OPTIMAL DETECTION OF DIGITAL DATA OVER THE NONSELECTIVE RAYLEIGH FADING CHANNEL WITH DIVERSITY RECEPTION

Based on the criterion of minimum symbol error probability, we consider symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulations over L independent diversity channels with AWGN and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear, and readily implementable, and can be interpreted as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of SNR and order of diversity. A main result of our work is that optimal data detection on a fading channel should be performed using MMSE estimates of the quadrature amplitudes of the channel fading processes as a coherent reference. Conventional receivers employing carrier loops to provide the coherent reference are not optimum, and lead to more complicated receiver structures.