563489578934

Sec. 7–4 Noncoherent Detection of Bandpass Binary Signals 517
Differential Phase-Shift Keying
Phase-shift-keyed signals cannot be detected incoherently. However, a partially coherent technique
can be used whereby the phase reference for the present signaling interval is provided
by a delayed version of the signal that occurred during the previous signaling interval. This is
illustrated by the receivers shown in Fig. 7–12, where differential decoding is provided by
the (one-bit) delay and the multiplier. If a BPSK signal (no noise) were applied to the receiver
input, the output of the sample-and-hold circuit, r 0 (t 0 ), would be positive (binary 1) if the present
data bit and the previous data bit were of the same sense; r 0 (t 0 ) would be negative (binary 0)
if the two data bits were different. Consequently, if the data on the BPSK signal are differentially
encoded (e.g., see the illustration in Table 3–4), the decoded data sequence will be
recovered at the output of this receiver. This signaling technique consisting of transmitting a
differentially encoded BPSK signal is known as DPSK.
The BER for these DPSK receivers can be derived under the following assumptions:
• The additive input noise is white and Gaussian.
• The phase perturbation of the composite signal plus noise varies slowly so that the
phase reference is essentially a constant from the past signaling interval to the present
signaling interval.
• The transmitter carrier oscillator is sufficiently stable so that the phase during the present
signaling interval is the same as that from the past signaling interval.
The BER for the suboptimum demodulator of Fig. 7–12a has been obtained by
J. H. Park for the case of a large input signal-to-noise ratio and for B T 7 2/T, but yet not too
large. The result is [Park, 1978]
P e = Q¢ C
(E b >N 0 )
1 + [(B T T>2)>(E b >N 0 )] ≤
(7–66a)
For typical values of B T and E b /N 0 in the range of B T = 3/T and E b /N 0 = 10, this BER can be
approximated by
P e = QA 3 E b >N 0 B
(7–66b)
Thus, the performance of the suboptimum receiver of Fig. 7–12a is similar to that obtained for
OOK and FSK as plotted in Fig. 7–14.
Figure 7–12b shows one form of an optimum DPSK receiver that can be obtained
[Couch, 1993, Fig. 8–25]. The BER for optimum demodulation of DPSK is
P e = 1 2 e-(E b>N 0 )
(7–67)
Other alternative forms of optimum DPSK receivers are possible [Lindsey and Simon, 1973;
Simon, 1978].
A plot of this error characteristic for the case of optimum demodulation of DPSK,
Eq. (7–67), is shown in Fig. 7–14. In comparing the error performance of BPSK and DPSK
with optimum demodulation, it is seen that for the same P e , DPSK signaling requires, at most,
1 dB more E b /N 0 than BPSK, provided that P e = 10 - 4 or less. In practice, DPSK is often used
instead of BPSK, because the DPSK receiver does not require a carrier synchronization circuit.