A Novel LBFGS Optimization Algorithm for RIS-Assisted MIMO Systems with Hardware Impairments

Reconfigurable Intelligent Surfaces (RIS) have emerged as a promising technology to overcome the spectral efficiency limitations of conventional MIMO systems, particularly under real-world conditions characterized by hardware imperfections and non-ideal reflection properties. This paper proposes an innovative Phase and Reflection Optimization Algorithm (PROA) that simultaneously optimizes both the base station beamforming and RIS phase configurations through a computationally efficient dual-stage iterative approach. By combining Singular Value Decomposition (SVD) for precoding with an Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) based phase optimization procedure that accounts for practical constraints such as amplitude-phase coupling, impedance variations, and imperfect channel state information (CSI), the proposed algorithm addresses the complex non-convex optimization problem inherent in RIS-assisted communications. The simulation results show that PROA achieves a spectral efficiency exceeding 80 bps/Hz while reducing the memory requirement by 80% and achieving speed improvements of up to three orders of magnitude compared with existing techniques. These results position PROA as a practical and high-performance solution for RIS deployment in 5G-Advanced and 6G networks.