# Spectrum Breathing: Protecting Over-the-Air Federated Learning Against Interference

arXiv: https://arxiv.org/abs/2305.05933 · HTML: https://mlsanity.com/paper/2305.05933/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 48 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 24 of 24)

- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [The Convergence of Sparsified Gradient Methods](https://mlsanity.com/paper/1809.10505/) (2018)
- [Model Pruning Enables Efficient Federated Learning on Edge Devices](https://mlsanity.com/paper/1909.12326/) (2019)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [The Roadmap to 6G -- AI Empowered Wireless Networks](https://mlsanity.com/paper/1904.11686/) (2019)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [Joint Device Scheduling and Resource Allocation for Latency Constrained Wireless Federated Learning](https://mlsanity.com/paper/2007.07174/) (2020)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Federated Dropout -- A Simple Approach for Enabling Federated Learning on Resource Constrained Devices](https://mlsanity.com/paper/2109.15258/) (2021)
- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [Federated Learning via Intelligent Reflecting Surface](https://mlsanity.com/paper/2011.05051/) (2020)
- [Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms](https://mlsanity.com/paper/1506.06438/) (2015)
- [Time-Correlated Sparsification for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2101.08837/) (2021)
- [Federated Learning over Energy Harvesting Wireless Networks](https://mlsanity.com/paper/2106.08809/) (2021)
- [Joint Parameter-and-Bandwidth Allocation for Improving the Efficiency of Partitioned Edge Learning](https://mlsanity.com/paper/2003.04544/) (2020)
- [Turning Channel Noise into an Accelerator for Over-the-Air Principal Component Analysis](https://mlsanity.com/paper/2104.10095/) (2021)
- [BEV-SGD: Best Effort Voting SGD for Analog Aggregation Based Federated Learning against Byzantine Attackers](https://mlsanity.com/paper/2110.09660/) (2021)
- [Simultaneous Signal-and-Interference Alignment for Two-Cell Over-the-Air Computation](https://mlsanity.com/paper/2001.03309/) (2020)

## Built on by (most cited first, 9 of 9)

- [Revisiting Outage for Edge Inference Systems](https://mlsanity.com/paper/2504.03686/) (2025)
- [SpaceMoE: Realizing Distributed Mixture-of-Experts Inference over Space Networks](https://mlsanity.com/paper/2605.00515/) (2026)
- [FedMeld: A Model-dispersal Federated Learning Framework for Space-ground Integrated Networks](https://mlsanity.com/paper/2412.17231/) (2024)
- [Optimal Batch-Size Control for Low-Latency Federated Learning with Device Heterogeneity](https://mlsanity.com/paper/2507.15601/) (2025)
- [FedLoDrop: Federated LoRA with Dropout for Generalized LLM Fine-tuning](https://mlsanity.com/paper/2510.12078/) (2025)
- [Unified Error Correction Code Transformer with Low Complexity](https://mlsanity.com/paper/2410.03364/) (2024)
- [LoLaFL: Low-Latency Federated Learning via Forward-only Propagation](https://mlsanity.com/paper/2412.14668/) (2024)
- [Generative Feature Imputing -- A Technique for Error-resilient Semantic Communication](https://mlsanity.com/paper/2508.17957/) (2025)
- [Efficient Resource Optimization for Split Federated Learning](https://mlsanity.com/paper/2608.17849/) (2026)

## Abstract (arXiv)

Federated Learning (FL) is a widely embraced paradigm for distilling artificial intelligence from distributed mobile data. However, the deployment of FL in mobile networks can be compromised by exposure to interference from neighboring cells or jammers. Existing interference mitigation techniques require multi-cell cooperation or at least interference channel state information, which is expensive in practice. On the other hand, power control that treats interference as noise may not be effective due to limited power budgets, and also that this mechanism can trigger countermeasures by interference sources. As a practical approach for protecting FL against interference, we propose Spectrum Breathing, which cascades stochastic-gradient pruning and spread spectrum to suppress interference without bandwidth expansion. The cost is higher learning latency by exploiting the graceful degradation of learning speed due to pruning. We synchronize the two operations such that their levels are controlled by the same parameter, Breathing Depth. To optimally control the parameter, we develop a martingale-based approach to convergence analysis of Over-the-Air FL with spectrum breathing, termed AirBreathing FL. We show a performance tradeoff between gradient-pruning and interference-induced error as regulated by the breathing depth. Given receive SIR and model size, the optimization of the tradeoff yields two schemes for controlling the breathing depth that can be either fixed or adaptive to channels and the learning process. As shown by experiments, in scenarios where traditional Over-the-Air FL fails to converge in the presence of strong interference, AirBreahing FL with either fixed or adaptive breathing depth can ensure convergence where the adaptive scheme achieves close-to-ideal performance.