Reconfigurable intelligent surfaces (RIS) can improve signal propagation environments by adjusting the phase of the incident signal. However, optimizing the phase shifts jointly with the beamforming vector at the access point is challenging due to the non-convex objective function and constraints. In this study, we propose an algorithm based on weighted minimum mean square error optimization and power iteration to maximize the weighted sum rate (WSR) of a RIS-assisted downlink multi-user multiple-input single-output system. To further improve performance, a model-driven deep learning (DL) approach is designed, where trainable variables and graph neural networks are introduced to accelerate the convergence of the proposed algorithm. We also extend the proposed method to include beamforming with imperfect channel state information and derive a two-timescale stochastic optimization algorithm. Simulation results show that the proposed algorithm outperforms state-of-the-art algorithms in terms of complexity and WSR. Specifically, the model-driven DL approach has a runtime that is approximately 3% of the state-of-the-art algorithm to achieve the same performance. Additionally, the proposed algorithm with 2-bit phase shifters outperforms the compared algorithm with continuous phase shift.

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