# Over-the-Air Federated Learning with Compressed Sensing: Is Sparsification Necessary?

arXiv: https://arxiv.org/abs/2310.03410 · HTML: https://mlsanity.com/paper/2310.03410/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [The Convergence of Sparsified Gradient Methods](https://mlsanity.com/paper/1809.10505/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Scheduling and Aggregation Design for Asynchronous Federated Learning over Wireless Networks](https://mlsanity.com/paper/2212.07356/) (2022)
- [Communication-Efficient Federated Learning via Quantized Compressed Sensing](https://mlsanity.com/paper/2111.15071/) (2021)
- [Optimal MIMO Combining for Blind Federated Edge Learning with Gradient Sparsification](https://mlsanity.com/paper/2203.12957/) (2022)
- [Over-the-Air Computation for Distributed Systems: Something Old and Something New](https://mlsanity.com/paper/2211.00767/) (2022)

## Built on by (most cited first, 1 of 1)

- [Age-Aware Edge-Blind Federated Learning via Over-the-Air Aggregation](https://mlsanity.com/paper/2602.02469/) (2026)

## Abstract (arXiv)

Over-the-Air (OtA) Federated Learning (FL) refers to an FL system where multiple agents apply OtA computation for transmitting model updates to a common edge server. Two important features of OtA computation, namely linear processing and signal-level superposition, motivate the use of linear compression with compressed sensing (CS) methods to reduce the number of data samples transmitted over the channel. The previous works on applying CS methods in OtA FL have primarily assumed that the original model update vectors are sparse, or they have been sparsified before compression. However, it is unclear whether linear compression with CS-based reconstruction is more effective than directly sending the non-zero elements in the sparsified update vectors, under the same total power constraint. In this study, we examine and compare several communication designs with or without sparsification. Our findings demonstrate that sparsification before compression is not necessary. Alternatively, sparsification without linear compression can also achieve better performance than the commonly considered setup that combines both.