Channel and Noise Covariance Matrix Estimation for MIMO Systems with Optimal Training Design

We investigate the performances of MIMO channel, signal-to-noise ratio (SNR) and noise covariance estimation in the presence of correlated noise. The Cramer-Rao lower bounds (CRLBs) for the estimated parameters are evaluated. The CRLB of the channel matrix estimation is minimized with respect to the training sequence. When the noise covariance matrix is available, the minimum variance and unbiased estimator (MVUE) of the channel matrix corresponds to the generalized least squares (GLS) estimator. When the covariance matrix is unknown, we propose to use the feasible generalized least squares (FGLS) technique. We prove that this two-step procedure is asymptotically equivalent to the GLS algorithm. The analytic analysis is confirmed by Monte Carlo simulations.