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Sec. 7–3 Coherent Detection of Bandpass Binary Signals 505
r(t)=s(t)+n(t)
Receiver
s
r(t)= +n(t)
(
1 (t)
or
s 2 (t)
Low-pass filter r 0 (t) Sample r 0 (t 0 )
or
and
N
where p 0
n (f)=
matched filter
hold
2 H(f)
(
2 cos ( c t+¨c)
(coherent reference)
Baseband
analog output
Threshold
device
~ m m ~
0
V T
r 0
Digital
output
(a) Receiver
s(t)
t
r(t)
t
(b) OOK Signaling
s(t)
t
r(t)
t
(c) BPSK Signaling
Figure 7–7
Coherent detection of OOK or BPSK signals.
where the PSD of n(t) is n (f ) = N 0 /2 and u n is a uniformly distributed random variable that
is independent of u c .
The receiving filter H(f ) of Fig. 7–7 may be some convenient LPF, or it may be a
matched filter. Of course, the receiver would be optimized (for the lowest P e ) if a matched
filter were used.
First, evaluate the performance of a receiver that uses an LPF where the filter has a
DC gain of unity. Assume that the equivalent bandwidth of the filter is B Ú 2/T, so that the