# Identification of Orbital Angular Momentum by Support Vector Machine in Ocean Turbulence

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Theory

#### 2.1. LG Beam

#### 2.2. Basic Principles of SVM

#### 2.3. HOG Features

**,**${G}_{y}(x,y)$, and $H(x,y)$ represent the horizontal gradient, vertical gradient and pixel value at pixel $(x,y)$ in the input image, respectively. The gradient magnitude and gradient direction at pixel $(x,y)$ are:

## 3. LG Beam Pattern Recognition Simulation Design

#### 3.1. Ocean Turbulence Random Phase Screen Model

#### 3.2. Simulation Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Wang, A.; Zhu, L.; Zhao, Y.; Li, S.; Lv, W.; Xu, J.; Wang, J. Adaptive water-air-water data information transfer using orbital angular momentum. Opt. Express
**2018**, 26, 8669–8678. [Google Scholar] [CrossRef] [PubMed] - Wang, W.; Wang, P.; Cao, T.; Tian, H.; Zhang, Y.; Guo, L. Performance Investigation of Underwater Wireless Optical Communication System Using M-ary OAMSK Modulation Over Oceanic Turbulence. IEEE Photonics J.
**2017**, 9, 1–15. [Google Scholar] [CrossRef] - Li, M. On Performance of Optical Wireless Communication With Spatial Multiplexing Towards 5G. IEEE Access
**2018**, 6, 28108–28113. [Google Scholar] [CrossRef] - Zhao, Y.; Xu, J.; Wang, A.; Lv, W.; Zhu, L.; Li, S.; Wang, J. Demonstration of data-carrying orbital angular momentum-based underwater wireless optical multicasting link. Opt. Express
**2017**, 25, 28743–28751. [Google Scholar] [CrossRef] - Yao, A.M.; Miles, J.P. Orbital Angular Momentum-Origins, Behavior and Applications. Adv. Opt. Photonics
**2011**, 3, 161–204. [Google Scholar] [CrossRef] - Cui, X.; Yin, X.; Chang, H.; Guo, Y.; Zheng, Z.; Sun, Z.; Liu, G.; Wang, Y. Analysis of an adaptive orbital angular momentum shift keying decoder based on machine learning under oceanic turbulence channels. Opt. Commun.
**2018**, 429, 138–143. [Google Scholar] [CrossRef] - Yan, Y.; Yue, Y.; Huang, H. Alan Willner. Multicasting in a Spatial Division Multiplexing System based on Optical Orbital Angular Momentum. Opt. Lett.
**2013**, 19, 3930–3933. [Google Scholar] [CrossRef] [PubMed] - Baghdady, J.; Miller, K.; Kelly, J.; Srimathi, I.R.; Li, W.; Johnson, E.G. Underwater Optical Communication Link Using Wavelength Division Multiplexing, Polarization Division Multiplexing and Orbital Angular Momentum Multiplexing. In Proceedings of the Frontiers in Optics 2016, OSA Technical Digest (online) (Optica Publishing Group, 2016), paper FTh4E.4. Rochester, NY, USA, 17–21 October 2016. [Google Scholar] [CrossRef]
- Ren, Y.; Li, L.; Zhao, Z.; Xie, G.; Wang, Z.; Ahmed, N.; Yan, Y.; Cao, Y.; Willner, A.J.; Liu, C.; et al. 4 Gbit/s Underwater Optical Transmission Using OAM Multiplexing and Directly Modulated Green Laser. In Proceedings of the Conference on Lasers and Electro-Optics, OSA Technical Digest (
**2016**) (Optica Publishing Group,**2016**), paper SW1F.4. San Jose, CA, USA, 5–10 June 2016. [Google Scholar] [CrossRef] - Wang, W.; Wang, P.; Guo, L. Performance Investigation of OAMSK Modulated Wireless Optical System over Turbulent Ocean Using Convolutional Neural Networks. J. Lightwave Technol.
**2020**, 38, 1753–1765. [Google Scholar] [CrossRef] - Sun, R.; Guo, L.; Cheng, M.; Li, J. Multiple Random Phase-Screen Simulation of Scintillation Effect of Bessel-Gaussian Beam in Ocean Turbulence. In Proceedings of the 2018 12th International Symposium on Antennas, Propagation and EM Theory (ISAPE), Hangzhou, China, 3–6 December 2018; pp. 1–4. [Google Scholar] [CrossRef]
- Cheng, M.; Guo, L.; Li, J.; Zhang, Y. Channel Capacity of the OAM-Based Free-Space Optical Communication Links With Bessel–Gauss Beams in Turbulent Ocean. IEEE Photonics J.
**2016**, 8, 1–11. [Google Scholar] [CrossRef] - Nikishov, V.V.; Nikishov, V.I. Spectrum of turbulent fluctuations of the seawater refraction index. Int. J. Fluid Mech. Res.
**2000**, 27, 82–98. [Google Scholar] [CrossRef] - Baykal, Y. Higher order mode laser beam intensity fluctuations in strong oceanic turbulence. Opt. Commun.
**2017**, 390, 72–75. [Google Scholar] [CrossRef] - Li, Y.; Yu, L.; Zhang, Y. Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean. Optics express
**2017**, 11, 12203–12215. [Google Scholar] [CrossRef] [PubMed] - Xiong, W. Convolutional Neural Network Assisted Optical Orbital Angular Momentum Identification of Vortex Beams. IEEE Access
**2020**, 8, 193801–193812. [Google Scholar] [CrossRef] - Wang, P. Convolutional Neural Network-Assisted Optical Orbital Angular Momentum Recognition and Communication. IEEE Access
**2019**, 7, 162025–162035. [Google Scholar] [CrossRef] - Wang, Z.; Guo, Z. Adaptive Demodulation Technique for Efficiently Detecting Orbital Angular Momentum (OAM) Modes Based on the Improved Convolutional Neural Network. IEEE Access
**2019**, 7, 163633–163643. [Google Scholar] [CrossRef] - Wang, Z. Efficient Recognition of the Propagated Orbital Angular Momentum Modes in Turbulences With the Convolutional Neural Network. IEEE Photonics J.
**2019**, 11, 1–14. [Google Scholar] [CrossRef] - Liu, W.; Jin, M.; Hao, Y.H. Efficient identification of orbital angular momentum modes carried by Bessel Gaussian beams in oceanic turbulence channels using convolutional neural network. Opt. Commun.
**2021**, 498, 127251. [Google Scholar] [CrossRef] - He, Y.; Liu, J.; Wang, X.; Wu, Y.; Zhou, X.; Cheng, Y.; Gao, Y.; Li, Y.; Chen, S.; Fan, D. Detecting Orbital Angular Momentum Modes of Vortex Beams Using Feed-Forward Neural Network. J. Lightwave Technol.
**2019**, 37, 5848–5855. [Google Scholar] [CrossRef] - Huang, Z.; Wang, P.; Liu, J.; Xiong, W.; He, Y.; Zhou, X.; Xiao, J.; Li, Y.; Chen, S.; Fan, D. Identification of hybrid orbital angular momentum modes with deep feedforward neural network. Results Phys.
**2019**, 15, 102790. [Google Scholar] [CrossRef] - Jing, G.; Chen, L.; Wang, P.; Xiong, W.; Huang, Z.; Liu, J.; Chen, Y.; Li, Y.; Fan, D.; Chen, S. Recognizing fractional orbital angular momentum using feed forward neural network. Results Phys.
**2021**, 28, 104619. [Google Scholar] [CrossRef] - Li, J.; Zhang, M.; Wang, D. Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying. IEEE Photonics Technol. Lett.
**2017**, 17, 1455–1458. [Google Scholar] [CrossRef] - Sun, R.; Guo, L.; Cheng, M.; Li, J.; Yan, X. Identifying orbital angular momentum modes in turbulence with high accuracy via machine learning. J. Opt.
**2019**, 21, 075703. [Google Scholar] [CrossRef] - Wang, S.; Guo, X.; Tie, Y.; Lee, I.; Qi, L.; Guan, L. Graph-Based Safe Support Vector Machine for Multiple Classes. IEEE Access
**2018**, 6, 28097–28107. [Google Scholar] [CrossRef] - Feng, K.; Yuan, F. Static hand gesture recognition based on HOG characters and support vector machines. In Proceedings of the 2013 2nd International Symposium on Instrumentation and Measurement, Sensor Network and Automation (IMSNA), Toronto, ON, Canada, 23–24 December 2013; pp. 936–938. [Google Scholar] [CrossRef]
- Li, B.; Huo, G. Face recognition using locality sensitive histograms of oriented gradients. Opt. -Int. J. Light Elect
**2016**, 6, 3489–3494. [Google Scholar] [CrossRef] - Xiang, Z.; Tan, H.; Ye, W. The Excellent Properties of a Dense Grid-Based HOG Feature on Face Recognition Compared to Gabor and LBP. IEEE Access
**2018**, 6, 29306–29319. [Google Scholar] [CrossRef] - Awais, M. Real-Time Surveillance Through Face Recognition Using HOG and Feedforward Neural Networks. IEEE Access
**2019**, 7, 121236–121244. [Google Scholar] [CrossRef]

