  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.
