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Sec. 7–2 Performance of Baseband Binary Systems 501
The performance of a matched-filter receiver is obtained by using Eq. (7–20), where the
sampling time is t 0 = T. The energy in the difference signal is E d = A 2 T, so that the BER is
P e = Q¢ C
A 2 T
2N 0
≤ = Q¢ C
E b
N 0
≤ (matched filter)
(7–24b)
where the average energy per bit is E b = A 2 T/2 because the energy for a binary 1 is A 2 T and
the energy for a binary 0 is 0. For the rectangular pulse shape, the matched filter is an integrator.
Consequently, the optimum threshold value is
V T = s 01 + s 02
2
= 1 2 a L
Often it is desirable to express the BER in terms of E b /N 0 , because it indicates the
average energy required to transmit one bit of data over a white (thermal) noise channel. By
expressing the BER in terms of E b /N 0 , the performance of different signaling techniques can
be easily compared.
A plot of Eq. (7–24b) is shown in Fig. 7–5.
0
T
A dt + 0b = AT
2
1.0
0.5
0 5
10 15
10 –1
10 –2
Matched-filter
reception of
unipolar baseband, coherent
OOK, or coherent FSK
P e =probability of bit error
10 –3
10 –4
Matched-filter
reception of
polar baseband,
BPSK, or QPSK
Q( 2(E b / N 0 ))
Q( E b / N 0 )
3 dB
10 –5
10 –6
Figure 7–5
10 –7
–1 0 1 2 3 4 5 6 7 8
(E b /N 0 ) (dB)
9 10 11 12
13 14 15
P e for matched-filter reception of several binary signaling schemes. (See Example7_02.m.)