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Sec. 7–6 Comparison of Digital Signaling Systems 521
P e = probability of bit error
1.0
0.5
10 1
10 2
10 3
10 4
10 5
Q( 2(E b / N 0 ))
Polar baseband,
BPSK, QPSK,
or MSK
1
e (E b / N 0
2
)
DPSK
Q( E b / N 0 )
Unipolar baseband,
coherent OOK, or
coherent FSK
1
e(1/2)(Eb / N0)
2
Noncoherent OOK, or
noncoherent FSK
10 6
10 7
1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(E b /N 0 ) (dB)
Figure 7–14 Comparison of the probability of bit error for several digital signaling schemes.
7–6 COMPARISON OF DIGITALSIGNALING SYSTEMS
Bit-Error Rate and Bandwidth
Table 7–1 compares the BER for the different signaling techniques that were described in the
previous sections. Also tabulated is the minimum bandwidth for these signals. The minimum
absolute bandwidth is attained when sin x/x data pulses are used, as described in Chapters 3
and 5 (except for the special case of MSK).
In Fig. 7–14, the BER curves are plotted using the equations presented in Table 7–1.
Except for the curves describing the noncoherent detection cases, all of these results assume
that the optimum filter—the matched filter—is used in the receiver. In practice, simpler filters
work almost as well as the matched filter. For example, in a computer simulation of a BPSK
system with a three-pole Butterworth receiving filter having a bandwidth equal to the bit rate,
the E b /N 0 needs to be increased no more than 0.4 dB to obtain the same BER as that obtained
when a matched filter is used (for error rates above 10 -12 ).