Complex-Valued Convolutions for Modulation Recognition using Deep Learning

Natural signals are inherently comprised of two components, real and imaginary components. Due to recent successes and progress in Deep Learning, specifically Convolutional Neural Networks (CNNs), this field of machine learning has become extremely popular when handling a wide variety of data, including natural signals. However, deep learning frameworks have been developed to deal with exclusively real-valued data and are unable to compute convolutions for complex-valued data. In this work, we present a linear combination that enables deep learning architectures to compute complex convolutions and learn features across the real and imaginary components of natural signals. When implemented into existing I/Q modulation classification architectures, this small change increases classification accuracy across a range of SNR levels by up to 35%.

[1]  Dumitru Erhan,et al.  Going deeper with convolutions , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[2]  Yonina C. Eldar,et al.  Fast Deep Learning for Automatic Modulation Classification , 2019, ArXiv.

[3]  Frans Coenen,et al.  FCNN: Fourier Convolutional Neural Networks , 2017, ECML/PKDD.

[4]  Jie Pan,et al.  Agnostic software-defined coherent optical receiver performing time-domain hybrid modulation format recognition , 2015, 2015 Optical Fiber Communications Conference and Exhibition (OFC).

[5]  John Salvatier,et al.  Theano: A Python framework for fast computation of mathematical expressions , 2016, ArXiv.

[6]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[7]  Tara N. Sainath,et al.  Convolutional, Long Short-Term Memory, fully connected Deep Neural Networks , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[8]  Stella X. Yu,et al.  Better than real: Complex-valued neural nets for MRI fingerprinting , 2017, 2017 IEEE International Conference on Image Processing (ICIP).

[9]  Alex Zhavoronkov,et al.  Applications of Deep Learning in Biomedicine. , 2016, Molecular pharmaceutics.

[10]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[11]  Yuan Xie,et al.  Applications of Deep Learning to Neuro-Imaging Techniques , 2019, Front. Neurol..

[12]  Yoshua Bengio,et al.  Unitary Evolution Recurrent Neural Networks , 2015, ICML.

[13]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[14]  T. Charles Clancy,et al.  Over-the-Air Deep Learning Based Radio Signal Classification , 2017, IEEE Journal of Selected Topics in Signal Processing.

[15]  Demis Hassabis,et al.  Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm , 2017, ArXiv.

[16]  T. Charles Clancy,et al.  Convolutional Radio Modulation Recognition Networks , 2016, EANN.

[17]  Yulei Rao,et al.  A deep learning framework for financial time series using stacked autoencoders and long-short term memory , 2017, PloS one.

[18]  Yuval Tassa,et al.  Continuous control with deep reinforcement learning , 2015, ICLR.

[19]  Yu-Dong Yao,et al.  Modulation Classification Based on Signal Constellation Diagrams and Deep Learning , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Ali Farhadi,et al.  You Only Look Once: Unified, Real-Time Object Detection , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[21]  Quoc V. Le,et al.  GPipe: Efficient Training of Giant Neural Networks using Pipeline Parallelism , 2018, ArXiv.

[22]  Marco Corazza,et al.  Testing different Reinforcement Learning con?gurations for ?nancial trading: Introduction and applications , 2018 .

[23]  Jie Pan,et al.  Stokes Space-Based Modulation Format Recognition for Autonomous Optical Receivers , 2015, Journal of Lightwave Technology.