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Sec. 7–8 Output Signal-to-Noise Ratios for Analog Systems 535
Rayleigh noise. This produces a threshold effect. That is, ( S>N) out becomes very small when
(SN) in 6 1. In fact, it can be shown that (SN) out is proportional to the square of (SN) in for the
case of (S/N) in 6 1 [Schwartz, Bennett, and Stein, 1966]. Although the envelope detector is
greatly inferior to the product detector for small (SN) in , this deficiency is seldom noticed in
practice for AM broadcasting applications. This is because the AM listener is usually interested
in listening to stations only if they have reasonably good (SN) out , say 25 dB or more.
Under these conditions the envelope detector performance is equivalent to that of the product
detector. Moreover, the envelope detector is inexpensive and does not require a coherent reference.
For these reasons the envelope detector is used almost exclusively in AM broadcast
receivers. For other applications, such as listening to weak AM stations or for AM data transmission
systems, product detection may be required to eradicate the multiplicative noise that
would occur with envelope detection of weak systems.
DSB-SC Systems
As indicated in Chapter 5, the DSB-SC signal is essentially an AM signal in which the discrete
carrier term has been suppressed (i.e., equivalent to infinite percent AM). The modulating
waveform m(t) is recovered from the DSB-SC signal by using coherent detection, as shown in
Fig. 7–19. For DSB-SC,
g s (t) = A c m(t)
Following the development leading to Eq. (7–89), the SNR for DSB-SC is
(7–96)
Using Eq. (7–90), we obtain
(S>N) out
(S>N) in
= 2
(S>N) out
(S>N) baseband
= 1
(7–97)
(7–98)
Thus, the noise performance of a DSB-SC system is the same as that of baseband signaling
systems, although the bandwidth requirement is twice as large (i.e., B T = 2B).
SSB Systems
The receiver for an SSB signal is also shown in Fig. 7–19, where the IF bandwidth is now
B T = B. The complex envelope for SSB is
g s (t) = A c [m(t) ; jmN (t)]
(7–99)
where the upper sign is used for USSB and the lower sign is used for LSSB. The complex
envelope for the (total) received SSB signal plus noise is
The output of the product detector is
g T (t) = [A c m(t) + x n (t)] + j[;A c mN (t) + y n (t)]
mN (t) = Re[g T (t)] = A c m(t) + x n (t)
(7–100)
(7–101)