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 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 is user-of-interest, are 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 ((Formula presented.)) 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.