–24.