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 the 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 notice that a Transformer tailored for precoding can reflect multiuser interference, which is essential for its generalizability to the number of users. Yet the tailored Transformer can only leverage partial permutation property of precoding policies and hence is not generalizable to the number of antennas, same as a GNN learning over a homogeneous graph. To provide useful insight, we establish the relation between Transformers and the GNNs that learn over heterogeneous graphs. Based on the 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 Transformers and GNNs via simulations.