Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

This paper derives the joint density of a particular trivariate non-central χ2χ2 distribution corresponding to the diagonal elements of a 3×3 complex non-central Wishart matrix. This distribution is important for a number of practical statistical signal processing applications, including synthetic aperture radar, extra-solar planet detection, and multi-antenna wireless communications. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute. The joint density of the diagonal elements of a 2×22×2 complex non-central Wishart matrix is also derived by simple reduction of the trivariate result.