# Energy and Spectrum Efficient Federated Learning via High-Precision Over-the-Air Computation

arXiv: https://arxiv.org/abs/2208.07237 · HTML: https://mlsanity.com/paper/2208.07237/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 15 Aug 2022.

## Builds on (most cited first, 23 of 23)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [The Convergence of Sparsified Gradient Methods](https://mlsanity.com/paper/1809.10505/) (2018)
- [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)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [Federated Learning with Compression: Unified Analysis and Sharp Guarantees](https://mlsanity.com/paper/2007.01154/) (2020)
- [Distributed Mean Estimation with Limited Communication](https://mlsanity.com/paper/1611.00429/) (2016)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Communication Compression for Decentralized Training](https://mlsanity.com/paper/1803.06443/) (2018)
- [Accelerating Federated Learning via Momentum Gradient Descent](https://mlsanity.com/paper/1910.03197/) (2019)
- [Communication-Efficient Distributed Blockwise Momentum SGD with Error-Feedback](https://mlsanity.com/paper/1905.10936/) (2019)
- [To Talk or to Work: Flexible Communication Compression for Energy Efficient Federated Learning over Heterogeneous Mobile Edge Devices](https://mlsanity.com/paper/2012.11804/) (2020)
- [Robust Federated Learning with Noisy Communication](https://mlsanity.com/paper/1911.00251/) (2019)
- [Reconfigurable Intelligent Surface Enabled Federated Learning: A Unified Communication-Learning Design Approach](https://mlsanity.com/paper/2011.10282/) (2020)
- [Energy Efficient Federated Learning over Heterogeneous Mobile Devices via Joint Design of Weight Quantization and Wireless Transmission](https://mlsanity.com/paper/2012.11070/) (2020)
- [Towards Energy Efficient Federated Learning over 5G+ Mobile Devices](https://mlsanity.com/paper/2101.04866/) (2021)
- [Joint Optimization of Communications and Federated Learning Over the Air](https://mlsanity.com/paper/2104.03490/) (2021)
- [Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications](https://mlsanity.com/paper/1601.04059/) (2016)
- [Balancing Accuracy and Integrity for Reconfigurable Intelligent Surface-aided Over-the-Air Federated Learning](https://mlsanity.com/paper/2207.08057/) (2022)
- [An Overview on 3GPP Device-to-Device Proximity Services](https://mlsanity.com/paper/1310.0116/) (2013)

## Built on by (most cited first, 6 of 6)

- [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)
- [Digital Over-the-Air Federated Learning in Multi-Antenna Systems](https://mlsanity.com/paper/2302.14648/) (2023)
- [Federated Learning with Integrated Sensing, Communication, and Computation: Frameworks and Performance Analysis](https://mlsanity.com/paper/2409.11240/) (2024)
- [How Can Incentives and Cut Layer Selection Influence Data Contribution in Split Federated Learning?](https://mlsanity.com/paper/2412.07813/) (2024)
- [Energy-Efficient Federated Learning for Edge Real-Time Vision via Joint Data, Computation, and Communication Design](https://mlsanity.com/paper/2508.01745/) (2025)

## Abstract (arXiv)

Federated learning (FL) enables mobile devices to collaboratively learn a shared prediction model while keeping data locally. However, there are two major research challenges to practically deploy FL over mobile devices: (i) frequent wireless updates of huge size gradients v.s. limited spectrum resources, and (ii) energy-hungry FL communication and local computing during training v.s. battery-constrained mobile devices. To address those challenges, in this paper, we propose a novel multi-bit over-the-air computation (M-AirComp) approach for spectrum-efficient aggregation of local model updates in FL and further present an energy-efficient FL design for mobile devices. Specifically, a high-precision digital modulation scheme is designed and incorporated in the M-AirComp, allowing mobile devices to upload model updates at the selected positions simultaneously in the multi-access channel. Moreover, we theoretically analyze the convergence property of our FL algorithm. Guided by FL convergence analysis, we formulate a joint transmission probability and local computing control optimization, aiming to minimize the overall energy consumption (i.e., iterative local computing + multi-round communications) of mobile devices in FL. Extensive simulation results show that our proposed scheme outperforms existing ones in terms of spectrum utilization, energy efficiency, and learning accuracy.