How to Improve Learning Efficiency of GNN for Precoding?

Learning precoding with deep neural networks (DNNs) enables real-time implementation and robustness to imperfect channels. However, existing DNNs for learning precoding suffer from high training complexity and weak generalization ability to problem scales, which impedes their practical use in wireless systems with user scheduling. In this paper, we propose a graph neural network (GNN) to learn precoding policies efficiently by resorting to the model of Taylor’s expansion of matrix pseudo-inverse. The GNN can capture the importance of neighbored edges when aggregating their information, which is critical for improving the learning efficiency. We also interpret the role of the trainable parameters on learning the powers and directions of the precoding vectors. Simulation results show that the proposed model-driven GNN can well-learn spectral and energy efficient precoding policies with low training complexity, and is generalizable to the numbers of users.

I. Introduction

Optimizing precoding is crucial for boosting spectral efficiency (SE) and energy efficiency (EE) of multi-input-multi-output (MIMO) systems. Learning precoding policies with deep neural networks (DNNs) enables the policies to be implemented in real-time [1], robust to channel estimation errors, and without explicit channel estimation [2]. While many DNNs such as fully connected neural networks (FNNs) [1] and convolutional neural networks [3], [4] have been designed for learning precoding policies, these DNNs are trained with high complexity and not guaranteed to be generalizable to every impact parameter such as the number of users. Since wireless systems are operated in open and dynamic environments, the learning efficiency of the DNNs in terms of generalization ability and training complexity is of paramount importance.