On the Statistics of the α-Beaulieu-Xie and Its Extreme Distributions With Their Applications

This letter presents a general $\alpha $ -Beaulieu-Xie ( $\alpha $ -BX) fading model and its extreme ( $\alpha $ -BXe) case. First, we derive the new expressions of statistical characteristics for these models by employing a mixture $\alpha - \mu $ distribution, including the probability density function and cumulative distribution function. Then, capitalizing on these new statistics, several exact and approximate properties of a selection combining system over the independent non-identically distributed $\alpha $ -BX and $\alpha $ -BXe fading channels are investigated in terms of outage probability and average symbol error probability, respectively. Finally, numerical analysis and simulations are performed to corroborate the availability of the theoretical analysis.