Joint Beamforming Design for IRS Aided Multiuser MIMO With Imperfect CSI

This paper investigates the joint beamforming design for the intelligent reflecting surface (IRS) aided multi-antenna multiuser (MU) multiple-input multiple-output (MIMO) downlink transmissions under imperfect channel state information (CSI), where the IRS can only take discrete PSs (PSs) at each element and the weighted sum rate (WSR) is adopted as the performance metric. By deriving the covariance matrix of the interference and noise at the users under the statistical channel estimation errors (CEEs) model, the joint WSR maximization problem is reformulated as an equivalent weighted minimum mean square error minimization problem and decoupled into two subproblems which are solved alternatively. In particular, two algorithms based on the majorization-minimization and gradient descent methods are proposed to obtain the optimal beamforming matrix at the IRS. Simulation results validate the accuracy of the proposed robust design and reveal that in case of imperfect CSI, the IRS can still achieve a significant improvement in WSR even with 2-bits PSs at the IRS. Moreover, it is also found that increasing the number of reflecting elements may not always be beneficial and that the optimal location of the IRS may be closer to the base station in the presence of CEEs.