A General Framework for the Distribution of the Eigenvalues of Wishart Matrices

This paper focuses on the stochastic analysis of Wishart matrices, which appear in many problems related to the performance analysis multiple-input- multiple-output (MIMO). We propose a general methodology to evaluate some multiple nested integrals of interest. With this methodology we obtain a closed-form expression for the joint probability density function (pdf) of k consecutive ordered eigenvalues and, as a special case, the pdf of the lth ordered eigenvalue of Wishart matrices.