Weighted Sum MSE Minimization for MIMO Broadcast Channel

A MIMO broadcast channel with linear transceiver schemes is considered in this paper. The base station (BS) is equipped with a scheduler, using a simple opportunistic beamforming strategy, which associates an intended user for each of the transmitted data streams. For the case when the channel of the scheduled users is available at the BS we propose an iterative algorithm for joint design of the transmit and the receive beamformers according to mean square error minimization criterion. The proposed method can handle multiple antennas at the BS and at the mobile user with single and/or multiple data streams per scheduled user. The optimization problems encountered in the beamformer design (e.g., covariance rank constraint) are not convex in general. Therefore, the problem of finding the global optimum is intrinsically non-tractable. However, by exploiting the uplink-downlink SINR duality, we decompose the original optimization problem as a series of simpler optimization problems which can be efficiently solved by using standard convex optimization tools. There is no guarantee that the global optimum has been found due to the nonconvexity of the problem, but, the simulations show that the algorithms converge fast to a solution, which can be a local optimum, but is still efficient