ERROR RATE CONSIDERATIONS FOR COHERENT PHASE-SHIFT KEYED SYSTEMS WITH CO-CHANNEL INTERFERENCE

In this paper we present a theoretical analysis of the performance of an m‐phase coherent phase‐shift keyed system in the presence of random gaussian noise and interference. An explicit expression is given for the probability of error of the phase angle of the received signal; we show that this probability of error can be expressed as a converging power series. We show that the coefficients of this series are expressible in terms of well‐known and well‐tabulated functions, and we give methods of evaluating the character error rates of the systems. We also show that this error rate is minimum when all the interference power is concentrated in a single interferer, and that it attains its maximum [Pm]max when the total interference power is equally distributed, amongst the K interferers. The limiting case when K goes to infinity is considered. The cases of K = 1, and m = 2, 4, 8, and 16 are treated in some detail, and the results are given graphically. The usefulness of the results ‐presented in this paper is that the designer can have at his disposal very simple expressions with which to evaluate the performance of any given Coherent Phase‐Shift Keyed sys‐tem when the received signal is corrupted by both interference and random gaussian noise. © 1969 The Bell System Technical Journal