Performance of receivers with linear detectors

The false-alarm and detection probabilities of a receiver summing M independent outputs of a linear detector are calculated by numerical saddlepoint integration. The saddlepoint approximation is also considered. Both constant-amplitude and Rayleigh-fading signals are treated, and the relative efficiency of the quadratic and the linear detectors for these is calculated for a broad range of values of M. The numerical integration method is the more efficient, the smaller the false-alarm probability or the false-dismissal probability, that is, under just those conditions for which the terms in the Gram-Charlier series oscillate most violently and the series becomes least reliable. The simpler saddlepoint approximation yields values that in those same regions have been found close enough to the exact probabilities to be adequate for most engineering purposes. The larger the number M of samples, the more efficient methods are.<
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