A Trivariate Nakagami-m Distribution with Arbitrary Covariance Matrix and Applications to Generalized-Selection Diversity Receivers

This paper deals with a trivariate Nakagami-m distribution derived from the diagonal elements of a Wishart matrix. For this distribution, infinite series representations for its probability density and cumulative distribution functions are derived having an arbitrary covariance matrix and integer-order fading parameters. Moreover, upper bounds on the error resulting from truncating the infinite series are obtained. Based on the derived formulas, the performance of triple-branch generalized selection combining (GSC) receivers is analyzed. For this type of receivers, the outage and the average bit error probability for a variety of modulation schemes are analytically obtained. The performance of GSC receivers is compared to that of conventional selection and maximal-ratio diversity schemes. In order to check the accuracy and convergence of the derived formulas, various performance evaluation results are presented and compared to equivalent simulation ones.