# Waveform Learning for Reduced Out-of-Band Emissions Under a Nonlinear Power Amplifier

arXiv: https://arxiv.org/abs/2201.05524 · HTML: https://mlsanity.com/paper/2201.05524/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 10 references that are in the map.
- First posted on arXiv 14 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [DeepRx: Fully Convolutional Deep Learning Receiver](https://mlsanity.com/paper/2005.01494/) (2020)
- [End-to-end Learning for OFDM: From Neural Receivers to Pilotless Communication](https://mlsanity.com/paper/2009.05261/) (2020)
- [OFDM-Autoencoder for End-to-End Learning of Communications Systems](https://mlsanity.com/paper/1803.05815/) (2018)
- [DeepRx MIMO: Convolutional MIMO Detection with Learned Multiplicative Transformations](https://mlsanity.com/paper/2010.16283/) (2020)
- [Trimming the Fat from OFDM: Pilot- and CP-less Communication with End-to-end Learning](https://mlsanity.com/paper/2101.08213/) (2021)
- [HybridDeepRx: Deep Learning Receiver for High-EVM Signals](https://mlsanity.com/paper/2106.16079/) (2021)

## Built on by (most cited first, 5 of 5)

- [DeepTx: Deep Learning Beamforming with Channel Prediction](https://mlsanity.com/paper/2202.07998/) (2022)
- [Probabilistic Constellation Shaping With Denoising Diffusion Probabilistic Models: A Novel Approach](https://mlsanity.com/paper/2309.08688/) (2023)
- [Low PAPR MIMO-OFDM Design Based on Convolutional Autoencoder](https://mlsanity.com/paper/2301.05017/) (2023)
- [Generative AI-Based Probabilistic Constellation Shaping With Diffusion Models](https://mlsanity.com/paper/2311.09349/) (2023)
- [Transfer-based Adversarial Poisoning Attacks for Online (MIMO-)Deep Receviers](https://mlsanity.com/paper/2409.02430/) (2024)

## Abstract (arXiv)

Machine learning (ML) has shown great promise in optimizing various aspects of the physical layer processing in wireless communication systems. In this paper, we use ML to learn jointly the transmit waveform and the frequency-domain receiver. In particular, we consider a scenario where the transmitter power amplifier is operating in a nonlinear manner, and ML is used to optimize the waveform to minimize the out-of-band emissions. The system also learns a constellation shape that facilitates pilotless detection by the simultaneously learned receiver. The simulation results show that such an end-to-end optimized system can communicate data more accurately and with less out-of-band emissions than conventional systems, thereby demonstrating the potential of ML in optimizing the air interface. To the best of our knowledge, there are no prior works considering the power amplifier induced emissions in an end-to-end learned system. These findings pave the way towards an ML-native air interface, which could be one of the building blocks of 6G.