4.6 P _e PERFORMANCE OF BINARY COHERENT PSK SYSTEMS

In this section the correlation receiver (matched filter) theory is applied to the P _e derivation of optimal coherent binary phase-shift-keyed (BPSK) systems. The carrier and symbol timing recovery circuits are assumed to provide ideal synchronization signals that are free from phase noise. The principles, design, and performance degradations caused by imperfect synchronization circuits are presented in Chapter 7.

The BPSK signals are

To simplify the P _e derivation, we assume that the frequency of the carrier generator, shown in Fig. 4.13, is an integer multiple of the bit rate; that is,

Figure 4.13: Coherent BPSK modulator, corresponding correlation receiver, and Nyquist receiver. (a) BPSK modulator. m(t), infinite bandwidth signal. s(t), bandlimited signal. (b) Correlation receiver. This correlation (matched filter) receiver is for the infinite bandwidth transmitter and channel model. (c) Nyquist receiver. LPF _R is the equivalent LPF of the bandpass channel (in some applications replaces the BPF _R filter). Its transfer function equals the square root of the raised-cosine channel.

In numerous applications the data rate fluctuates (e.g., the source rate could change 50 b/s of its nominal 10-Mb/s rate). On the other hand, the carrier frequency and the radiated spectra must be tightly controlled. Thus, to satisfy equation (4.85), a fairly complex modem including a bit stuffing device may be required [Intelsat, 1980]. Fortunately, even though equation (4.85) is not satisfied, the P _e performance degradation is practically negligible