A Size-Generalizable Graph Neural Network for Learning Multi-User Multi-Stream MIMO Precoding

Learning precoding with deep neural networks (DNNs) is promising for real-time implementation and joint optimization with channel acquisition. To improve learning efficiency in terms of reducing training complexity and enabling size-generalizability, permutation equivariance properties can be leveraged by designing graph neural networks (GNNs). However, the size-generalizability cannot be ensured unless the GNN is judiciously designed. Mathematical models can also be harnessed for efficient learning, but the applications of the model-based DNNs are restricted by the incorporated models. In this paper, we propose a purely data-driven GNN for learning precoding in a multi-user multi-antenna system, where each user is equipped with multi-antennas for receiving multi-streams. By re-expressing the iterative equation of an algorithm for optimizing precoding as the update equation of a well-trained GNN, we can find key components in the update equation that affect the size-generalizability. Then, a size-generalizable GNN can be designed by letting the components trainable. Simulation results validate the size-generalizability of the proposed GNN for learning precoding policies.