Robust MMSE Precoding in MIMO Channels With Pre-Fixed Receivers

In this paper, we design robust precoders, under the minimum mean square error (MMSE) criterion, for different types of channel state information (CSI) in multiple-input multiple-output (MIMO) channels. We consider low-complexity pre-fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter. In particular, three types of CSI are taken into account: i) perfect CSI, ii) statistical CSI in the form of mean feedback, and iii) deterministic imperfect CSI assuming that the actual channel is within the neighborhood of a nominal channel, which leads to the worst-case robust design that is the focus of this paper. Interestingly, it is found that, under some mild conditions, the optimal transmit directions, i.e., the left singular vectors of the precoder, are equal to the right singular vectors of the channel, the channel mean, and the nominal channel for perfect CSI, statistical CSI, and the worst-case design, respectively. Consequently, the matrix-valued problems can be simplified to scalar power allocation problems that either admit closed-form solutions or can be efficiently solved by the proposed algorithm.