Linear Precoder and Equalizer Design for Uplink Multiuser MIMO Systems with Imperfect Channel State Information

This paper considers a joint design of linear precoders and equalizers for uplink multiuser multiple-input multiple-output communications systems over uncorrelated flat-fading channels with imperfect channel state information at both the transmitters and the receivers. By minimizing the mean square error (MSE) of all users, or equivalently the sum-MSE, under a sum-power constraint, we model the linear transceiver design as an optimization problem. Instead of relying on complex iterative algorithms, the authors propose a low-complexity, non-iterative but close-to-optimal precoder design solution by relaxing the problem into a simpler convex optimization problem. In this way, a closed-form linear transceiver structure can be derived by using the Karush-Kuhn-Tucker (KKT) optimality conditions. Based on the closed-form solution and random matrix theory, the authors obtain a simple asymptotic expression on the average sum-MSE, which can provide useful design insights.