N∗Nakagami: A Novel Stochastic Model for Cascaded Fading Channels

A generic and novel distribution, referred to as N∗Nakagami, constructed as the product of N statistically independent, but not necessarily identically distributed, Nakagami-m random variables (RVs), is introduced and analyzed. The proposed distribution turns out to be a very convenient tool for modelling cascaded Nakagami-m fading channels and analyzing the performance of digital communications systems operating over such channels. The moments-generating, probability density, cumulative distribution, and moments functions of the N∗Nakagami distribution are developed in closed form using the Meijer’s Gfunction. Using these formulas, generic closed-form expressions for the outage probability, amount of fading, and average error probabilities for several binary and multilevel modulation signals of digital communication systems operating over the N∗Nakagami fading and the additive white Gaussian noise channel are presented. Complementary numerical and computer simulation performance evaluation results verify the correctness of the proposed formulation. The suitability of the N∗Nakagami fading distribution to approximate the lognormal distribution is also being investigated. Using Kolmogorov–Smirnov tests, the rate of convergence of the central limit theorem as pertaining to the multiplication of Nakagami-m RVs is quantified.