A Model-based GNN for Learning Precoding

TL;DR

This paper introduces a novel graph neural network approach for learning precoding policies in multi-user MIMO systems, addressing training complexity and generalization issues of previous neural network methods.

Contribution

The paper proposes a GNN based on Taylor's expansion of matrix pseudo-inverse, improving learning efficiency and generalization for precoding in multi-user systems.

Findings

Effective in learning spectral and energy-efficient precoding policies

Low training complexity compared to existing methods

Generalizes well to varying numbers of users

Abstract

Learning precoding policies with neural networks enables low complexity online implementation, robustness to channel impairments, and joint optimization with channel acquisition. However, existing neural networks suffer from high training complexity and poor generalization ability when they are used to learn to optimize precoding for mitigating multi-user interference. This impedes their use in practical systems where the number of users is time-varying. In this paper, we propose a graph neural network (GNN) to learn precoding policies by harnessing both the mathematical model and the property of the policies. We first show that a vanilla GNN cannot well-learn pseudo-inverse of channel matrix when the numbers of antennas and users are large, and is not generalizable to unseen numbers of users. Then, we design a GNN by resorting to the Taylor's expansion of matrix pseudo-inverse, which allows for capturing the importance of the neighbored edges to be aggregated that is crucial for learning precoding policies efficiently. Simulation results show that the proposed GNN can well learn spectral efficient and energy efficient precoding policies in single- and multi-cell multi-user multi-antenna systems with low training complexity, and can be well generalized to the numbers of users.