Extreme Eigenvalue Distributions of Gamma-Wishart Random Matrices

This paper derives analytical expressions for the eigenvalues of so-called gamma-Wishart random matrices, which arise in the context of multiple-input multiple-output (MIMO) transmission over land-mobile-satellite (LMS) communication channels. Such matrices are representative of complex noncentral Wishart matrices, but with randomly varying noncentrality parameter following a distribution closely related to the matrix-variate gamma. For these matrices, we derive exact closed form expressions for the distribution functions of the extreme eigenvalues (i.e., the maximum and minimum). These results are remarkably simple, and are useful for the performance analysis of MIMO transmission techniques over LMS channels.