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This paper derives the distribution of the maximum end-to-end (e2e) signal tonoise ratio (SNR) in an opportunistic relay selection based cooperativerelaying (CR) network having large number of non-identical relay links betweenthe source and destination node. The source node is assumed to be simultaneouswireless information and power transfer (SWIPT) enabled and the relays arecapable of both time splitting (TS) and power splitting (PS) based energyharvesting (EH). Contrary to the majority of literature in communication, whichuses extreme value theory (EVT) to derive the statistics of extremes ofsequences of independent and identically distributed (i.i.d.) random variables(RVs), we demonstrate how tools from EVT can be used to derive the asymptoticstatistics of sequences of independent and non-identically distributed(i.n.i.d.) normalised SNR RVs and hence characterise the distribution of themaximum e2e SNR RV. Using these results we derive the expressions for ergodicand outage capacities at the destination node. Finally, we present the utilityof the asymptotic results for deciding the optimum TS and PS factors of thehybrid EH relays that (i) minimise outage probability and (ii) maximise ergodiccapacity at the destination. Furthermore, we demonstrate how stochasticordering results can be utilised for simplifying these optimisation problems.

Cooperative relaying in a SWIPT network:Asymptotic analysis using extreme value theory for non-identically distributed RVs