A Size-Generalizable GNN for Learning Precoding

Graph neural networks (GNNs) have been shown promising in optimizing power allocation and link scheduling with good size generalizability and low sample complexity, which are important for learning wireless policies under dynamic environments. This attributes to their matched permutation equivariance (PE) properties to the policies to be learned. Nonetheless, existing works have demonstrated that only satisfying the PE property cannot ensure a GNN for learning precoding policy to be generalizable to the unseen problem scales, say the number of users. Incorporating models with neural networks helps improve size generalizability, which however is only applicable to specific problems. In this paper, we strive to design a size generalizable GNN that does not depend on any mathematical model, such that the GNN can learn wireless policies including but not limited to baseband and hybrid precoding in multi-user multi-antenna systems. To this end, we first identify the key characteristics of the update equation of a GNN that affect its size generalization ability. Then, we design a size-generalizable GNN that is with these key characteristics and satisfies the PE property of a precoding policy in a recursive manner. Simulation results show that the proposed GNN can be well-generalized to the number of users for learning precoding policies.