Error Probablity for Optimal and Suboptimal Quadratic Receivers in Rapid Rayleigh Fading Channels

The exact performance of optimal and suboptimal quadratic receivers in a binary hypothesis test between jointly distributed zero mean complex Gaussian variates is derived. The probability of error is given as a function of the characteristic values of a generalized eigenvalue problem set up in terms of the covariance matrix of the received signal-plus-noise and in the matrix of the quadratic form of the receiver. The results include the exact performance of various types of suboptimal receivers including those previously derived for the envelope matched filter for MFSK and the noncoherent DBPSK receiver in rapid Rayleigh fading, nonfrequency-selective channels. Also, the performance of near-optimal stationary process-long observation time [SPLOT] receivers, "energy detectors," and other approximately optimal receivers may be calculated for noncoherent signaling in the same channel.