Asynchronous Distributed Beamforming for Beyond-Diagonal RIS-Aided Movable Antenna Systems

Movable antenna (MA) technology has recently attracted significant research attention as a promising solution for enhancing wireless network performance. However, conventional MAs can only effectively serve users in close proximity, resulting in restricted coverage. To overcome this limitation, in this paper, we explore a beyond-diagonal reconfigurable intelligent surface (BD-RIS)-aided MA system. First, we propose a penalty-based block coordinate descent optimization algorithm tailored to the new constraints imposed by BD-RIS-aided MA systems. Specifically, our method decouples the inherently non-convex and coupled antenna distance constraints by introducing auxiliary optimization variables. Subsequently, the resulting problem is efficiently addressed via alternating optimization, with closed-form updates for the auxiliary variables. Furthermore, recognizing the challenges posed by large-scale BD-RIS deployments, which have the potential for serving a substantial number of users, traditional centralized optimization frameworks encounter considerable difficulties, including high computational complexity, excessive communication overheads, as well as limited scalability with increasing system size. To address these limitations, we propose an efficient asynchronous alternating direction method of multipliers (AS-ADMM) scheme aimed at maximizing the sum rate. Our numerical results demonstrate that the BD-RIS-aided MA system achieves superior performance compared to both conventional fixed position antenna and BD-RIS-aided systems. Furthermore, the proposed AS-ADMM framework can achieve a trade-off between performance and computational overhead, highlighting its potential for practical implementation in large-scale wireless communication networks.