# Optimized Power Control Design for Over-the-Air Federated Edge Learning

arXiv: https://arxiv.org/abs/2106.09316 · HTML: https://mlsanity.com/paper/2106.09316/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2021.

## Built on by (most cited first, 30 of 48)

- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [Interference Management for Over-the-Air Federated Learning in Multi-Cell Wireless Networks](https://mlsanity.com/paper/2206.02398/) (2022)
- [Scalable Hierarchical Over-the-Air Federated Learning](https://mlsanity.com/paper/2211.16162/) (2022)
- [Over-the-Air Federated Learning via Second-Order Optimization](https://mlsanity.com/paper/2203.15488/) (2022)
- [Training Machine Learning models at the Edge: A Survey](https://mlsanity.com/paper/2403.02619/) (2024)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [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)
- [Integrated Sensing, Communication, and Computation for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2508.15185/) (2025)
- [CFLIT: Coexisting Federated Learning and Information Transfer](https://mlsanity.com/paper/2207.12884/) (2022)
- [Federated Distributionally Robust Optimization with Non-Convex Objectives: Algorithm and Analysis](https://mlsanity.com/paper/2307.14364/) (2023)
- [AirFL-Mem: Improving Communication-Learning Trade-Off by Long-Term Memory](https://mlsanity.com/paper/2310.16606/) (2023)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [Multiple Access in the Era of Distributed Computing and Edge Intelligence](https://mlsanity.com/paper/2403.07903/) (2024)
- [Federated Learning With Energy Harvesting Devices: An MDP Framework](https://mlsanity.com/paper/2405.10513/) (2024)
- [Biased Federated Learning under Wireless Heterogeneity](https://mlsanity.com/paper/2503.06078/) (2025)
- [Leveraging Channel Noise for Sampling and Privacy via Quantized Federated Langevin Monte Carlo](https://mlsanity.com/paper/2202.13932/) (2022)
- [Pre-Training and Personalized Fine-Tuning via Over-the-Air Federated Meta-Learning: Convergence-Generalization Trade-Offs](https://mlsanity.com/paper/2406.11569/) (2024)
- [Latency Minimization for UAV-Enabled Federated Learning: Trajectory Design and Resource Allocation](https://mlsanity.com/paper/2412.07428/) (2024)
- [Convergence Analysis of Over-the-Air FL with Compression and Power Control via Clipping](https://mlsanity.com/paper/2305.11135/) (2023)
- [Matching Pursuit Based Scheduling for Over-the-Air Federated Learning](https://mlsanity.com/paper/2206.06679/) (2022)
- [Adaptive Top-K in SGD for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/2210.13532/) (2022)
- [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)
- [Federated Learning over Hierarchical Wireless Networks: Training Latency Minimization via Submodel Partitioning](https://mlsanity.com/paper/2310.17890/) (2023)
- [Optimal Batch Allocation for Wireless Federated Learning](https://mlsanity.com/paper/2404.02395/) (2024)

## Abstract (arXiv)

This paper investigates the transmission power control in over-the-air federated edge learning (Air-FEEL) system. Different from conventional power control designs (e.g., to minimize the individual mean squared error (MSE) of the over-the-air aggregation at each round), we consider a new power control design aiming at directly maximizing the convergence speed. Towards this end, we first analyze the convergence behavior of Air-FEEL (in terms of the optimality gap) subject to aggregation errors at different communication rounds. It is revealed that if the aggregation estimates are unbiased, then the training algorithm would converge exactly to the optimal point with mild conditions; while if they are biased, then the algorithm would converge with an error floor determined by the accumulated estimate bias over communication rounds. Next, building upon the convergence results, we optimize the power control to directly minimize the derived optimality gaps under both biased and unbiased aggregations, subject to a set of average and maximum power constraints at individual edge devices. We transform both problems into convex forms, and obtain their structured optimal solutions, both appearing in a form of regularized channel inversion, by using the Lagrangian duality method. Finally, numerical results show that the proposed power control policies achieve significantly faster convergence for Air-FEEL, as compared with benchmark policies with fixed power transmission or conventional MSE minimization.