Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices

Let W be a correlated complex non-central Wishart matrix defined through W = (XX)-X-H, where X is an n x m (n >= m) complex Gaussian with non-zero mean Gamma and non-trivial covariance Sigma. We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of W for some particular cases. These results are quite simple, involving rapidly converging infinite series, and apply for the practically important case where Gamma has rank one. We also derive analogous results for a certain class of gamma-Wishart random matrices, for which Gamma(H)Gamma follows a matrix-variate gamma distribution. The eigenvalue distributions in this paper have various applications to wireless communication systems, and arise in other fields such as econometrics, statistical physics, and multivariate statistics. (C) 2011 Elsevier Inc. All rights reserved.