Bivariate nakagami-m distribution with arbitrary correlation and fading parameters

• Published in: IEEE transactions on wireless communications Vol. 7; no. 12; pp. 5227 - 5232
• Main Authors: de Souza, R.A.A., Yacoub, M.D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Bivariate distribution; combiners; Convergence; Correlation; Correlation coefficients; Distribution functions; Exact sciences and technology; Fading; fading channels; Gaussian; Mathematical analysis; Nakagami distribution; Nakagami-m; Polynomials; Power generation; Probability density function; Probability density functions; Signal generators; Signal to noise ratio; Statistical distributions; Statistics; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Fading channels; Correlation coefficient; Multivariate process; Generating function; Outage; Bivariate distribution; Laguerre polynomial; Nakagami-m fading channels; Joint distribution; Statistical method; Nakagami fading; correlation; combiners; Probability density function; Distribution function; Signal to noise ratio
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/T-WC.2008.071152

New, exact expressions concerning the bivariate Nakagami-m processes with arbitrary correlation and fading parameters are derived. More specifically, the following are obtained in the present work: joint moment generating function; joint probability density function; joint cumulative distribution function; power correlation coefficient; and several statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability, probability density function, and mean SNR. The expressions make use of the well known generalized Laguerre polynomials. They are mathematically tractable and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment. We maintain, however, that a relation among the correlation coefficients of the corresponding Gaussian components must be kept so that convergence is attained.