Joint Distribution of an Arbitrary Subset of the Ordered Eigenvalues of Wishart Matrices

The distribution of the eigenvalues of Wishart matrices and Gaussian quadratic forms is of great interest in communication theory, especially in relation to multiple-input multiple-output (MIMO) systems. In this paper we present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of Wishart matrices, using the tensor operator T?(.), which was first introduced in [1]. We obtain both the joint probability distribution function (p.d.f.) of the eigenvalues and the expectation of arbitrary functions of the eigenvalues, including the moments, for the case of both ordered and unordered eigenvalues. These expressions are extremely compact and easy to handle. Application to MIMO systems are discussed.