**Figure 4.**Spatial phase map HOG characteristics of different OAM modes (L = 1~10) under ocean turbulence.

**Figure 6.**OAM single mode recognition rate under different values: (

**a**) L = 1~5; (

**b**) L = 1~6; (

**c**) L = 1~7; (

**d**) L = 1~8; (

**e**) L = 1~9; (

**f**) L = 1~10.

**Figure 7.**OAM (L = 1~5, 1~6, 1~7, 1~8, 1~9, 1~10) modal recognition rate under different $w$ values.

$\mathit{w}$ | L = 1~5 | L = 1~6 | L = 1~7 | L = 1~8 | L = 1~9 | L = 1~10 |
---|---|---|---|---|---|---|

−2.0 | 0.9893 | 0.9889 | 0.9733 | 0.9666 | 0.9540 | 0.9533 |

−1.75 | 0.9759 | 0.9644 | 0.9581 | 0.9516 | 0.9466 | 0.9240 |

−1.5 | 0.9600 | 0.9466 | 0.9276 | 0.9217 | 0.9214 | 0.9133 |

−1.25 | 0.8792 | 0.8726 | 0.8656 | 0.8383 | 0.8148 | 0.8017 |

−1.0 | 0.8613 | 0.8488 | 0.8228 | 0.8199 | 0.7896 | 0.7854 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, X.; Huang, J.; Sun, L.
Identification of Orbital Angular Momentum by Support Vector Machine in Ocean Turbulence. *J. Mar. Sci. Eng.* **2022**, *10*, 1284.
https://doi.org/10.3390/jmse10091284

**AMA Style**

Li X, Huang J, Sun L.
Identification of Orbital Angular Momentum by Support Vector Machine in Ocean Turbulence. *Journal of Marine Science and Engineering*. 2022; 10(9):1284.
https://doi.org/10.3390/jmse10091284

**Chicago/Turabian Style**

Li, Xiaoji, Jiemei Huang, and Leiming Sun.
2022. "Identification of Orbital Angular Momentum by Support Vector Machine in Ocean Turbulence" *Journal of Marine Science and Engineering* 10, no. 9: 1284.
https://doi.org/10.3390/jmse10091284