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.

翻译：可重构智能表面（RIS）能够通过调整入射信号的相位来改善信号传播环境。然而，由于目标函数和约束条件的非凸性，联合优化接入点的波束成形向量与RIS相移具有较大挑战性。本研究提出一种基于加权最小均方误差优化和幂迭代的算法，以最大化RIS辅助下行多用户多输入单输出系统的加权和速率（WSR）。为进一步提升性能，本文设计了一种模型驱动深度学习方法，通过引入可训练变量和图神经网络加速所提算法的收敛速度。我们还将所提方法扩展至包含非完美信道状态信息的波束成形场景，并推导出双时间尺度随机优化算法。仿真结果表明，所提算法在复杂度和WSR方面均优于现有最优算法。具体而言，模型驱动深度学习方法的运行时间仅为达到相同性能时现有最优算法的约3%。此外，采用2比特移相器的所提算法性能甚至优于采用连续移相器的对比算法。