This paper derives the distribution of the maximum end-to-end (e2e) signal to noise ratio (SNR) in an opportunistic relay selection based cooperative relaying network having a large number of non-identical relay links. The source is simultaneous wireless information and power transfer enabled, and the relays are capable of both time splitting (TS) and power splitting (PS) based energy harvesting (EH). Contrary to the majority of literature in communication, which uses extreme value theory (EVT) to derive the statistics of extremes of sequences of independent and identically distributed random variables (RVs), we demonstrate how EVT can be used to derive the maximum statistics of sequences of independent and non-identically distributed normalised SNR and hence the distribution of the maximum SNR. Using these results, we derive simple expressions for evaluating the outage capacity, and achievable throughput at the destination. Finally, we present the utility of the results for deciding the optimum TS and PS factors of the hybrid EH relays that maximise outage capacity, and achievable throughput at the destination. Furthermore, we establish the stochastic ordering of the e2e SNR, which in turn allows the characterisation of the variations in the e2e performance with respect to the variations in different system parameters.

中文翻译：

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SWIPT 网络中的协作中继：使用极值理论对非同分布 RV 进行渐近分析


本文推导了具有大量不同中继链路的基于机会中继选择的协作中继网络中最大端到端（e2e）信噪比（SNR）的分布。该源支持同时无线信息和功率传输，并且继电器能够基于时间分割（TS）和功率分割（PS）的能量收集（EH）。与大多数传播学文献相反，大多数文献使用极值理论（EVT）来导出独立同分布随机变量（RV）序列的极值统计量，我们演示了如何使用 EVT 来导出序列的最大统计量独立且不同分布的归一化 SNR 的分布，从而得出最大 SNR 的分布。利用这些结果，我们得出了用于评估停电容量和目的地可实现吞吐量的简单表达式。最后，我们展示了结果的实用性，用于确定混合 EH 中继的最佳 TS 和 PS 因子，从而最大限度地提高停电容量和目的地可实现的吞吐量。此外，我们建立了 e2e SNR 的随机排序，这反过来又允许表征 e2e 性能随不同系统参数变化的变化。