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.

[1]  Jørgen Bach Andersen.  Stastistical distributions in mobile communications using multiple scattering , 2002 .

[2]  M. Nakagami.  The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[3]  Jonathan Ling,et al.  Comparisons of a Computer-Based Propagation Prediction Tool with Experimental Data Collected in Urban Microcelluar Environments , 1997, IEEE J. Sel. Areas Commun..

[4]  Mohamed-Slim Alouini,et al.  Digital Communication over Fading Channels: Simon/Digital Communications 2e , 2004 .

[5]  Hyundong Shin,et al.  Performance analysis of space-time block codes over keyhole Nakagami-m fading channels , 2004, IEEE Transactions on Vehicular Technology.

[6]  Rodney G. Vaughan,et al.  A statistical basis for lognormal shadowing effects in multipath fading channels , 1998, IEEE Trans. Commun..

[7]  Victor Adamchik,et al.  The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system , 1990, ISSAC '90.

[8]  Larry J. Greenstein,et al.  Guest editorial channel and propagation models for wireless system design I , 2002, IEEE J. Sel. Areas Commun..

[9]  George L. Turin,et al.  A statistical model of urban multipath propagation , 1972 .

[10]  F.I. Meno,et al.  Mobile fading—Rayleigh and lognormal superimposed , 1977, IEEE Transactions on Vehicular Technology.

[11]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[12]  R. Valenzuela,et al.  Capacities of multi-element transmit and receive antennas: Correlations and keyholes , 2000 .

[13]  Reinaldo A. Valenzuela,et al.  Keyholes, correlations, and capacities of multielement transmit and receive antennas , 2002, IEEE Trans. Wirel. Commun..

[14]  George K. Karagiannidis,et al.  Performance analysis of dual selection diversity in correlated Weibull fading channels , 2004, IEEE Transactions on Communications.