Maximal-ratio combining over Nakagami fading channels with an arbitrary branch covariance matrix

The error probability of maximal ratio combiners (MRCs) in a correlated Nakagami environment with an arbitrary branch covariance matrix is not available in the literature although some work has been done for two special cases with constant and exponential correlations. Correlation structures of this type, though of theoretical interest, may not match to practical situations, even for an antenna array of a totally symmetrical configuration. In this paper, we tackle the general problem by virtue of characteristic functions, avoiding the difficulty of explicitly obtaining the probability density function (PDF) for the signal-to-noise ratio (SNR) at the MRC output. We derive a simple closed-form solution for arbitrarily correlated channels with an integral fading parameter and a solution in the form of a one-fold integral for a fading parameter of nonintegral values. Simple algorithms have also been developed for their efficient implementation. The formulas are then used to analyze two possible antenna configurations for a base station, ending up with some findings of interest to system design