Learning Beamforming for RIS-aided Systems with Permutation Equivariant Graph Neural Networks

Reconfigurable intelligent surface (RIS) is capable of controlling environment smartly for improving the performance of wireless communications. To reduce the pilot overhead of estimating the high-dimensional channels in RIS-aided systems, deep neural networks have been introduced to learn the beamforming policy with received pilot sequences in an end-to-end (E2E) manner. However, existing works either ignore or only consider part of the permutation equivariant (PE) properties of the E2E policy. As a result, the designed neural networks suffer from high sample complexity. In this paper, we analyze the PE property of an E2E active and passive beamforming policy in a RIS-aided multi-user multi-antenna system, and design a graph neural network (GNN) architecture with matched inductive bias to learn the policy. By taking sum rate maximization problem as an example, simulation results demonstrate the benefits of the proposed GNN in terms of reducing the sample complexity to achieve the expected sum rate.