Mutual Coupling-Aware Channel Estimation and Beamforming for RIS-Assisted Communications

This work studies the problems of channel estimation and beamforming for active reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) communication, incorporating the mutual coupling (MC) effect through an electromagnetically consistent model. We first demonstrate that MC can be incorporated into a compressed sensing (CS) formulation, albeit with an increase in the dimensionality of the sensing matrix. To overcome this increased complexity, we propose a two-stage strategy. Initially, a low-complexity MC-unaware CS estimation is performed to obtain a coarse channel estimate, which is then used to implement a dictionary reduction (DR) for the MC-aware estimation, effectively reducing the dimensionality of the sensing matrices. This method achieves estimation accuracy close to the direct MC-aware CS method with less overall computational complexity. Furthermore, we consider the joint optimization of RIS configuration, base station precoding, and user combining in a single-user MIMO system. We employ an alternating optimization strategy to optimize these three beamformers. The primary challenge lies in optimizing the RIS configuration, as the MC effect renders the problem non-convex and intractable. To address this, we propose a novel algorithm based on the successive convex approximation (SCA) and the Neumann series expansion. Within the SCA framework, we propose a surrogate function that rigorously satisfies both convexity and equal-gradient conditions to update the iteration direction. Numerical results validate our proposal, demonstrating that the proposed channel estimation and beamforming methods effectively manage the MC in RIS, achieving higher spectral efficiency compared to state-of-the-art approaches.