Linear MMSE MIMO Channel Estimation with Imperfect Channel Covariance Information

In this paper, we investigate the effects of imperfect knowledge of the channel covariance matrix on the performance of a linear minimum mean-square-error (MMSE) estimator for multiple-input multiple-output (MIMO) channels. The estimation mean-square-error (MSE) is analytically analyzed by providing both a very tight lower bound and an upper bound. The proposed analysis is useful for the understanding of how estimation accuracy of the channel covariance matrix impacts on system performance, depending on the average signal-to-noise ratio (SNR) and specific propagation conditions. Conclusions are fully supported by numerical results.