The Nakagami–Lomax Distribution: A Hyper Composite Fading Model

In this paper, a new composite fading model is introduced, where the small- and large-scale effects are respectively modeled by the Nakagami-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> and Lomax distributions. Other distributions, such as the Nakagami-Rayleigh and the double Rayleigh distributions, coincide with this new distribution. Statistical expressions for the cumulative distribution function (CDF), probability density function (PDF), and generalized moment-generating function are derived in closed-form. To assess the performance of a communication system operating under the Nakagami-Lomax model, closed-form expressions for the outage probability, average bit error probability, and channel capacity are derived and evaluated. Moreover, to validate the proposed model, the theoretical CDF is compared with empirical CDFs from field measurements obtained for device-to-device communications in both outdoor and indoor environments. Furthermore, the theoretical PDF is compared with empirical PDF from field measurements obtained for body area networks. The results show that the proposed distribution outperforms the Fisher-Snedecor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cal {F}$</tex-math></inline-formula> distribution in the aforementioned applications.