Structure of Optimal Input Covariance Matrices for MIMO Systems with Covariance Feedback under General Correlated Fading

We describe the structure of optimal Input covariance matrices for single user multiple-input/multiple-output (MIMO) communication system with covariance feedback and for general correlated fading. Our approach is based on the novel concept of right commutant and recovers previously derived results for the Kronecker product models. Conditions are derived which allow a significant simplification of the optimization problem.