In reconfigurable intelligent surface (RIS) aided systems, the joint optimization of the precoder matrix at the base station and the phase shifts of the RIS elements involves significant complexity. In this paper, we propose a complex-valued, geometry aware meta-learning neural network that maximizes the weighted sum rate in a multi-user multiple input single output system. By leveraging the complex circle geometry for phase shifts and spherical geometry for the precoder, the optimization occurs on Riemannian manifolds, leading to faster convergence. We use a complex-valued neural network for phase shifts and an Euler inspired update for the precoder network. Our approach outperforms existing neural network-based algorithms, offering higher weighted sum rates, lower power consumption, and significantly faster convergence. Specifically, it converges faster by nearly 100 epochs, with a 0.7 bps improvement in weighted sum rate and a 1.8 dBm power gain when compared with existing work.

翻译：在可重构智能表面（RIS）辅助系统中，基站预编码器矩阵与RIS单元相位偏移的联合优化涉及较高复杂度。本文提出一种复数域几何感知元学习神经网络，用于最大化多用户多输入单输出系统中的加权和速率。通过利用相位偏移的复圆几何特性与预编码器的球面几何特性，优化过程在黎曼流形上进行，从而获得更快的收敛速度。我们采用复数神经网络处理相位偏移，并基于欧拉思想设计预编码器网络的更新机制。所提方法在加权和速率、功耗及收敛速度方面均优于现有基于神经网络的算法：相较于现有工作，收敛速度提升近100个训练周期，加权和速率提高0.7 bps，同时获得1.8 dBm的功率增益。