# On Analog Gradient Descent Learning over Multiple Access Fading Channels

arXiv: https://arxiv.org/abs/1908.07463 · HTML: https://mlsanity.com/paper/1908.07463/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2019.

## Built on by (most cited first, 30 of 62)

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- [Accelerated Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/2107.12452/) (2021)
- [A Survey on Integrated Sensing, Communication, and Computation](https://mlsanity.com/paper/2408.08074/) (2024)
- [Federated Learning over Wireless Networks: A Band-limited Coordinated Descent Approach](https://mlsanity.com/paper/2102.07972/) (2021)
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- [Over-the-Air Federated Learning with Joint Adaptive Computation and Power Control](https://mlsanity.com/paper/2205.05867/) (2022)
- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [Communication-Efficient Split Learning Based on Analog Communication and Over the Air Aggregation](https://mlsanity.com/paper/2106.00999/) (2021)
- [Client Selection for Generalization in Accelerated Federated Learning: A Multi-Armed Bandit Approach](https://mlsanity.com/paper/2303.10373/) (2023)
- [Robust Federated Learning via Over-The-Air Computation](https://mlsanity.com/paper/2111.01221/) (2021)
- [Federated Learning via Lattice Joint Source-Channel Coding](https://mlsanity.com/paper/2403.01023/) (2024)
- [Differentially Private Federated Learning via Reconfigurable Intelligent Surface](https://mlsanity.com/paper/2203.17028/) (2022)
- [Communication and Energy Efficient Wireless Federated Learning with Intrinsic Privacy](https://mlsanity.com/paper/2304.07460/) (2023)
- [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)
- [Over-The-Air Federated Learning under Byzantine Attacks](https://mlsanity.com/paper/2205.02949/) (2022)
- [Riemannian Low-Rank Model Compression for Federated Learning with Over-the-Air Aggregation](https://mlsanity.com/paper/2306.02433/) (2023)
- [AirFL-Mem: Improving Communication-Learning Trade-Off by Long-Term Memory](https://mlsanity.com/paper/2310.16606/) (2023)
- [Rendering Wireless Environments Useful for Gradient Estimators: A Zero-Order Stochastic Federated Learning Method](https://mlsanity.com/paper/2401.17460/) (2024)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [NCAirFL: CSI-Free Over-the-Air Federated Learning Based on Non-Coherent Detection](https://mlsanity.com/paper/2411.13000/) (2024)
- [Over-the-Air Statistical Estimation](https://mlsanity.com/paper/2103.04014/) (2021)

## Abstract (arXiv)

We consider a distributed learning problem over multiple access channel (MAC) using a large wireless network. The computation is made by the network edge and is based on received data from a large number of distributed nodes which transmit over a noisy fading MAC. The objective function is a sum of the nodes' local loss functions. This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning. We develop a novel Gradient-Based Multiple Access (GBMA) algorithm to solve the distributed learning problem over MAC. Specifically, the nodes transmit an analog function of the local gradient using common shaping waveforms and the network edge receives a superposition of the analog transmitted signals used for updating the estimate. GBMA does not require power control or beamforming to cancel the fading effect as in other algorithms, and operates directly with noisy distorted gradients. We analyze the performance of GBMA theoretically, and prove that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks. Specifically, we establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. Furthermore, we provide energy scaling laws for approaching the centralized convergence rate as the number of nodes increases. Finally, experimental results support the theoretical findings, and demonstrate strong performance of GBMA using synthetic and real data.