Asymptotic maximal order statistic for SIR in κ-μ shadowed fading
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Using tools from extreme value theory (EVT), it is proved that the limiting distribution of the maximum of L independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Frechet distribution, when the user and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) κ-μ shadowed fading. This limiting distribution is used to analyze the outage probability for selection combining (SC). Further, the moments of the maximum is shown to converge to the moments of the Frechet RV. This is used in deriving results for the asymptotic rate for SC. Finally, the rate of convergence of the actual maximum distribution to the Frechet distribution is derived and is analyzed for different κ and μ parameters. Further, results from stochastic ordering are used to analyze the variations in the limiting distribution with respect to variations in the source fading parameters. A close match is observed between Monte-Carlo simulations and the limiting distributions for outage probability and rate.
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