A semidefinite relaxation based conservative approach to robust transmit beamforming with probabilistic sinr constraints

This paper considers a multiuser transmit beamforming design in the presence of Gaussian distributed channel errors at the transmitter. We study a stochastic robust design problem that minimizes the transmission power subject to probabilistic signal-to-interference-plus-noise ratio (SINR) constraints on the receivers. While the probabilistically-constrained design problem is difficult to solve, we present a conservative approximation formulation that guarantees the satisfaction of the probabilistic SINR requirements. The proposed conservative formulation is reminiscent of the worst-case robust design problem with spherically bounded channel errors, and can be efficiently handled by semidefinite relaxation. The presented simulation results show that the proposed approach outperforms the existing methods and requires less transmission powers under the same SINR requirement.