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.

💡 Research Summary

This paper proposes a robust resource‑allocation framework for a downlink multi‑user system that jointly exploits three emerging 6G technologies: movable antennas (MAs) at the base station, a reconfigurable intelligent surface (RIS) deployed to assist the blocked direct links, and rate‑splitting multiple access (RSMA) as the physical‑layer multiple‑access scheme. The authors assume that all links (BS‑RIS, RIS‑user) are subject to imperfect channel state information (CSI). To guarantee reliable operation under the worst‑case channel realization, the channel estimation errors are modeled as bounded norm‑uncertainty sets. This robust modeling leads to a worst‑case sum‑rate maximization problem subject to quality‑of‑service (QoS) constraints for each user, a total transmit‑power budget, common‑stream decoding constraints, and practical mutual‑coupling limits on the movable antennas.

The resulting optimization problem is highly non‑convex because (i) the transmit precoders, RIS phase‑shift matrix, common‑rate allocation, and MA positions are coupled; (ii) the RIS phases are unit‑modulus; and (iii) the channel uncertainty introduces semi‑infinite constraints. To tackle these difficulties, the authors adopt an alternating‑optimization (AO) strategy that decomposes the original problem into three tractable sub‑problems, each solved iteratively while keeping the other variables fixed.

1. Precoding sub‑problem – With RIS phases and MA positions fixed, the robust SINR constraints are transformed into linear matrix inequalities (LMIs) via the S‑procedure. The precoding vectors are then obtained by solving a semidefinite programming (SDP) problem. This SDP formulation guarantees that the worst‑case SINR constraints are satisfied for all admissible channel errors.

2. RIS phase‑shift sub‑problem – Holding the precoders and MA locations constant, the RIS design remains non‑convex because of the unit‑modulus constraint and the channel‑uncertainty terms. The authors apply successive convex approximation (SCA) to linearize the non‑convex parts around the current iterate, yielding a convex surrogate that can be expressed as an SDP. After solving the SDP, a Gaussian‑randomization step recovers feasible unit‑modulus phase values.

3. MA position sub‑problem – The positions of the movable antennas affect the phase of each propagation path. The authors again use SCA to approximate the non‑linear dependence of the channel on the antenna coordinates, and then employ a block‑coordinate descent (BCD) scheme that updates one antenna at a time while keeping the others fixed. This yields a convex sub‑problem that can be solved efficiently.

Each sub‑problem is convex, guaranteeing monotonic improvement of the objective and convergence of the AO loop after a modest number of iterations (typically 15–20). The computational complexity is dominated by the SDP solves; however, the authors discuss low‑rank exploitation and ADMM‑based solvers to keep the runtime practical for realistic RIS sizes.

Numerical results compare the proposed MA‑RIS‑RSMA scheme against several baselines: (i) fixed‑antenna RSMA without RIS, (ii) fixed‑antenna RSMA with RIS, (iii) MA‑RSMA without RIS, and (iv) a non‑robust version of the proposed algorithm. The simulations show that (a) the mobility of the antennas provides an additional 3–5 dB channel‑gain boost, translating into roughly 20 % higher sum‑rate; (b) the RIS further enhances the common‑stream decoding gain, adding another 15 % improvement; (c) the robust design mitigates the performance loss caused by CSI errors, preserving QoS where the non‑robust counterpart suffers up to a 10 % SINR degradation; and (d) the overall algorithm converges quickly.

In summary, the paper delivers a comprehensive, mathematically rigorous solution that integrates spatial adaptability (MAs), intelligent propagation control (RIS), and flexible interference management (RSMA) while explicitly accounting for channel uncertainty. The proposed framework advances the state‑of‑the‑art in robust beamforming for future 6G networks and opens several avenues for future work, such as dynamic trajectory planning for MAs, multi‑RIS coordination, and real‑time CSI acquisition mechanisms.