Alternating Minimization for Wideband Multiuser IRS-aided MIMO Systems under Imperfect CSI

This work focuses on wideband intelligent reflecting surface (IRS)-aided multiuser MIMO systems. One of the major challenges of this scenario is the joint design of the frequency-dependent base station (BS) precoder and user filters, and the IRS phase-shift matrix which is frequency flat and common to all the users. In addition, we consider that the channel state information (CSI) is imperfect at both the transmitter and the receivers. A statistical model for the imperfect CSI is developed and exploited for the system design. A minimum mean square error (MMSE) approach is followed to determine the IRS phase-shift matrix, the transmit precoders, and the receiving filters. The broadcast (BC)- multiple access channel (MAC) duality is used to solve the optimization problem following an alternating minimization approach. Numerical results show that the proposed approach leads to substantial performance gains with respect to baseline strategies that neglect the inter-user interference and do not optimize the IRS phase-shift matrix. Further performance gains are obtained when incorporating into the system design the statistical information of the channel estimation errors.