The $\alpha$-$\mathcal {F}$ Composite Fading Distribution: Statistical Characterization and Applications

In this paper, the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> composite fading distribution is introduced. It is worth highlighting that the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> distribution offers more flexibility as it includes the composite <inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> and the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> distributions, and their inclusive ones, as special cases. Moreover, unlike the composite <inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> and the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> distributions, the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> distribution jointly considers two important effects, namely the shadowing and the non-linearity of the propagation medium. Novel exact closed-form expressions for the probability density function (PDF), cumulative density function (CDF), moment-generating function, and higher order moments of the instantaneous signal-to-noise ratio are derived. The PDF and CDF are then employed to analyze the performance of a wireless communication system. To this end, we derive closed-form expressions for the outage probability, average channel capacity, and average bit error rate for binary coherent and non-coherent modulation schemes as well as for <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-ary modulation schemes. The analytical results are verified through numerical and Monte-Carlo simulations. The results demonstrate that the system performance improves as the non-linearity of the propagation medium and (or) the multipath parameter increase(s). Additionally, the system performance improves as the shadowing parameter increases. To demonstrate practical applications of the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> distribution, we apply it to realistic channel measurements obtained for two different wireless emerging applications, namely underwater acoustic and device-to-device communications. The results demonstrate that the PDF of the <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> distribution provide a good fit to the measured data PDFs compared with other well-known distributions, namely <inline-formula><tex-math notation="LaTeX">$\mathcal {K}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> shadowed, and <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> distributions.