Joint Active and Passive Beamforming Design for IRS-Assisted Multi-User MIMO Systems: A VAMP-Based Approach

• Published in: IEEE transactions on communications 2021-10, Vol.69 (10), p.6734-6749
• Main Authors: Ur Rehman, Haseeb, Bellili, Faouzi, Mezghani, Amine, Hossain, Ekram
• Format: Article
• Language: English
• Subjects: Algorithms; Array signal processing; Attenuation; Beamforming; Communications systems; Computational geometry; Convexity; Downlink; Intelligent reflective surface (IRS); IRS-assisted multi-user MIMO; joint active and passive beamforming; Massive MIMO; Mean square errors; Message passing; MIMO communication; MISO communication; Optimization; Precoding; Throughput; vector approximate message passing (VAMP)
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2021.3094509

This paper tackles the problem of joint active and passive beamforming optimization for an intelligent reflective surface (IRS)-assisted multi-user downlink multiple-input multiple-output (MIMO) communication system under both ideal and practical IRS phase shifts. We aim to maximize the spectral efficiency of the users by minimizing the sum mean square error (MSE) of the users' received symbols. For this, a joint non-convex optimization problem is formulated under the sum minimum mean square error (MMSE) criterion. Alternating minimization is used to break the original joint optimization problem into the separate optimization of the active precoding matrix for the base station (BS) and the matrix of phase shifts for the IRS. While the MMSE active precoder is obtained in closed-form, the IRS phase shifts are optimized iteratively using a modified version (developed in this paper) of the vector approximate message passing (VAMP) algorithm. Moreover, the underlying joint optimization problem is solved under two different models for the IRS phase shifts, namely by assuming i ) a unimodular (i.e., ideal) constraint on the reflection coefficients and ii ) a more practical reflection elements termination by a variable reactive load (which inherently introduces the phase-dependent amplitude attenuation in the IRS phase shifts). Simulation results are presented to illustrate the performance of the proposed method under both perfect and imperfect channel state information (CSI) and to show the effect of the practical constraint on the system throughput. The results validate the superiority of the proposed method over the state-of-the-art techniques both in terms of throughput and computational complexity.