Robust downlink beamforming using positive semi-definite covariance constraints

We study the problem of multiuser downlink beamforming under the assumption that only an erroneous channel state information (CSI) is available at the transmitter. The optimization criterion is to minimize the total transmit power subject to the constraints that the user worst-case signal-to-interference-plus-noise ratios (SINRs) are above a pre-defined quality of service (QoS) threshold. In contrast to the earlier approaches to this problem, we take into account positive semi-definiteness of the mismatched channel covariance matrices. Two approaches to solve the resulting robust downlink beamforming problem are proposed using semidefinite programming (SDP). Simulation results validate the robustness of the proposed techniques.