Learning End-to-End Precoding for Time-Varying Channels with Graph Neural Networks

End-to-end (E2E) precoding leverages deep neural networks (DNNs) to learn the downlink precoding policies directly from the uplink sounding reference signals in multi-user multi-antenna time-division duplexing systems, bypassing explicit channel prediction for real-time inference in dynamic channels. However, the existing DNNs face high training complexity due to their inability to harness permutation properties in E2E precoding policies, a kind of crucial prior knowledge that has the capability to significantly reduce the training complexity. Furthermore, these DNNs lack generalizability to different problem sizes (e.g., the number of users) and suffer severe performance degradation with changing channel distributions, limiting their applicability in dynamic wireless environments. This paper addresses these challenges by first investigating the permutation equivariance (PE) properties of E2E precoding policies in time-varying channels. Based on this understanding, we propose a hybrid graph neural network (GNN) structure to match these desired PE properties. Additionally, we incorporate an appropriate attention mechanism and develop training methods to enhance the size and distribution generalization capabilities of the GNN. Simulation results validate that our proposed methods outperform existing E2E approaches in dynamic wireless environments.