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Effect of Channel Uncertainty on MIMO Systems with Covariance Information at the Transmitter

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In this paper, we study the effect of channel estimation error on mutual information in a multiple input multiple output (MIMO) channel with correlated Rayleigh fading. We assume that perfect knowledge of the channel correlation is available at the receiver and find the upper bounds and the lower bounds on mutual information. We also assume that the covariance information is available to the transmitter and prove that transmitting towards the direction of the eigenvectors of the transmit covariance matrix maximizes the bounds on the mutual information. We further find the mutual information bounds for beamforming and prove that the difference between these two bounds does not exceed a certain value which depends on the number of non-zero eigenvalues of the receive correlation matrix. Numerical simulations are conducted to corroborate theoretical results.