  In this work, we study the statistically robust beamforming design for an
intelligent reflecting surfaces (IRS) assisted multiple-input single-output
(MISO) wireless system under imperfect channel state information (CSI), where
the channel estimation errors are assumed to be additive Gaussian. We aim at
jointly optimizing the transmit/receive beamformers and IRS phase shifts to
minimize the average mean squared error (MSE) at the user. In particular, to
tackle the non-convex optimization problem, an efficient algorithm is developed
by capitalizing on alternating optimization and majorization-minimization
techniques. Simulation results show that the proposed scheme achieves robust
MSE performance in the presence of CSI error, and substantially outperforms
conventional non-robust methods.
