Sum Rate optimization for RIS-Aided RSMA system with Movable Antenna

Rate-Splitting Multiple Access (RSMA) is regarded as a key enabling technique for sixth-generation (6G) wireless systems for its powerful interference management substantially enhancing link throughput. Reconfigurable Intelligent Surface (RIS) can effectively shape the wireless propagation to match the environment and improve communication performance. However, in conventional RSMA-RIS architectures, the antenna elements are fixed, which underutilizes spatial degrees of freedom and hence constrains system performance. To address this limitation, we propose a movable-antenna (MA) assisted RSMA-RIS framework and formulate a sum-rate maximization problem that jointly optimizes the transmit beamforming matrix, the RIS reflection matrix, the common-rate partition, and the MA positions. The original problem is equivalently transformed by employing the fractional programming (FP) method, and a closed-form solution for the common rate splitting is derived. Leveraging the Karush-Kuhn-Tucker (KKT) conditions, we obtain iterative updates for the Lagrange multipliers together with a closed-form expression for the beamforming matrix. We then develop an update rule for the RIS reflection matrix via the dual problem, and finally determine the optimal antenna locations using a gradient-ascent procedure. Numerical results indicate that, even in the presence of RIS assistance, incorporating MAs yields additional performance improvements for RSMA. Moreover, relative to space-division multiple access (SDMA), the assistance of MA yields a greater performance gain for RSMA.