Novel representations for the multivariate non-central chi-square distribution with constant correlation and applications

Novel representations for the multivariate probability density function (PDF) and cumulative distribution function (CDF) of the equi-correlated non-central chi-square (χ²) distribution are derived. The new representations are given as single integral solutions in terms of well known mathematical functions which are available in common mathematical software packages. The advantage of the new representations is that only a single integral computation is needed to evaluate the PDF and CDF for an arbitrary number of dimensions. The new representations are used to numerically evaluate the outage probability of a single user multiple input multiple output system with receiver antenna selection diversity, operating in correlated Rician fading channels. The well known constant (equal) correlation model, which is considered to be a useful model for a closely placed set of antennas, is used for the analysis in this paper. A novel single-integral representation for the joint characteristic function of the equi-correlated non-central χ² distribution is also given.