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

Abstract

In this paper, the $\alpha$ - $\mathcal {F}$ composite fading distribution is introduced. It is worth highlighting that the $\alpha$ - $\mathcal {F}$ distribution offers more flexibility as it includes the composite $\mathcal {F}$ and the $\alpha$ - $\mu$ distributions, and their inclusive ones, as special cases. Moreover, unlike the composite $\mathcal {F}$ and the $\alpha$ - $\mu$ distributions, the $\alpha$ - $\mathcal {F}$ 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 $M$ -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 $\alpha$ - $\mathcal {F}$ 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 $\alpha$ - $\mathcal {F}$ distribution provide a good fit to the measured data PDFs compared with other well-known distributions, namely $\mathcal {K}$ , $\kappa$ - $\mu$ shadowed, and $\alpha$ - $\mu$ distributions.