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

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

2012-02-12

arxiv.org/abs/1202.2576v2

Computer Science

Information Theory

Submitted to IEEE Transactions on Communications, 5 figures, 4 tables

Scientific paper

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 \={H} function for integer valued and non-integer valued diversity orders (i.e., m fading parameter of Nakagami fading environment), respectively. Further analysis, particularly on bit error rate via PDF-based approach, too is represented in closed form in terms of Meijer's G function and Fox's \={H} function for integer valued diversity orders, and extended Fox's \={H} function ($\hat{H}$) for non-integer valued diversity orders. The proposed results complement previous elegant results that are either evolved in closed-form, or expressed in terms of infinite sums or higher order derivatives of the diversity order m.

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