On Convergence Properties of Joint Optimal Power Control and Transmit-Receive Beamforming in Multi-User MIMO Systems

We consider SDMA in a multi-user downlink MIMO system with several access points, each serving one or more users. The problem of minimizing the total transmitted power satisfying the SINR requirements at all users is considered. This is a non-linear and non-convex optimization problem with three sets of variables: the transmitter powers, the transmitter weights and the receiver weights. Global system knowledge will be assumed at the access points and the provided results can be seen as benchmarks in system performance. We present a new initialization strategy and investigate its convergence behavior for a proposed algorithm. A numerical study is performed to analyze the dependence of the target SINRs on the optimal solution. The performance of this initialization process is evaluated and compared to an existing beamforming algorithm