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

Authors:
Prathapasinghe Dharmawansa;Matthew R. McKay
Affiliations:
-;-
Venue:
Journal of Multivariate Analysis
Year:
2011

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Abstract

Let W be a correlated complex non-central Wishart matrix defined through W=X^HX, where X is an nxm(n=m) complex Gaussian with non-zero mean @U and non-trivial covariance @S. 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 @U has rank one. We also derive analogous results for a certain class of gamma-Wishart random matrices, for which @U^H@U 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.