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536
Performance of Communication Systems Corrupted by Noise Chap. 7
The corresponding SNR is
(S/N) out = A c 2 m 2 (t)
x n 2 (t)
= A c 2 m 2 (t)
N 0 B
(7–102)
where x 2 n = n 2 = 2(N 0 >2) (B). Using Eq. (6–133g), we see that the input signal power is
P s = 1 2 |g s(t)| 2 = A c 2
(7–103)
2 3m2 + (mN ) 2 4 = A 2 c m 2
and that the input noise power is P n = n 2 (t) = N 0 B. Thus,
Similarly,
(S>N) out
(S>N) in
= 1
(S>N) out
(S>N) baseband
= 1
(7–104)
(7–105)
SSB is exactly equivalent to baseband signaling, in terms of both the noise performance
and the bandwidth requirements (i.e., B T = B). Furthermore, Eqs. (7–98) and (7–105) show
that DSB, SSB, and baseband signaling systems are all equivalent in output SNR.
PM Systems
As shown in Fig. 7–21, the modulation on a PM signal is recovered by a receiver that uses a
(coherent) phase detector. (In Chapter 4, it was found that a phase detector could be realized
by using a limiter that followed a product detector when b p is small.) The PM signal has a
complex envelope of
g s (t) = A c e ju s(t)
(7–106a)
where
u s (t) = D p m(t)
The complex envelope of the composite signal plus noise at the detector input is
g T (t) = |g T (t)e juT(t) = [g s (t) + g n (t)]
= A c e jus(t) + R n (t) e ju n(t)
(7–106b)
(7–107)
Angle modulated
signal plus noise
r(t)=Re{g T
(t) e j(ct֬c) }
r 0 (t)= g T (t), for PM
d g T (t)
r 0 (t)= , for FM
dt
IF filter
Bandwidth=B T
Detector
(PM or FM)
Low-pass
filter
Bandwidth=B
m(t) ~
Figure 7–21
Receiver for angle-modulated signals.