Noncentral complex Wishart matrices: Moments and correlation of minors

Complex Wishart matrices are a class of random matrices with numerous emerging applications. In particular, the statistical characterization of such class of random matrices is essential for solving problems in various fields, including statistics, finance, physics and engineering. This paper establishes a new way to solve such problems based on the statistical moments and correlation of the minors. The first two minors' moments and correlation for noncentral complex Wishart matrices are derived as a function of size and degrees of freedom, as well as of covariance and noncentrality matrices. As a case study, the findings are applied to the statistical characterization of the capacity of wireless multiple-input-multiple-output systems.