Cooperative relaying with energy harvesting relays : Asymptotic analysis using extreme value theory for non-identically distributed RVs
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This paper derives the limiting distribution of the maximum end-to-end signal to noise ratio (SNR) in a cooperative relaying (CR) scenario with multiple relays capable of both time splitting (TS) and power splitting (PS) based energy harvesting (EH). Considering an opportunistic relay selection scenario, we derive the limiting distribution of end-to-end SNR over independent and non-identical relay links between the source and the destination. 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 (i.i.d.) random variables (RVs), we demonstrate how tools from EVT can be used to derive the limiting statistics of sequences of independent and non-identically distributed (i.n.i.d.) SNR RVs and hence derive the corresponding expressions for asymptotic ergodic and outage capacities. Finally, we present the utility of the asymptotic results for deciding the optimum TS and PS factors of the hybrid EH relays to minimize outage probability at the destination. Furthermore, we demonstrate how results from stochastic ordering can be utilized for simplifying the corresponding optimization problem.
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