Learning Precoding in Multi-User Multi-Antenna Systems: Transformer or Graph Transformer?

Transformers have been designed for channel acquisition tasks such as channel prediction and other tasks such as precoding, while graph neural networks (GNNs) have been demonstrated to be efficient for learning a multitude of communication tasks. Nonetheless, whether or not Transformers are efficient for tasks other than channel acquisition and how to reap the benefits of both architectures are less understood. In this paper, we take learning precoding policies in multi-user multi-antenna systems as an example to answer the questions. We first show how to tailor the Transformer for precoding. By leveraging the permutation properties of precoding policies and reflecting multi-user interference with attention mechanism, the tailored Transformer can be generalized to the number of users. Yet a part of the permutation property is still overlooked, leading to non-generalizability to the number of antennas. To gain useful insights, we establish the relation between Transformers and the GNNs learning over heterogeneous graphs. Based on this relation, we propose Graph Transformers, namely 2D- and 3D-Gformers, for exploiting the permutation properties of baseband precoding and hybrid precoding policies. The learning performance, inference and training complexity, and size-generalizability of the Gformers are evaluated and compared with existing counterparts via simulations.