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 $\mathcal {F}$ 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 $\mathcal {F}$ 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.

中文翻译：

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Fisher-Snedecor的总和 F 随机变量及其应用

随机变量（RVs）之和的统计表征对于研究无线通信系统的性能很有用。我们为概率密度函数（PDF）和累积分布函数（CDF）的独立但不相同分布（inid）Fisher-Snedecor的总和得出精确的封闭形式表达式 $ \数学{F} $ 房车。PDF和CDF均以多元Fox表示 $ H $ -功能。此外，可以简单准确地近似inid Fisher-Snedecor的总和 $ \数学{F} $ 使用矩匹配法表示变量。所获得的PDF和CDF用于评估无线通信应用程序的性能，包括四种不同的自适应传输策略下的中断概率，有效容量和信道容量。而且，获得了相应的近似表达式以为无线通信系统的设计和部署提供有用的见解。此外，我们在高信噪比条件下为所提出的数学分析推导了简单的渐近表达式。最后，数值结果证明了导出表达式的准确性。