Graph Neural Networks over the Air for Decentralized Tasks in Wireless Networks

TL;DR

This paper introduces AirGNNs, a novel GNN architecture designed for wireless networks that accounts for channel impairments like fading and noise, enhancing robustness in decentralized tasks.

Contribution

It proposes a new GNN model over the air that incorporates wireless channel effects, along with training strategies for scenarios with and without channel state information.

Findings

AirGNNs outperform traditional GNNs in wireless environments.

The proposed training methods ensure convergence to a stationary solution.

Experiments demonstrate improved decentralized task performance over wireless channels.

Abstract

Graph neural networks (GNNs) model representations from networked data and allow for decentralized inference through localized communications. Existing GNN architectures often assume ideal communications and ignore potential channel effects, such as fading and noise, leading to performance degradation in real-world implementation. Considering a GNN implemented over nodes connected through wireless links, this paper conducts a stability analysis to study the impact of channel impairments on the performance of GNNs, and proposes graph neural networks over the air (AirGNNs), a novel GNN architecture that incorporates the communication model. AirGNNs modify graph convolutional operations that shift graph signals over random communication graphs to take into account channel fading and noise when aggregating features from neighbors, thus, improving architecture robustness to channel impairments during testing. We develop a channel-inversion signal transmission strategy for AirGNNs when channel state information (CSI) is available, and propose a stochastic gradient descent based method to train AirGNNs when CSI is unknown. The convergence analysis shows that the training procedure approaches a stationary solution of an associated stochastic optimization problem and the variance analysis characterizes the statistical behavior of the trained model. Experiments on decentralized source localization and multi-robot flocking corroborate theoretical findings and show superior performance of AirGNNs over wireless communication channels.