Analysis of the biquadratic and bilinear noncoherent receivers over two-path Rayleigh fading with known amplitudes

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 complicated to implement or analyze. Two suboptimal receivers are considered: the “biquadratic” receiver, optimum at low SNR´s, and the “bilinear” receiver, optimum at high SNR´s. The bilinear receiver 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 show their improvement compared to the basic quadratic noncoherent 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 function (CF) fails. We present the exact analytical expressions for the biquadratic receiver, and the numerically computed results for the GLRT receiver. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest