Over-the-Air Federated Learning in Heterogeneous Mobile Wireless Networks

2026-09-26

AI Summary

This study addresses the noise amplification and convergence bias issues in over-the-air computation-based federated learning under heterogeneous wireless channels by proposing the FedOAG framework. This method achieves efficient model aggregation through gradient normalization and an implicit gossip protocol, eliminating the need for synchronous transmission across all devices or specific channel prior knowledge. Furthermore, it automatically satisfies energy consumption constraints while significantly suppressing receiver-side noise. Theoretically, we prove that FedOAG converges to an unbiased stationary point at the optimal rate of $O(1/\sqrt{T})$ under non-convex optimization settings. Experimental evaluations on real-world datasets validate the effectiveness of the proposed approach.

Abstract

Over-the-air computation has emerged as a scalable and efficient solution for deploying federated learning algorithms in wireless networks by exploiting waveform superposition for simultaneous model aggregation. Most existing work struggles with heterogeneous fading channels. These approaches either enforce unbiased updates from all devices or allow partial device contributions, requiring careful tuning of the convergence bound to mitigate bias under specific fading models. However, the former significantly amplifies receiver noise due to the weakest channel, whereas the latter is sensitive to fading model mismatch and converges only to a biased objective. To tackle these challenges, we propose FedOAG, which employs algorithmic components to automatically satisfy energy constraints via gradient normalization and evenly mix devices'updates through implicit gossiping. Importantly, FedOAG does not require transmission from all devices, nor does it rely on a specific fading model or knowledge of time-varying statistical channel distributions. We show that FedOAG converges to a stationary point of an unbiased non-convex objective at the best possible rate $O(1/\sqrt{T})$ for any stochastic first-order method. We corroborate our analysis with numerical experiments over dynamic wireless conditions on real-world datasets.

Problem

• Over-the-Air Federated Learning
• Heterogeneous Fading Channels
• Mobile Wireless Networks
• Receiver Noise Amplification
• Biased Objective

Innovation

• Over-the-Air Federated Learning
• Heterogeneous Fading Channels
• Gradient Normalization
• Implicit Gossiping
• Unbiased Convergence