# End-to-end Waveform Learning Through Joint Optimization of Pulse and Constellation Shaping

arXiv: https://arxiv.org/abs/2106.15158 · HTML: https://mlsanity.com/paper/2106.15158/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [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)
- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Trainable Communication Systems: Concepts and Prototype](https://mlsanity.com/paper/1911.13055/) (2019)
- [End-to-end Deep Learning of Optical Fiber Communications](https://mlsanity.com/paper/1804.04097/) (2018)
- [Trimming the Fat from OFDM: Pilot- and CP-less Communication with End-to-end Learning](https://mlsanity.com/paper/2101.08213/) (2021)

## Built on by (most cited first, 4 of 4)

- [Waveform Learning for Next-Generation Wireless Communication Systems](https://mlsanity.com/paper/2109.00998/) (2021)
- [DeepTx: Deep Learning Beamforming with Channel Prediction](https://mlsanity.com/paper/2202.07998/) (2022)
- [Learning OFDM Waveforms with PAPR and ACLR Constraints](https://mlsanity.com/paper/2110.10987/) (2021)
- [Generative AI-Based Probabilistic Constellation Shaping With Diffusion Models](https://mlsanity.com/paper/2311.09349/) (2023)

## Abstract (arXiv)

As communication systems are foreseen to enable new services such as joint communication and sensing and utilize parts of the sub-THz spectrum, the design of novel waveforms that can support these emerging applications becomes increasingly challenging. We present in this work an end-to-end learning approach to design waveforms through joint learning of pulse shaping and constellation geometry, together with a neural network (NN)-based receiver. Optimization is performed to maximize an achievable information rate, while satisfying constraints on out-of-band emission and power envelope. Our results show that the proposed approach enables up to orders of magnitude smaller adjacent channel leakage ratios (ACLRs) with peak-to-average power ratios (PAPRs) competitive with traditional filters, without significant loss of information rate on an additive white Gaussian noise (AWGN) channel, and no additional complexity at the transmitter.