Multivariate Gamma distributions and their numerical evaluations for M‐branch selection diversity study

Abstract

AbstractIn radio wave propagation and wireless communication fields, it is known that rainfall attenuation (or rainfall intensity) in an area with small reception power or time ratio under a fading environment can be well approximated by a Gamma distribution (Nakagami‐m distribution). To investigate the selection diversity method, a joint probability function that takes correlation into consideration for multiple random variables must be used to quantitatively evaluate its results. In this paper, the authors derive an exact representation according to an infinite series for a general multivariate (M‐dimensional) Gamma distribution function with correlation. In addition, besides investigating the numerical behavior of the exact representation, they obtain an extremely effective approximate representation for practical use. That approximation, which is a revision of the probability distribution with no correlation according to the determinant of a matrix having the square roots of the correlation coefficients as its elements, not only is easy to handle, but also provides an excellent physical interpretation. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 87(8): 1–12, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10224