Geometry Aware Meta-Learning Neural Network for Joint Phase and Precoder Optimization in RIS

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 dB power gain when compared with existing work. Further it outperforms the state-of-the-art alternating optimization algorithm by 0.86 bps with a 2.6 dB power gain.