# Joint Optimization of Communications and Federated Learning Over the Air

arXiv: https://arxiv.org/abs/2104.03490 · HTML: https://mlsanity.com/paper/2104.03490/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 41 references that are in the map.
- First posted on arXiv 8 Apr 2021.

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

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [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)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [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)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms](https://mlsanity.com/paper/1808.07576/) (2018)
- [DoubleSqueeze: Parallel Stochastic Gradient Descent with Double-Pass Error-Compensated Compression](https://mlsanity.com/paper/1905.05957/) (2019)
- [LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/1805.09965/) (2018)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [Wireless Network Intelligence at the Edge](https://mlsanity.com/paper/1812.02858/) (2018)
- [Energy-Efficient Radio Resource Allocation for Federated Edge Learning](https://mlsanity.com/paper/1907.06040/) (2019)
- [Communication-Computation Efficient Gradient Coding](https://mlsanity.com/paper/1802.03475/) (2018)
- [Cell-Free Massive MIMO for Wireless Federated Learning](https://mlsanity.com/paper/1909.12567/) (2019)
- [Energy-Aware Analog Aggregation for Federated Learning with Redundant Data](https://mlsanity.com/paper/1911.00188/) (2019)
- [Asynchronous Stochastic Coordinate Descent: Parallelism and Convergence Properties](https://mlsanity.com/paper/1403.3862/) (2014)
- [On Maintaining Linear Convergence of Distributed Learning and Optimization under Limited Communication](https://mlsanity.com/paper/1902.11163/) (2019)
- [Collaborative Machine Learning at the Wireless Edge with Blind Transmitters](https://mlsanity.com/paper/1907.03909/) (2019)

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

- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Over-the-Air Federated Learning via Second-Order Optimization](https://mlsanity.com/paper/2203.15488/) (2022)
- [Channel and Gradient-Importance Aware Device Scheduling for Over-the-Air Federated Learning](https://mlsanity.com/paper/2305.16854/) (2023)
- [BEV-SGD: Best Effort Voting SGD for Analog Aggregation Based Federated Learning against Byzantine Attackers](https://mlsanity.com/paper/2110.09660/) (2021)
- [Energy and Spectrum Efficient Federated Learning via High-Precision Over-the-Air Computation](https://mlsanity.com/paper/2208.07237/) (2022)
- [Multiple Access in the Era of Distributed Computing and Edge Intelligence](https://mlsanity.com/paper/2403.07903/) (2024)
- [Distributed Swarm Learning for Edge Internet of Things](https://mlsanity.com/paper/2403.20188/) (2024)
- [Over-the-Air Federated Edge Learning with Error-Feedback One-Bit Quantization and Power Control](https://mlsanity.com/paper/2303.11319/) (2023)
- [Over-the-Air Federated Averaging with Limited Power and Privacy Budgets](https://mlsanity.com/paper/2305.03547/) (2023)
- [Semi-Federated Learning: Convergence Analysis and Optimization of A Hybrid Learning Framework](https://mlsanity.com/paper/2310.02559/) (2023)
- [Waveform Design for Over-the-Air Computing](https://mlsanity.com/paper/2405.20877/) (2024)
- [Multi-Worker Selection based Distributed Swarm Learning for Edge IoT with Non-i.i.d. Data](https://mlsanity.com/paper/2509.18367/) (2025)
- [Hidden in Rounds: Predicting the Time Cost of 802.11 Contention in Federated Learning](https://mlsanity.com/paper/2609.12903/) (2026)

## Abstract (arXiv)

Federated learning (FL) is an attractive paradigm for making use of rich distributed data while protecting data privacy. Nonetheless, nonideal communication links and limited transmission resources may hinder the implementation of fast and accurate FL. In this paper, we study joint optimization of communications and FL based on analog aggregation transmission in realistic wireless networks. We first derive closed-form expressions for the expected convergence rate of FL over the air, which theoretically quantify the impact of analog aggregation on FL. Based on the analytical results, we develop a joint optimization model for accurate FL implementation, which allows a parameter server to select a subset of workers and determine an appropriate power scaling factor. Since the practical setting of FL over the air encounters unobservable parameters, we reformulate the joint optimization of worker selection and power allocation using controlled approximation. Finally, we efficiently solve the resulting mixed-integer programming problem via a simple yet optimal finite-set search method by reducing the search space. Simulation results show that the proposed solutions developed for realistic wireless analog channels outperform a benchmark method, and achieve comparable performance of the ideal case where FL is implemented over noise-free wireless channels.