  This paper investigates the joint design of the beamforming scheme in
intelligent reflecting surface (IRS) assisted multiuser (MU) multiple-input
multiple-output (MIMO) downlink transmissions. Channel estimation errors
associated with the minimum mean square error (MMSE) estimation are assumed and
the weighted sum rate (WSR) is adopted as the performance metric.
Low-resolution phase shifters (PSs) in practical implementations are taken into
account as well. Under the constraint of the transmit power and discrete phase
shifters (PSs), an optimization problem is formulated to maximize the WSR of
all users. To obtain the optimal beamforming matrices at the IRS, two solutions
based on the majorization-minimization (MM) and successive convex approximation
(SCA) methods, respectively, are proposed. Through simulation results, both of
the proposed two schemes achieve a significant improvement in WSR. Furthermore,
the superiority of the SCA-based solution is demonstrated. Overall, two viable
solutions to the joint beamforming design in IRS-aided MU-MIMO downlink
communication systems with channel estimation errors are provided.
