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Sec. 7–2 Performance of Baseband Binary Systems 499
r(t)=s(t) + n(t)
where
n(t)=colored noise
Prewhitening filter
H p (f)=
1 ,
p n (f)
where p n ( f ) is the
PSD of the colored
input noise, n(t)
~
r(t)=s(t)+n(t)
~ ~
Processing
circuits
Baseband analog
output
Sample
and
r 0 (t)
hold
at t 0
r 0 (t 0 )
Threshold
device
~ m
0
V T
r 0
m ~
Figure 7–3
Clock
Matched-filter receiver for colored noise.
'
so that the noise that appears at the filter output, n (t), is white. We have now converted the
colored noise problem into a white noise problem, so that the design techniques presented in
the preceding section are applicable. The matched filter in the processing circuits is now
matched to the filtered waveshapes,
s ' (t) = s ' 1(t) = s 1 (t) * h p (t) (binary 1)
' '
s (t) = s 2(t) = s 2 (t) * h p (t) (binary 0)
(7–22a)
(7–22b)
where h p (t) = - 1 [H p (f)]. Since the prewhitening will produce signals s1(t)
and s2(t),
which
are spread beyond the T-second signaling interval, two types of degradation will result:
• The signal energy of the filtered signal that occurs beyond the T-second interval will not
be used by the matched filter in maximizing the output signal.
• The portions of signals from previous signaling intervals that occur in the present signaling
interval will produce ISI. (See Chapter 3.)
Both of these effects can be reduced if the duration of the original signal is made less than
the T-second signaling interval, so that almost all of the spread signal will occur within that
interval.
'
'
7–2 PERFORMANCE OF BASEBAND BINARY SYSTEMS
Unipolar Signaling
As illustrated in Fig. 7–4b, the two baseband signaling waveforms are
s 1 (t) =+A, 0 6 t … T (binary 1)
s 2 (t) = 0, 0 6 t … T (binary 0)
(7–23a)
(7–23b)
where A 7 0. This unipolar signal plus white Gaussian noise is present at the receiver input.
First, evaluate the performance of a receiver that uses an LPF, H(f), with unity gain.
Choose the equivalent bandwidth of this LPF to be B 7 2/T, so that the unipolar signaling
waveshape is preserved (approximately) at the filter output, yet the noise will be reduced by