Joint design of tx-rx beamformers in MIMO downlink channel

We consider a single-cell multiple-input multiple-output (MIMO) downlink channel where linear transmission and reception strategy is employed. The base station (BS) transmitter 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 a general method for joint design of the transmit and the receive beamformers according to different optimization criteria, including weighted sum rate maximization, weighted sum mean square error minimization, minimum signal-to-interference-plus-noise ratio (SINR) maximization and sum power minimization under a minimum SINR constraint. 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 nontractable. 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. Even though each subproblem is optimally solved, there is no guarantee that the global optimum has been found due to the nonconvexity of the problem. However, the simulations show that the algorithms converge fast to a solution, which can be a local optimum, but is still efficient.