Sum-rate maximization for downlink MISO networks with multiple reconfigurable intelligent surfaces

Reconfigurable intelligent surface (RIS) is emerging as a key technology for next-generation wireless communication systems, with the potential to significantly enhance performance. Meanwhile, rate-splitting multiple access (RSMA) has been demonstrated to effectively improve spectral efficiency. This paper investigates the problem of maximizing the sum-rate in a downlink RSMA transmission system assisted by multiple RISs, where RISs are used to enhance signal coverage and improve the sum-rate when the direct link between the base station (BS) and users is severely blocked. The non-convex sum-rate maximization problem is decomposed into three subproblems, alternately optimizing the user rate allocation, the BS beamforming, and the RIS phase shift. This paper considers both ideal and non-ideal RIS models and proposes two corresponding optimization algorithms. Firstly, a closed-form expression for the optimal user rate allocation is derived. Then, the weighted minimum mean squared error (WMMSE) method is used to acquire the near-optimal BS beamforming and the ideal RIS phase shift matrix. Finally, another algorithm based on successive convex approximation (SCA) and penalty method is proposed to optimize the non-ideal RIS phase shift matrix. Simulation results show that the proposed algorithms outperform benchmark methods in terms of sum-rate performance. Specifically, the RISassisted RSMA achieves an increase of 11.14% and 20.03% compared to RIS-assisted space division multiple access (SDMA) and non-orthogonal multiple access (NOMA), respectively.