Asymptotic maximum order statistic for SIR in $\kappa-\mu$ shadowed fading

TL;DR

This paper applies extreme value theory to characterize the asymptotic distribution of maximum SIR in $ppa-mu$ shadowed fading, showing it converges to a Frechet distribution and analyzing its implications for antenna selection and scheduling.

Contribution

It introduces the asymptotic distribution of maximum SIR in $ppa-mu$ shadowed fading using EVT, providing new insights for system performance analysis.

Findings

Maximum SIR distribution converges to Frechet distribution.

Moments of maximum SIR converge to Frechet moments.

Derived bounds for antenna selection and scheduling performance.

Abstract

Using tools from extreme value theory (EVT), it is proved that, when the user signal and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) $\kappa-\mu$ shadowed fading, 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. It is observed that this limiting distribution is close to the true distribution of maximum, for maximum SIR evaluated over moderate $L$. Further, moments of the maximum RV is shown to converge to the moments of the Frechet RV. Also, the rate of convergence of the actual distribution of the maximum to the Frechet distribution is derived and is analyzed for different $\kappa$ and $\mu$ parameters. Finally, results from stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters. These results are then used to derive upper bound for the rate in Full Array Selection (FAS) schemes for antenna selection and the asymptotic outage probability and the ergodic rate in maximum-sum-capacity (MSC) scheduling systems.