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 (H ̂ ) 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 . Copyright © 2014 John Wiley & Sons, Ltd.