The N * Nakagami Fading Channel Model

A generic distribution, referred to as N* Nakagami, constructed as the product of N statistically independent, but not necessarily identically distributed, Nakagami-m random variables (RV)s, is introduced and analyzed. The proposed distribution turns out to be an extremely convenient tool for analyzing the performance of digital communication systems over generalized fading channels. The main result contributions of the paper are two-fold. Firstly, the moments-generating function (MGF), probability density function, cumulative distribution function (CDF), and moments of the N* Nakagami distribution are derived in closed-form. Using these formulae, generic closed-form expressions for the outage probability, amount of fading, and average symbol error probability for several binary and multilevel modulation signals of digital communication systems operating over the N* Nakagami fading channel model are presented. Various numerical and computer simulation results verify the correctness of the proposed formulation. Secondly, the suitability of the N* Nakagami fading distribution to approximate the lognormal distribution is being investigated. Using Kolmogorov-Smirnov tests, the rate of convergence of the central limit theorem as pertaining to the multiplication of RVs is quantified.