Non-central quadratic forms on complex random matrices and applications

In this paper, the densities of non-central quadratic forms on complex random matrices and their joint eigenvalue densities are derived for applications to information theory. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials and invariant polynomials. One of the special cases of studied quadratic forms is complex non-central Wishart matrices. We also show that the joint eigenvalue density of a complex non-central Wishart matrix can be expressed by an easily computable bounded density function. The derived densities are used to evaluate the capacity of multiple-input multiple-output (MIMO) Rician distributed channels