# PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning

arXiv: https://arxiv.org/abs/2301.10110 · HTML: https://mlsanity.com/paper/2301.10110/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 13 of 13)

- [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)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [Accelerated Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/2107.12452/) (2021)
- [Over-the-air Function Computation in Sensor Networks](https://mlsanity.com/paper/1612.02307/) (2016)
- [Temporal-Structure-Assisted Gradient Aggregation for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2103.02270/) (2021)
- [Over-the-Air Statistical Estimation](https://mlsanity.com/paper/2103.04014/) (2021)

## Abstract (arXiv)

We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ~30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.