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 G-function. 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.