# Over-the-Air Federated Edge Learning with Hierarchical Clustering

arXiv: https://arxiv.org/abs/2207.09232 · HTML: https://mlsanity.com/paper/2207.09232/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [Federated learning with hierarchical clustering of local updates to improve training on non-IID data](https://mlsanity.com/paper/2004.11791/) (2020)
- [Client-Edge-Cloud Hierarchical Federated Learning](https://mlsanity.com/paper/1905.06641/) (2019)
- [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)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Hierarchical Federated Learning Across Heterogeneous Cellular Networks](https://mlsanity.com/paper/1909.02362/) (2019)
- [Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation](https://mlsanity.com/paper/1910.13067/) (2019)
- [Byzantine-Resilient Secure Federated Learning](https://mlsanity.com/paper/2007.11115/) (2020)
- [HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learning](https://mlsanity.com/paper/2002.11343/) (2020)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Convergence of Update Aware Device Scheduling for Federated Learning at the Wireless Edge](https://mlsanity.com/paper/2001.10402/) (2020)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [Scheduling for Cellular Federated Edge Learning with Importance and Channel Awareness](https://mlsanity.com/paper/2004.00490/) (2020)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [Federated Edge Learning with Misaligned Over-The-Air Computation](https://mlsanity.com/paper/2102.13604/) (2021)
- [Communicate to Learn at the Edge](https://mlsanity.com/paper/2009.13269/) (2020)
- [Byzantine-Resilient SGD in High Dimensions on Heterogeneous Data](https://mlsanity.com/paper/2005.07866/) (2020)
- [Hierarchical Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2112.11167/) (2021)
- [Federated Learning with Downlink Device Selection](https://mlsanity.com/paper/2107.03510/) (2021)

## Built on by (most cited first, 10 of 10)

- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [Update Estimation and Scheduling for Over-the-Air Federated Learning with Energy Harvesting Devices](https://mlsanity.com/paper/2501.18298/) (2025)
- [A Generalized Hierarchical Federated Learning Framework with Theoretical Guarantees](https://mlsanity.com/paper/2505.08145/) (2025)
- [Federated Learning over Hierarchical Wireless Networks: Training Latency Minimization via Submodel Partitioning](https://mlsanity.com/paper/2310.17890/) (2023)
- [Mitigating Heterogeneity-Induced Drift in Hierarchical Sign-Based Federated Learning](https://mlsanity.com/paper/2602.02355/) (2026)
- [SCENE OTA-FD: Self-Centering Noncoherent Estimator for Over-the-Air Federated Distillation](https://mlsanity.com/paper/2602.15326/) (2026)
- [Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design](https://mlsanity.com/paper/2605.00931/) (2026)
- [Cluster-Aware Over-the-Air Federated Learning with Energy-Harvesting Devices: From Global Training to Model Personalization](https://mlsanity.com/paper/2608.01426/) (2026)

## Abstract (arXiv)

We examine federated learning (FL) with over-the-air (OTA) aggregation, where mobile users (MUs) aim to reach a consensus on a global model with the help of a parameter server (PS) that aggregates the local gradients. In OTA FL, MUs train their models using local data at every training round and transmit their gradients simultaneously using the same frequency band in an uncoded fashion. Based on the received signal of the superposed gradients, the PS performs a global model update. While the OTA FL has a significantly decreased communication cost, it is susceptible to adverse channel effects and noise. Employing multiple antennas at the receiver side can reduce these effects, yet the path-loss is still a limiting factor for users located far away from the PS. To ameliorate this issue, in this paper, we propose a wireless-based hierarchical FL scheme that uses intermediate servers (ISs) to form clusters at the areas where the MUs are more densely located. Our scheme utilizes OTA cluster aggregations for the communication of the MUs with their corresponding IS, and OTA global aggregations from the ISs to the PS. We present a convergence analysis for the proposed algorithm, and show through numerical evaluations of the derived analytical expressions and experimental results that utilizing ISs results in a faster convergence and a better performance than the OTA FL alone while using less transmit power. We also validate the results on the performance using different number of cluster iterations with different datasets and data distributions. We conclude that the best choice of cluster aggregations depends on the data distribution among the MUs and the clusters.