Bounds on the error probability of FSK and PSK receivers due to non-Gaussian noise in fading channels

Abstract

This paper derives upper and lower bounds on binary error probability as a function of signal-to-noise ratio for several digital data systems operating over a complex Gaussian fading channel. Bounds of varying degrees of tightness are obtained by placing certain physically meaningful constraints on the allowable detected noise probability distributions. Detailed derivations are given for bounds corresponding to constraints on the "crest-factor" of the detected noise and on the ratio of peak noise power to average signal power. The calculations include the effects of diversity corn-billing and are applicable to frequency-shift keying (FSK), binary and quaternary phase-shift keying (PSK) using a pilot tone as reference, and binary and quaternary PSK using the previous signaling element as a phase reference. It is an interesting result of this paper that for moderate noise crest factors the upper and lower bounds can be rather close. In the particular case of nondiversity operation, for example, the lower bound actually becomes approximately equal to the upper bound at SNR's of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">30</tex> dB or greater for noises with a crest factor as high as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</tex> dB.