# Convergence of Federated Learning over a Noisy Downlink

arXiv: https://arxiv.org/abs/2008.11141 · HTML: https://mlsanity.com/paper/2008.11141/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2020.

## Built on by (most cited first, 29 of 29)

- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [A Decentralized Federated Learning Framework via Committee Mechanism with Convergence Guarantee](https://mlsanity.com/paper/2108.00365/) (2021)
- [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)
- [Hierarchical Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2112.11167/) (2021)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Unified Analysis of Decentralized Gradient Descent: a Contraction Mapping Framework](https://mlsanity.com/paper/2503.14353/) (2025)
- [Fast Federated Edge Learning with Overlapped Communication and Computation and Channel-Aware Fair Client Scheduling](https://mlsanity.com/paper/2109.06710/) (2021)
- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [Federated Learning over Noisy Channels: Convergence Analysis and Design Examples](https://mlsanity.com/paper/2101.02198/) (2021)
- [Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneity](https://mlsanity.com/paper/2401.01442/) (2024)
- [Decentralized Federated Learning Over Imperfect Communication Channels](https://mlsanity.com/paper/2405.12894/) (2024)
- [Collaborative Learning over Wireless Networks: An Introductory Overview](https://mlsanity.com/paper/2112.05559/) (2021)
- [CSIT-Free Model Aggregation for Federated Edge Learning via Reconfigurable Intelligent Surface](https://mlsanity.com/paper/2102.10749/) (2021)
- [Over-the-Air Statistical Estimation](https://mlsanity.com/paper/2103.04014/) (2021)
- [Federated Learning with Downlink Device Selection](https://mlsanity.com/paper/2107.03510/) (2021)
- [Energy-Efficient Channel Decoding for Wireless Federated Learning: Convergence Analysis and Adaptive Design](https://mlsanity.com/paper/2407.13703/) (2024)
- [How Robust is Federated Learning to Communication Error? A Comparison Study Between Uplink and Downlink Channels](https://mlsanity.com/paper/2310.16652/) (2023)
- [Over-The-Air Clustered Wireless Federated Learning](https://mlsanity.com/paper/2211.03363/) (2022)
- [BSAC-CoEx: Coexistence of URLLC and Distributed Learning Services via Device Selection](https://mlsanity.com/paper/2212.11805/) (2022)
- [Federated Learning-based Collaborative Wideband Spectrum Sensing and Scheduling for UAVs in UTM Systems](https://mlsanity.com/paper/2406.01727/) (2024)
- [Noise-Robust and Resource-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2409.13451/) (2024)
- [Task-Agnostic Federation over Decentralized Data: Research Landscape and Visions](https://mlsanity.com/paper/2503.03140/) (2025)
- [Robust Federated Learning against Model Perturbation in Edge Networks](https://mlsanity.com/paper/2505.24728/) (2025)
- [Federated learning over physical channels: adaptive algorithms with near-optimal guarantees](https://mlsanity.com/paper/2509.02538/) (2025)
- [Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm](https://mlsanity.com/paper/2606.22466/) (2026)
- [Mixed-Timescale Differential Coding for Downlink Model Broadcast in Wireless Federated Learning](https://mlsanity.com/paper/2607.13119/) (2026)

## Abstract (arXiv)

We study federated learning (FL), where power-limited wireless devices utilize their local datasets to collaboratively train a global model with the help of a remote parameter server (PS). The PS has access to the global model and shares it with the devices for local training, and the devices return the result of their local updates to the PS to update the global model. This framework requires downlink transmission from the PS to the devices and uplink transmission from the devices to the PS. The goal of this study is to investigate the impact of the bandwidth-limited shared wireless medium in both the downlink and uplink on the performance of FL with a focus on the downlink. To this end, the downlink and uplink channels are modeled as fading broadcast and multiple access channels, respectively, both with limited bandwidth. For downlink transmission, we first introduce a digital approach, where a quantization technique is employed at the PS to broadcast the global model update at a common rate such that all the devices can decode it. Next, we propose analog downlink transmission, where the global model is broadcast by the PS in an uncoded manner. We consider analog transmission over the uplink in both cases. We further analyze the convergence behavior of the proposed analog approach assuming that the uplink transmission is error-free. Numerical experiments show that the analog downlink approach provides significant improvement over the digital one, despite a significantly lower transmit power at the PS. The experimental results corroborate the convergence results, and show that a smaller number of local iterations should be used when the data distribution is more biased, and also when the devices have a better estimate of the global model in the analog downlink approach.