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

Abstract

This letter presents a general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -Beaulieu-Xie ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -BX) fading model and its extreme ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -BXe) case. First, we derive the new expressions of statistical characteristics for these models by employing a mixture <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha - \mu $ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -BX and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -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.