Gradient based Information Aggregation of GNN for Precoder Learning

Employing graph neural networks (GNNs) for learning the multiuser multi-input multi-output precoder has gained significant attention recently. By modeling the precoder optimization problem in a graph format, GNN can effectively capture the representation of the precoder by leveraging the information aggregated and propagated across the graph. In this paper, we strive to design the information aggregation mechanism of GNN. By analyzing the behavior of the numerical gradient descent algorithm for precoder optimization, we identify the relevant information and the appropriate form for aggregation, enabling us to develop new update equations for GNNs. Simulation results demonstrate the advantages of the proposed GNNs in learning and generalization performance.

I. Introduction

Precoder optimization for multiuser multi-input multi-output (MU-MIMO) systems with the objective of sum rate maximization is a widely recognized challenging problem. Various numerical methods have been studied, e.g., the weighted minimum mean square error (WMMSE) algorithm [1]. Although the numerical algorithms exhibit good performance, the significant computational cost remains a major hurdle for real-time implementation.