Feasible Generalized Least Squares Estimation of Channel and Noise Covariance Matrices for MIMO Systems

This paper investigates the performances of multiple-input multiple-output channel and noise covariance estimation in the presence of correlated noise. The Cramer-Rao lower bounds (CRLBs) for the estimated parameters are evaluated. The optimal training sequence is designed in order to minimize the CRLB of the channel matrix estimation. When the noise covariance matrix is available, the minimum variance and unbiased estimator of the channel matrix corresponds to the generalized least squares (GLS) estimator. When the covariance matrix is unknown, we propose use of the feasible GLS technique. We prove that this two-step procedure is asymptotically equivalent to the GLS algorithm. The theoretical analysis is confirmed by Monte Carlo simulations.