Abstract
The statistical characterization of a sum of random variables (RVs) is useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of a sum of independent but not identically distributed (i.n.i.d.) Fisher-Snedecor F RVs. Both PDF and CDF are expressed in terms of the multivariate Fox's H-function. Besides, a simple and accurate approximation to the sum of i.n.i.d. Fisher-Snedecor F variates is presented using the moment matching method. The obtained PDF and CDF are used to evaluate the performance of wireless communication applications including the outage probability, the effective capacity, and the channel capacities under four different adaptive transmission strategies. Moreover, the corresponding approximate expressions are obtained to provide useful insights for the design and deployment of wireless communication systems. In addition, we derive simple asymptotic expressions for the proposed mathematical analysis in the high signal-to-noise ratio regime. Finally, the numerical results demonstrate the accuracy of the derived expressions.
Highlights
R ECENTLY, the Fisher-Snedecor F distribution was proposed [1] as a tractable fading model to describe the combined effects of shadowing and multipath fading in future wireless communications
Fisher-Snedecor F random variables (RVs) and leverage the probability density function (PDF) and cumulative distribution function (CDF) expressions to analyze the performance of the maximal-ratio combining (MRC) receiver in terms of outage probability, channel capacity, and effective capacity
SUM OF FISHER-SNEDECOR F RANDOM VARIABLES we investigate the statistical characterization of the sum of Fisher-Snedecor F RVs and derive exact closed-form expressions for PDF and CDF
Summary
R ECENTLY, the Fisher-Snedecor F distribution was proposed [1] as a tractable fading model to describe the combined effects of shadowing and multipath fading in future wireless communications. For the i.i.d. case, the difficulty of calculation will not be reduced either To fill this gap, we re-investigate the statistical characterization of the sum of i.n.i.d. Fisher-Snedecor F RVs and leverage the PDF and CDF expressions to analyze the performance of the MRC receiver in terms of outage probability, channel capacity, and effective capacity. The single F distribution is a highly accurate approximation to the sum of F RVs
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