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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.

Cooperative Relaying in a SWIPT Network: Asymptotic Analysis Using Extreme Value Theory for Non-Identically Distributed RVs