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Performance of Communication Systems Corrupted by Noise Chap. 7
r(t)=s(t)+n(t)
(
s 1 (t)
r(t)= or
s 2 (t)
(
+n(t)
N 0
Low-pass filter
or
matched filter
H( f )
r 0 (t) Sample
and
r 0 (t 0 )
hold
where p n (f)= 2
Figure 7–4 Receiver for baseband binary signaling.
Threshold
device
~ m
0
V T
r 0
Threshold
device
m ~
(a) Receiver
s(t)
t
r(t)
(b) Unipolar Signaling
t
s(t)
t
r(t)
t
(c) Polar Signaling
the filter. † Thus, s 01 (t 0 ) ≈ A and s 02 (t 0 ) ≈ 0. The noise power at the output of the filter is
s 2 0 = (N 0 >2) (2B), where B is the equivalent bandwidth of the filter. The optimum threshold
setting is then V T = 1 2 A. When we use Eq. (7–17), the BER is
A
P e = Q¢ 2
≤ (low-pass filter)
C 4N 0 B
for a receiver that uses an LPF with an equivalent bandwidth of B.
(7–24a)
† From Eq. (3–39b), the PSD of a unipolar signal (rectangular pulse shape) is proportional to
[sin (pfT)/(pfT)] 2 , so that the second null bandwidth is 2/T. Referring to study-aid examples SA7–1 and SA7–2, it
is shown that if the equivalent bandwidth of the LPF is greater than 2/T, the filtered signal will consist of pulses that
are almost rectangular in shape and the peak values of the pulses are approximately equal to A.