Convergence analysis of downlink MIMO antenna systems using second-order cone programming

Promoting spectral reuse in the spatial domain has an obvious advantage of high bandwidth efficiency. In downlink, this can be realized by employing multiple-input multiple-output (MIMO) antennas at the transmitter and/or the receivers. In this multiuser MIMO setting, co-channel users can be well separated in space by generalized zeroforcing. The objective of this paper is to study the sum-power minimization of a downlink multiuser MIMO system subject to individual signal-to-interference plus noise ratio (SINR) constraints from the users. The difficulty of this problem lies in the fact that the original optimization problem is non-convex and thus hard to tackle. The main contribution of the paper is that we propose an iterative algorithm, which combines second-order cone programming (SOCP) with minimummean- square-error (MMSE) receiver processing for the sumpower minimization. Furthermore, we show analytically that the proposed iterative algorithm converges to a limit, and the sumpower is monotonically decreasing from one iteration to the next. Simulation results also show considerable performance gain over generalized zeroforcing schemes.