Partially coherent, suboptimal detectors over Rayleigh fading diversity channels

Detection over Rayleigh fading diversity channels with unknown amplitudes, and perfectly estimated phases is studied for binary, uniformly orthogonal signaling. The optimum receiver is derived. Two suboptimal receivers are considered: linear equal gain combining (LEGC) and quadratic coherent combining, which is also a generalized likelihood ratio test (GLRT) receiver. Conditional, average and asymptotic BER expressions are derived for the GLRT receiver. LEGC and GLRT are compared with respect to asymptotic BER, and exact BER for dual diversity. The authors show that LEGC is better over fading channels, while quadratic coherent combining is conditionally better whenever the different branch signals are significantly disproportionate.