AirGNN: Graph Neural Network over the Air

Graph neural networks (GNNs) are information processing architectures that model representations from networked data and allow for decentralized implementation through localized communications. Existing GNN architectures often assume ideal communication links, and ignore channel effects, such as fading and noise, leading to performance degradation in real-world implementation. This paper proposes graph neural networks over the air (AirGNNs), a novel GNN architecture that incorporates the communication model into the architecture. The AirGNN modifies the graph convolutional operation that shifts graph signals over random communication graphs to take into account channel fading and noise when aggregating features from neighbors, thus, improving the architecture robustness to channel impairments during testing. We propose a stochastic gradient descent based method to train the AirGNN, and show that the training procedure converges to a stationary solution. Numerical simulations on decentralized source localization and multi-robot flocking corroborate theoretical findings and show superior performance of the AirGNN over wireless communication channels.