Optimal transmit strategies in MIMO Ricean channels with MMSE receiver

We study a MIMO system with MMSE receiver in a flat-fading environment. We assume that the receiver has perfect CSI and the transmitter knows only the mean channel matrix, either by feedback or channel estimation. First, we derive the properties of the average normalized MSE and its dependence on the singular values of the mean component. Next, we show that the optimal transmit strategy is to transmit in the direction of the eigenvectors of the squared mean component. In addition to this, we characterize the optimal power allocation using the necessary and sufficient optimality conditions. Furthermore, the optimal strategy for small SNR values is to perform beamforming, i.e., to transmit only in direction of the largest mean matrix eigenvalue.