In this paper, the performance of the selection combining (SC) scheme over Fisher-Snedecor $\mathcal{F}$ fading channels with independent and non-identically distributed (i.n.i.d.) branches is analysed. The probability density function (PDF) and the moment generating function (MGF) of the maximum i.n.i.d. Fisher-Snedecor $\mathcal{F}$ variates are derived first in terms of the multivariate Fox's $H$-function that has been efficiently implemented in the technical literature by various software codes. Based on this, the average bit error probability (ABEP) and the average channel capacity (ACC) of SC diversity with i.n.i.d. receivers are investigated. Moreover, we analyse the performance of the energy detection that is widely employed to perform the spectrum sensing in cognitive radio networks via deriving the average detection probability (ADP) and the average area under the receiver operating characteristics curve (AUC). To validate our analysis, the numerical results are affirmed by the Monte Carlo simulations.

中文翻译：

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非相同分布Fisher-Snedecor F衰落信道的选择组合方案

在本文中，分析了选择组合 (SC) 方案在具有独立和非相同分布 (inid) 分支的 Fisher-Snedecor $\mathcal{F}$ 衰落信道上的性能。最大 inid Fisher-Snedecor $\mathcal{F}$ 变量的概率密度函数 (PDF) 和矩生成函数 (MGF) 首先根据已在各种软件代码的技术文献。在此基础上，研究了具有inid接收器的SC分集的平均误码率（ABEP）和平均信道容量（ACC）。而且，我们通过推导平均检测概率 (ADP) 和接收器操作特性曲线 (AUC) 下的平均面积，分析了在认知无线电网络中广泛用于执行频谱感知的能量检测的性能。为了验证我们的分析，蒙特卡罗模拟证实了数值结果。