  It is challenging to precisely configure the phase shifts of the reflecting
elements at the reconfigurable intelligent surface (RIS) due to inherent
hardware impairments (HIs). In this paper, the mean square error (MSE)
performance is investigated in an RIS-aided single-user multiple-input
multipleoutput (MIMO) communication system with transceiver HIs and RIS phase
noise. We aim to jointly optimize the transmit precoder, linear received
equalizer, and RIS reflecting matrices to minimize the MSE. To tackle this
problem, an iterative algorithm is proposed, wherein the beamforming matrices
are alternately optimized. Specifically, for the beamforming optimization
subproblem, we derive the closed-form expression of the optimal precoder and
equalizer matrices. Then, for the phase shift optimization subproblem, an
efficient algorithm based on the majorization-minimization (MM) method is
proposed. Simulation results show that the proposed MSE-based RIS-aided
transceiver scheme dramatically outperforms the conventional system algorithms
that do not consider HIs at both the transceiver and the RIS.
