Probabilistic SINR constrained robust transmit beamforming: A Bernstein-type inequality based conservative approach

Recently, robust transmit beamforming has drawn considerable attention because it can provide guaranteed receiver performance in the presence of channel state information (CSI) errors. Assuming complex Gaussian distributed CSI errors, this paper investigates the robust beamforming design problem that minimizes the transmission power subject to probabilistic signal-to-interference-plus-noise ratio (SINR) constraints. The probabilistic SINR constraints in general have no closed-form expression and are difficult to handle. Based on a Bernstein-type inequality for quadratic forms of complex Gaussian random variables, we propose a conservative formulation to the robust single-cell beamforming design problem. The semidefinite relaxation technique can be applied to efficiently handle the proposed conservative formulation. Simulation results show that, in comparison with existing methods, the proposed method is more power efficient and is able to support higher target SINR values for receivers.