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Performance of Communication Systems Corrupted by Noise Chap. 7
Channel
n(t)
m(t)=s(t)
Message (modulation)
signal
B=bandwidth of m(t)
p n =
N 0
2
Receiver
Low-pass
filter
Bandwidth=B
m(t)=s(t)+n(t)
~
P
(S/N) baseband = s
N 0 B
Figure 7–18
Baseband system.
baseband (modulating) signal where the same baseband modulating signal is used for all
cases so that the same basis of comparison will be realized. [If B were chosen to be the
bandwidth of the input-modulated signal, B T , the comparison would not be on an equal
noise PSD basis of N 0 2 for a fixed value of (SN) baseband because the B T values for AM and
FM signals are different.]
The SNR at the receiver input can also be obtained; it is
a S N b in
=
P s
N 0 B T
= a S N b a B b
baseband B T
(7–85)
where B T is the bandwidth of the bandpass signal at the receiver input.
(SN) out will now be evaluated for several different systems.
AM Systems with Product Detection
Figure 7–19 illustrates the receiver for an AM system with coherent detection. From Eq. (5–3),
the complex envelope of the AM signal is
g s (t) = A c [1 + m(t)]
The complex envelope of the composite received signal plus noise is
g T (t) = [A c + A c m(t) + x n (t)] + jy n (t)
(7–86)
Modulated signal
plus noise in
r(t)=s(t)+n(t)=Re[g T
(t) e j( ct+¨c) ]
Bandwidth=
(
IF filter
2B, for AM and
DSB-SC
B, for SSB
(
Product detector
Low-pass
filter
Bandwidth = B
m(t)= ~
Re[g T (t)]
(S/N) out
2 cos( c t+¨c)
Figure 7–19
Coherent receiver.