  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 of complex Gaussian random
variables, we propose a conservative formulation to the robust beamforming
design problem. The semidefinite relaxation technique can be applied to
efficiently handle the proposed conservative formulation. Simulation results
show that, in comparison with the existing methods, the proposed method is more
power efficient and is able to support higher target SINR values for receivers.
