New results on the sum of Gamma random variates with application to the performance of wireless communication systems over Nakagami-m fading channels

The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed Gamma variates, applicable to the output statistics of maximal ratio combining (MRC) receiver operating over Nakagami-m fading channels or in other words to the statistical analysis of the scenario where the sum of squared Nakagami-m distributions are user-of-interest, is presented in closed-form in terms of well-known Meijer’s G function and easily computable Fox’s H̄ function for integer valued and non-integer valued m fading parameters. Further analysis, particularly on bit error rate via a PDF-based approach is also offered in closed form in terms of Meijer’s G function and Fox’s H̄ function for integer valued fading parameters, and extended Fox’s H̄ function (Ĥ) for non-integer valued fading parameters. Our proposed results complement previous known results that are either expressed in terms of infinite sums, nested sums, or higher order derivatives of the fading parameter m.