Joint Precoder, Reflection Coefficients, and Equalizer Design for IRS-Assisted MIMO Systems

The incorporation of intelligent reflecting surface (IRS) into wireless communication systems can extend the coverage and enhance the data transmission rate. This paper studies the joint transceiver and IRS designs in IRS-assisted multi-input multi-output (MIMO) systems under both perfect channel state information (CSI) and imperfect CSI. Specifically, the transmit precoder, reflection coefficients at the IRS, and receive equalizer are jointly optimized to minimize the data detection mean square error (MSE), subject to the transmission power constraint and the modulus constraints for IRS reflection coefficients. The design problems, non-convex and challenging, are tackled under the framework of alternating optimization. For the design with perfect CSI, we successively optimize the IRS reflection coefficients given the precoder and present the closed-form optimal angle of one reflection coefficient given the others. For the robust design with imperfect CSI, we first average the detection MSE over channel uncertainties by using a generalized statistical CSI error model. Then, the averaged MSE is approximated by a more tractable upper bound. Subsequently, the robust design problem is elaborately transformed into a form similar to the problem with perfect CSI. Numerical results demonstrate the effectiveness of the proposed designs as compared to various benchmark schemes.