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Performance of Communication Systems Corrupted by Noise Chap. 7
The output SNR can also be expressed in terms of the equivalent baseband system by substituting
Eq. (7–84) into Eq. (7–115), where P s = A 2 c >2:
(S>N) out
= b 2 (7–120)
(S>N) p a m 2
b
baseband V p
This equation shows that the improvement of a PM system over a baseband signaling
system depends on the amount of phase deviation that is used. It seems to indicate that we can
make the improvement as large as we wish simply by increasing b p . This depends on the types
of circuits used. If the peak phase deviation exceeds p radians, special “phase unwrapping”
techniques have to be used in some circuits to obtain the true value (as compared with the
relative value) of the phase at the output. Thus, the maximum value of b p m(t)/V p = D p m(t)
might be taken to be p. For sinusoidal modulation, this would provide an improvement of
D 2 p m 2 = p 2 >2, or 6.9 dB, over baseband signaling.
It is emphasized that the results obtained previously for (S/N) out are valid only when the
input signal is above the threshold [i.e., when (SN) in 7 1].
FM Systems
The procedure that we will use to evaluate the output SNR for FM systems is essentially the
same as that used for PM systems, except that the output of the FM detector is proportional to
du T (t)/dt, whereas the output of the PM detector is proportional to u T (t). The detector in the
angle modulated receiver of Fig. 7–21 is now an FM detector. The complex envelope of the
FM signal (only) is
where
g s (t) = A c e ju s(t)
t
u s (t) = D f m(l) dl
L
(7–121a)
(7–121b)
It is assumed that an FM signal plus white noise is present at the receiver input.
The output of the FM detector is proportional to the derivative of the composite phase at
the detector input:
r 0 (t) = a K (7–122)
2p b d lgT(t)
= a K dt 2p b du T (t)
dt
In this equation, K is the FM detector gain. Using the same procedure as that leading to
Eqs. (7–108), (7–110), and (7–111), we can approximate the detector output by
-q
r 0 (t) L s 0 (t) + n 0 (t)
(7–123)
where, for FM,
and
s 0 (t) = a K 2p b du s (t)
dt
= a KD f
2p b m(t)
(7–124a)