On the Statistics of the Maximum of α-F Variates and Their Applications

In this letter, a statistical characterization is provided for the instantaneous signal-to-noise ratio (SNR) resulting from the maximum of independent and non-identically distributed random variables characterized by the
$\alpha $
-
$\mathcal {F}$
distribution. Based on this study, new expressions are derived for the probability density function, cumulative distribution function and moment generating function of the resulting instantaneous SNR. Asymptotic expressions are also provided. The aforementioned new expressions can be used to determine metrics for the performance evaluation of multiple branch selection combining based receivers. In this context, bit error probability and outage probability curves are presented for different parameters that characterize the channel. All the expressions are corroborated by Monte-Carlo simulations.