# Scalable Hierarchical Over-the-Air Federated Learning

arXiv: https://arxiv.org/abs/2211.16162 · HTML: https://mlsanity.com/paper/2211.16162/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [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)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learning](https://mlsanity.com/paper/2002.11343/) (2020)
- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Hierarchical Federated Learning with Quantization: Convergence Analysis and System Design](https://mlsanity.com/paper/2103.14272/) (2021)
- [Convergence of Federated Learning over a Noisy Downlink](https://mlsanity.com/paper/2008.11141/) (2020)
- [Federated Learning in Unreliable and Resource-Constrained Cellular Wireless Networks](https://mlsanity.com/paper/2012.05137/) (2020)
- [Interference Management for Over-the-Air Federated Learning in Multi-Cell Wireless Networks](https://mlsanity.com/paper/2206.02398/) (2022)
- [Turning Channel Noise into an Accelerator for Over-the-Air Principal Component Analysis](https://mlsanity.com/paper/2104.10095/) (2021)
- [FedChain: Chained Algorithms for Near-Optimal Communication Cost in Federated Learning](https://mlsanity.com/paper/2108.06869/) (2021)
- [Hierarchical Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2112.11167/) (2021)
- [3GPP-inspired HetNet Model using Poisson Cluster Process: Sum-product Functionals and Downlink Coverage](https://mlsanity.com/paper/1705.01699/) (2017)

## Built on by (most cited first, 14 of 14)

- [Blind Federated Learning via Over-the-Air q-QAM](https://mlsanity.com/paper/2311.04253/) (2023)
- [Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneity](https://mlsanity.com/paper/2401.01442/) (2024)
- [Federated Learning via Lattice Joint Source-Channel Coding](https://mlsanity.com/paper/2403.01023/) (2024)
- [Compute-Update Federated Learning: A Lattice Coding Approach Over-the-Air](https://mlsanity.com/paper/2409.06343/) (2024)
- [Over-the-Air Federated Learning via Weighted Aggregation](https://mlsanity.com/paper/2409.07822/) (2024)
- [Hierarchical Federated ADMM](https://mlsanity.com/paper/2409.18796/) (2024)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [A Generalized Hierarchical Federated Learning Framework with Theoretical Guarantees](https://mlsanity.com/paper/2505.08145/) (2025)
- [A Hierarchical Federated Learning Approach for the Internet of Things](https://mlsanity.com/paper/2403.01540/) (2024)
- [A Green Multi-Attribute Client Selection for Over-The-Air Federated Learning: A Grey-Wolf-Optimizer Approach](https://mlsanity.com/paper/2409.11442/) (2024)
- [Mitigating Heterogeneity-Induced Drift in Hierarchical Sign-Based Federated Learning](https://mlsanity.com/paper/2602.02355/) (2026)
- [Federated Multi Agent Deep Learning and Neural Networks for Advanced Distributed Sensing in Wireless Networks](https://mlsanity.com/paper/2603.16881/) (2026)
- [Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design](https://mlsanity.com/paper/2605.00931/) (2026)
- [AirPASS: Over-the-Air Federated Learning via Pinching Antenna Systems](https://mlsanity.com/paper/2607.06768/) (2026)

## Abstract (arXiv)

When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a new two-level learning method designed to address these challenges, along with a scalable over-the-air aggregation scheme for the uplink and a bandwidth-limited broadcast scheme for the downlink that efficiently use a single wireless resource. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of uplink and downlink interference is minimized through optimized receiver normalizing factors. We present a comprehensive mathematical approach to derive the convergence bound for the proposed algorithm, applicable to a multi-cluster wireless network encompassing any count of collaborating clusters, and provide special cases and design remarks. As a key step to enable a tractable analysis, we develop a spatial model for the setup by modeling devices as a Poisson cluster process over the edge servers and rigorously quantify uplink and downlink error terms due to the interference. Finally, we show that despite the interference and data heterogeneity, the proposed algorithm not only achieves high learning accuracy for a variety of parameters but also significantly outperforms the conventional hierarchical learning algorithm.