Optimal Beamforming for Sum-MSE Minimization in MIMO Downlink Channe1s

In this paper, we address the joint transmit and receive beamforming design of a 2-user (2, 2) downlink system. Our aim is to minimize the aggregate mean-square-error (MSE) (or sum-MSE in short) subject to the total power constraint. By exploiting the uplink-downlink duality, the problem can be converted to the equivalent uplink system and so solved using semidefinite programming relaxation (SDPR). Due to the rank relaxation, however, SDPR will generally not give the optimal solution of the original problem. In particular, for some cases, we can show analytically that the exact optimal beamforming solution can be retrieved from the SDPR. For the other cases, a convergent iterative algorithm is proposed to provide a solution