When Movable Antennas Meet RSMA and RIS: Robust Beamforming Design With Channel Uncertainty

In this work, we propose an intelligent optimization framework for a multi-user communication system integrating movable antennas (MAs) and a reconfigurable intelligent surface (RIS) under the rate-splitting multiple access (RSMA) protocol. The system sum-rate is maximized through joint optimization of transmit precoding vectors, RIS reflection matrix, common-rate allocation, and MA positions, subject to quality-of-service (QoS), power-budget, common-rate decoding, and mutual coupling constraints. Imperfect channel state information (CSI) is considered for all links, where robustness is ensured by modeling channel estimation errors within a bounded uncertainty region, guaranteeing worst-case performance reliability. The resulting non-convex problem is solved using an alternating optimization framework. The precoding subproblem is reformulated as a semidefinite programming (SDP) problem via linear matrix inequalities derived using the S-procedure. The RIS reflection matrix is optimized using successive convex approximation (SCA), yielding an equivalent SDP formulation. The MA position optimization is addressed through SCA combined with block coordinate descent (BCD) method. Numerical results validate the effectiveness of the proposed framework and demonstrate fast convergence.