Performance of the noncoherent biquadratic and GLRT receivers overtwo-path channels with known amplitudes and Rayleigh fading

Noncoherent detection over Rayleigh fading diversity channels with known or perfectly estimated amplitudes is studied for binary, uniformly orthogonal signaling. The optimum receiver is well known, but is too difficult to implement. Hence, two suboptimal receivers are considered: the “biquadratic” receiver, optimum at low signal-to-noise ratios (SNR's), and the “bilinear” receiver (optimum at high SNR's) which is also a generalized likelihood ratio test (GLRT) receiver for this case. We analyze the performances of the two suboptimal receivers over two-path channels and compare them to the basic quadratic receiver. For this purpose we present a general method for computing the error probability that can be applied to any dual-diversity binary detection problem whenever the method of characteristic functions fails. We present the exact analytical expressions for the biquadratic receiver, and the numerically computed results for the GLRT receiver, in terms of the conditional, average and asymptotic error probabilities. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest