MIMO LMMSE Transceiver Design with Imperfect CSI at Both Ends

This paper presents a new result on minimum total mean squared error (MSE) joint transceiver design for multiple-input multiple-output (MIMO) systems, with imperfect channel state information (CSI) at both ends and subject to a total power constraint. The channel knowledge here is the channel mean and transmit correlation information. The joint design is formulated into an optimization problem, to which the closed-form optimum solution is found. The optimum precoder consists of a linear filter, a matrix which collects effective channel eigenmodes, and a diagonal power allocation matrix. The linear filter balances the suppression of channel noise and the additional noise induced by channel estimation error. Given the precoder, the optimum decoder is simply a linear minimum MSE (LMMSE) data estimator. The performance degradations due to imperfect channel estimation and/or transmit correlation are demonstrated by simulation results. The relation between the minimum total MSE design and the maximum mutual information design is determined as well, under the above mentioned imperfect CSI.