# Non-Coherent Over-the-Air Decentralized Gradient Descent

arXiv: https://arxiv.org/abs/2211.10777 · HTML: https://mlsanity.com/paper/2211.10777/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Builds on (most cited first, 30 of 33)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (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)
- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [Federated Learning with Cooperating Devices: A Consensus Approach for Massive IoT Networks](https://mlsanity.com/paper/1912.13163/) (2019)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [Semi-Decentralized Federated Learning with Cooperative D2D Local Model Aggregations](https://mlsanity.com/paper/2103.10481/) (2021)
- [Wireless Communications for Collaborative Federated Learning](https://mlsanity.com/paper/2006.02499/) (2020)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Multi-Stage Hybrid Federated Learning over Large-Scale D2D-Enabled Fog Networks](https://mlsanity.com/paper/2007.09511/) (2020)
- [A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free!](https://mlsanity.com/paper/2011.01697/) (2020)
- [An Exact Quantized Decentralized Gradient Descent Algorithm](https://mlsanity.com/paper/1806.11536/) (2018)
- [Convergence of Federated Learning over a Noisy Downlink](https://mlsanity.com/paper/2008.11141/) (2020)
- [A general framework for decentralized optimization with first-order methods](https://mlsanity.com/paper/2009.05837/) (2020)
- [Quantized Decentralized Stochastic Learning over Directed Graphs](https://mlsanity.com/paper/2002.09964/) (2020)
- [Massive Access for 5G and Beyond](https://mlsanity.com/paper/2002.03491/) (2020)
- [Over-the-Air Decentralized Federated Learning](https://mlsanity.com/paper/2106.08011/) (2021)
- [On Maintaining Linear Convergence of Distributed Learning and Optimization under Limited Communication](https://mlsanity.com/paper/1902.11163/) (2019)
- [Decentralized SGD with Over-the-Air Computation](https://mlsanity.com/paper/2003.04216/) (2020)
- [Semi-Decentralized Federated Learning with Collaborative Relaying](https://mlsanity.com/paper/2205.10998/) (2022)
- [Finite-Bit Quantization For Distributed Algorithms With Linear Convergence](https://mlsanity.com/paper/2107.11304/) (2021)
- [Asynchronous Decentralized Learning over Unreliable Wireless Networks](https://mlsanity.com/paper/2202.00955/) (2022)
- [Decentralized optimization over noisy, rate-constrained networks: Achieving consensus by communicating differences](https://mlsanity.com/paper/2010.11292/) (2020)
- [A Compressed Gradient Tracking Method for Decentralized Optimization with Linear Convergence](https://mlsanity.com/paper/2205.12623/) (2022)
- [Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow](https://mlsanity.com/paper/1811.04644/) (2018)

## Built on by (most cited first, 9 of 9)

- [Unified Analysis of Decentralized Gradient Descent: a Contraction Mapping Framework](https://mlsanity.com/paper/2503.14353/) (2025)
- [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)
- [Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off](https://mlsanity.com/paper/2510.26722/) (2025)
- [Interference-Robust Non-Coherent Over-the-Air Computation for Decentralized Optimization](https://mlsanity.com/paper/2602.12426/) (2026)
- [Resource-Element Energy Difference for Noncoherent Over-the-Air Federated Learning](https://mlsanity.com/paper/2605.07263/) (2026)
- [Decentralized Gradient Descent: Bottleneck Regimes and Budget Complexity](https://mlsanity.com/paper/2607.12172/) (2026)
- [Distributed Optimization with Streaming Data: A Temporal Weighting Perspective](https://mlsanity.com/paper/2608.09565/) (2026)
- [Non-Coherent Over-the-Air Federated Learning: Protocol, Convergence, and Device Scheduling](https://mlsanity.com/paper/2609.08312/) (2026)

## Abstract (arXiv)

Implementing Decentralized Gradient Descent (DGD) in wireless systems is challenging due to noise, fading, and limited bandwidth, necessitating topology awareness, transmission scheduling, and the acquisition of channel state information (CSI) to mitigate interference and maintain reliable communications. These operations may result in substantial signaling overhead and scalability challenges in large networks lacking central coordination. This paper introduces a scalable DGD algorithm that eliminates the need for scheduling, topology information, or CSI (both average and instantaneous). At its core is a Non-Coherent Over-The-Air (NCOTA) consensus scheme that exploits a noisy energy superposition property of wireless channels. Nodes encode their local optimization signals into energy levels within an OFDM frame and transmit simultaneously, without coordination. The key insight is that the received energy equals, on average, the sum of the energies of the transmitted signals, scaled by their respective average channel gains, akin to a consensus step. This property enables unbiased consensus estimation, utilizing average channel gains as mixing weights, thereby removing the need for their explicit design or for CSI. Introducing a consensus stepsize mitigates consensus estimation errors due to energy fluctuations around their expected values. For strongly-convex problems, it is shown that the expected squared distance between the local and globally optimum models vanishes at a rate of O(1/sqrt{k}) after k iterations, with suitable decreasing learning and consensus stepsizes. Extensions accommodate a broad class of fading models and frequency-selective channels. Numerical experiments on image classification demonstrate faster convergence in terms of running time compared to state-of-the-art schemes, especially in dense network scenarios.