The multivariate α-μ distribution

• Published in: IEEE transactions on wireless communications 2010-01, Vol.9 (1), p.45-50
• Main Authors: de Souza, R.A.A., Yacoub, M.D.
• Format: Article
• Language: English
• Subjects: Applied sciences; Approximation; Closed-form solution; Correlated fading; Correlation; Detection, estimation, filtering, equalization, prediction; Distribution functions; Diversity reception; diversity systems; Exact sciences and technology; Exact solutions; Genetic expression; Information, signal and communications theory; Mathematical analysis; Nakagami distribution; Nakagami-m fading; Outages; Probability density function; Probability density functions; Rayleigh channels; Signal and communications theory; Signal, noise; Telecommunications and information theory; US Department of Transportation; Weibull fading channels; Wireless communication; α-μ distribution
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2010.01.090030

An infinite series formulation for the multivariate α-μ joint probability density function with arbitrary correlation matrix and non-identically distributed variates is derived. The expression is exact and general and includes all of the results previously published in the literature concerning the distributions comprised by the α-μ distribution. The general expression is then particularized to an indeed very simple, approximate closed-form solution. In addition, a multivariate joint cumulative distribution function is obtained, again in simple, closed-form manner. As an application example, the exact and approximate performances of the selection combining scheme given in terms of the outage probability is shown. Approximate and exact results are very close to each other for small as well as medium values of correlation.