PSK Error Performance with Gaussian Noise and Interference

Phase shift keying (psk) is becoming more popular as a modulation scheme for transmitting digital information. Lately much analysis has been done for both coherent and differentially coherent detection. Unfortunately the analyses done to date have generally considered only two signal degradations: channel anomalies (such as distortion, gain and delay variations, and so on) and thermally generated noise modeled by a gaussian random process. This article considers the effects of a spurious signal, or interference, falling in the band of the desired signal, as well as gaussian noise. It is understood t h a t both the noise and the interference additively corrupt the desired signal; these are the only perturbing factors. For coherent detection, the phase probability density function for the received composite of signal, noise, and interference is found. From this, the theoretical error probability may be evaluated for 413 414 T H E BELL SYSTEM TECHNICAL JOURNAL, FEBRUARY 1969 any M-phase system. We give comprehensive numerical results for the important cases, M = 2,3,4. For differential detection we present analysis and results for M = 2, 4, 8, and 16. In the binary case a simple closed form solution was found which yields both a good approximation and exact bounds to the actual error probability. T h e solutions to the multilevel M > 2 differential detection problem, which are exact, required machine computation of a double integral; complete numerical results are given. Finally, we draw general comparisons between coherent and differential detection error performance as affected by interference.