New Results on the Sum of Gamma Random Variates With Application to the Performance of Wireless Communication Systems over Nakagami-m Fading Channels

摘要

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