MRC reception of rectangular M-ary QAM signals over frequency-flat Rayleigh fading channels with distinctive branch fading amplitudes

The usual approach to calculate the symbol error rate (SER) for multilevel (M-ary) signalling over a fading channel is to first find the average SER in an additive white Gaussian noise channel conditioned on a fixed fading parameter and then average this SER over the fading parameter (averaging over the fading parameter at the last stage). This usual approach is called the postaveraging method. A different approach, called the preaveraging method, that is the averaging over the fading parameter is performed on the probability density function of per symbol estimate error in an earlier stage of the derivation process. By doing so, it is possible to obtain an exact closed-form expression of SER for the special case of maximal ratio combining reception of arbitrary rectangular M-ary quadrature amplitude modulation (QAM) signalling over frequency-flat Rayleigh fading channels, which has not been obtained using the usual postaveraging method. For the case under study, it is assumed that all diversity channels have independent, but distinctive, fading amplitudes. The SER results can be applied to any M-size rectangular QAM constellation. The method can be readily extended to square M-ary QAM, M-ary pulse amplitude modulation (PAM) and binary antipodal signalling. It is thought that this method and the closed-form SER result have never been treated and exposed elsewhere for the arbitrary rectangular QAM case under consideration. Monte Carlo simulations prove to be in excellent agreement with the theoretical results.