# Non-Coherent Over-the-Air Federated Learning: Protocol, Convergence, and Device Scheduling

arXiv: https://arxiv.org/abs/2609.08312 · HTML: https://mlsanity.com/paper/2609.08312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Achieving Linear Speedup with Partial Worker Participation in Non-IID Federated Learning](https://mlsanity.com/paper/2101.11203/) (2021)
- [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)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Scheduling for Cellular Federated Edge Learning with Importance and Channel Awareness](https://mlsanity.com/paper/2004.00490/) (2020)
- [Fast-Convergent Federated Learning](https://mlsanity.com/paper/2007.13137/) (2020)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Gradient and Channel Aware Dynamic Scheduling for Over-the-Air Computation in Federated Edge Learning Systems](https://mlsanity.com/paper/2212.00491/) (2022)
- [Random Orthogonalization for Federated Learning in Massive MIMO Systems](https://mlsanity.com/paper/2201.12490/) (2022)
- [Efficient Federated Meta-Learning over Multi-Access Wireless Networks](https://mlsanity.com/paper/2108.06453/) (2021)
- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [Channel and Gradient-Importance Aware Device Scheduling for Over-the-Air Federated Learning](https://mlsanity.com/paper/2305.16854/) (2023)
- [Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow](https://mlsanity.com/paper/1811.04644/) (2018)
- [AirFL-Mem: Improving Communication-Learning Trade-Off by Long-Term Memory](https://mlsanity.com/paper/2310.16606/) (2023)
- [NCAirFL: CSI-Free Over-the-Air Federated Learning Based on Non-Coherent Detection](https://mlsanity.com/paper/2411.13000/) (2024)
- [Biased Federated Learning under Wireless Heterogeneity](https://mlsanity.com/paper/2503.06078/) (2025)
- [Pre-Training and Personalized Fine-Tuning via Over-the-Air Federated Meta-Learning: Convergence-Generalization Trade-Offs](https://mlsanity.com/paper/2406.11569/) (2024)
- [Robust and Efficient Average Consensus with Non-Coherent Over-the-Air Aggregation](https://mlsanity.com/paper/2504.05729/) (2025)

## Abstract (arXiv)

To mitigate the scalability bottleneck in the radio access network (RAN) in federated edge learning (FEEL), over-the-air federated learning (AirFL) exploits waveform superposition over multiple-access channels (MACs) for analog model aggregation. However, coherent AirFL typically relies on stringent PHY-layer conditions such as accurate channel state information (CSI), tight time/frequency synchronization, and frequent transceiver calibration for signal alignment. However, these requirements, if not impossible to be met, incur substantial communication and computation overhead. In this paper, we propose a non-coherent AirFL (NCAirFL) protocol over a broadband single-antenna MAC, leveraging binary dithering, unbiased non-coherent detection, and long-term error feedback to waive the need for instantaneous CSI. For NCAirFL with general smooth non-convex objectives and a constant learning rate, we establish a convergence bound achieving the convergence rate in the same order of O(1/√T) as communication-ideal FedAvg, where T is the total number of communication rounds. To further improve communication efficiency under data and wireless resource heterogeneity, we also derive a lower bound on the expected single-round objective decrease in the global loss conditioned on device scheduling, building upon which a surrogate objective function is obtained for jointly optimal device selection and power control. Experimental results on MNIST and CIFAR-10 corroborate that NCAirFL achieves learning performance close to FedAvg in practical settings, with the proposed device scheduling policy substantially accelerating convergence.