On the Diagonal Distribution of a Complex Wishart Matrix and Its Application to the Analysis of MIMO Systems
The statistical properties of Wishart matrices have been extensively used to analyze the performance of Multiple-Input Multiple-Output (MIMO) systems. In particular, the Signal-to-Noise Ratio (SNR) output statistics of several MIMO systems depends on the diagonal distribution of a complex Wishart matrix. In this paper, the authors derive the joint density of the diagonal elements of a complex Wishart matrix, which follows a multivariate chi-square distribution. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute. This expression is used to obtain the distribution of the maximum of the diagonal elements, which allows analyzing the performance of two different MIMO systems under practical conditions.