Reconfigurable intelligent surface (RIS) has become a promising technology to realize the programmable wireless environment via steering the incident signal in fully customizable ways. However, a major challenge in RIS-aided communication systems is the simultaneous design of the precoding matrix at the base station (BS) and the phase shifting matrix of the RIS elements. This is mainly attributed to the highly non-convex optimization space of variables at both the BS and the RIS, and the diversity of communication environments. Generally, traditional optimization methods for this problem suffer from the high complexity, while existing deep learning based methods are lack of robustness in various scenarios. To address these issues, we introduce a gradient-based manifold meta learning method (GMML), which works without pre-training and has strong robustness for RIS-aided communications. Specifically, the proposed method fuses meta learning and manifold learning to improve the overall spectral efficiency, and reduce the overhead of the high-dimensional signal process. Unlike traditional deep learning based methods which directly take channel state information as input, GMML feeds the gradients of the precoding matrix and phase shifting matrix into neural networks. Coherently, we design a differential regulator to constrain the phase shifting matrix of the RIS. Numerical results show that the proposed GMML can improve the spectral efficiency by up to 7.31\%, and speed up the convergence by 23 times faster compared to traditional approaches. Moreover, they also demonstrate remarkable robustness and adaptability in dynamic settings.

翻译：可重构智能表面（RIS）通过以完全可定制的方式调控入射信号，已成为实现可编程无线环境的一项有前景的技术。然而，RIS辅助通信系统中的主要挑战在于如何联合设计基站的预编码矩阵与RIS单元的相移矩阵。这主要源于基站与RIS两端变量高度非凸的优化空间，以及通信环境的多样性。传统优化方法通常复杂度较高，而现有基于深度学习的方法在不同场景下缺乏鲁棒性。针对这些问题，我们提出了一种基于梯度的流形元学习方法（GMML），该方法无需预训练且对RIS辅助通信具有强鲁棒性。具体而言，所提方法融合元学习与流形学习，以提升整体频谱效率并降低高维信号处理的复杂度。与直接以信道状态信息为输入的深度学习不同，GMML将预编码矩阵与相移矩阵的梯度馈入神经网络。同时，我们设计了一个微分调节器以约束RIS的相移矩阵。数值结果表明，与传统方法相比，所提GMML可将频谱效率提升高达7.31%，并将收敛速度加快23倍。此外，该方法在动态场景中展现出卓越的鲁棒性与适应性。