# Complex-Valued Neural Networks for Data-Driven Signal Processing and Signal Understanding

arXiv: https://arxiv.org/abs/2309.07948 · HTML: https://mlsanity.com/paper/2309.07948/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [MobileViT: Light-weight, General-purpose, and Mobile-friendly Vision Transformer](https://mlsanity.com/paper/2110.02178/) (2021)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Better than Real: Complex-valued Neural Nets for MRI Fingerprinting](https://mlsanity.com/paper/1707.00070/) (2017)
- [On Complex Valued Convolutional Neural Networks](https://mlsanity.com/paper/1602.09046/) (2016)
- [Enhanced Radar Imaging Using a Complex-valued Convolutional Neural Network](https://mlsanity.com/paper/1712.10096/) (2017)
- [Theory and Implementation of Complex-Valued Neural Networks](https://mlsanity.com/paper/2302.08286/) (2023)
- [A Vision Transformer Approach for Efficient Near-Field Irregular SAR Super-Resolution](https://mlsanity.com/paper/2305.02074/) (2023)
- [An FCNN-Based Super-Resolution mmWave Radar Framework for Contactless Musical Instrument Interface](https://mlsanity.com/paper/2305.01995/) (2023)
- [Improved Static Hand Gesture Classification on Deep Convolutional Neural Networks using Novel Sterile Training Technique](https://mlsanity.com/paper/2305.02039/) (2023)
- [C-SURE: Shrinkage Estimator and Prototype Classifier for Complex-Valued Deep Learning](https://mlsanity.com/paper/2006.12590/) (2020)
- [ChaRRNets: Channel Robust Representation Networks for RF Fingerprinting](https://mlsanity.com/paper/2105.03568/) (2021)
- [Near-Field MIMO-ISAR Millimeter-Wave Imaging](https://mlsanity.com/paper/2305.02030/) (2023)
- [Efficient CNN-based Super Resolution Algorithms for mmWave Mobile Radar Imaging](https://mlsanity.com/paper/2305.02092/) (2023)
- [SurReal: Fr'echet Mean and Distance Transform for Complex-Valued Deep Learning](https://mlsanity.com/paper/1906.10048/) (2019)
- [Deep Learning-Based Multiband Signal Fusion for 3-D SAR Super-Resolution](https://mlsanity.com/paper/2305.02017/) (2023)
- [Efficient 3-D Near-Field MIMO-SAR Imaging for Irregular Scanning Geometries](https://mlsanity.com/paper/2305.02064/) (2023)
- [Novel Hybrid-Learning Algorithms for Improved Millimeter-Wave Imaging Systems](https://mlsanity.com/paper/2306.15341/) (2023)
- [Dual Radar SAR Controller](https://mlsanity.com/paper/2309.00006/) (2023)

## Built on by (most cited first, 2 of 2)

- [PhaseGen: A Diffusion-Based Approach for Complex-Valued MRI Data Generation](https://mlsanity.com/paper/2504.07560/) (2025)
- [Emerging Approaches for THz Array Imaging: A Tutorial Review and Software Tool](https://mlsanity.com/paper/2309.08844/) (2023)

## Abstract (arXiv)

Complex-valued neural networks have emerged boasting superior modeling performance for many tasks across the signal processing, sensing, and communications arenas. However, developing complex-valued models currently demands development of basic deep learning operations, such as linear or convolution layers, as modern deep learning frameworks like PyTorch and Tensor flow do not adequately support complex-valued neural networks. This paper overviews a package built on PyTorch with the intention of implementing light-weight interfaces for common complex-valued neural network operations and architectures. Similar to natural language understanding (NLU), which as recently made tremendous leaps towards text-based intelligence, RF Signal Understanding (RFSU) is a promising field extending conventional signal processing algorithms using a hybrid approach of signal mechanics-based insight with data-driven modeling power. Notably, we include efficient implementations for linear, convolution, and attention modules in addition to activation functions and normalization layers such as batchnorm and layernorm. Additionally, we include efficient implementations of manifold-based complex-valued neural network layers that have shown tremendous promise but remain relatively unexplored in many research contexts. Although there is an emphasis on 1-D data tensors, due to a focus on signal processing, communications, and radar data, many of the routines are implemented for 2-D and 3-D data as well. Specifically, the proposed approach offers a useful set of tools and documentation for data-driven signal processing research and practical implementation.