  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.
