Maximum mutual information design for MIMO systems with imperfect channel knowledge

Abstract—New results on maximum mutual information design for multiple-input multiple-output (MIMO) systems are presented, assuming that both transmitter and receiver know only an estimate of the channel state as well as the transmit and receive correlation. Since an exact capacity expression is difficult to obtain for this case, a tight lower-bound on the mutual information between the input and the output of a MIMO channel has been previously formulated as a design criterion. However, in the previous literature, there has been no analytical expression of the optimum transmit covariance matrix for this lower-bound. Here it is shown that for the general case with channel correlation at both ends, there exists a unique and globally optimum transmit covariance matrix whose explicit expression can be conveniently determined. For the special case with transmit correlation only, the closed-form optimum transmit covariance matrix is presented. Interestingly, the optimal trans-mitters for the maximum mutual information design and the min-imum total mean-square error design share the same structure, as they do in the case with perfect channel state information. Simula-tion results are provided to demonstrate the effects of channel esti-mation errors and channel correlation on the mutual information. Index Terms—Channel state information (CSI), mean-square error (MSE), multiple-input multiple-output (MIMO), mutual information, optimization. I