# Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Multidimensional Asynchronous Delay-Tap Plot Entropy

**Figure 2.**The left and middle columns show eye diagrams and asynchronous delay-tap plots (ADTPs) when the optical SNR (OSNR) = 20 dB without chromatic dispersion (CD) for 10-Gb return-to-zero (RZ), 40-Gb NRZ-differential phase-shift keying (DPSK), 40-Gb duo-binary optical (DUO), 40-Gb RZ-differential quadrature phase-shift keying (DQPSK), 100-Gb polarization-multiplexed (PM)-RZ-QPSK and 200-Gb PM-NRZ-16 quadrature amplitude modulation (16QAM), while the right column shows ADTPs when OSNR = 20 dB and CD = 500 ps/nm.

- The Shannon entropy:$${E}_{1}({P}_{{1}_{i,j}})=-{\displaystyle \sum _{i=1,j=1}^{i=N,j=N}{P}_{{1}_{i,j}}\mathrm{log}2({P}_{{1}_{i,j}})}$$
- The exponent entropy:$${E}_{2}({P}_{{1}_{i,j}})={\displaystyle \sum _{i=1,j=1}^{i=N,j=N}{P}_{{1}_{i,j}}{e}^{1-{P}_{{1}_{i,j}}}}$$
- The singular Shannon entropy:$${E}_{3}({P}_{{2}_{i}})=-{\displaystyle \sum _{i=1}^{i=N}{P}_{{2}_{i}}\mathrm{log}({P}_{{2}_{i}})}$$
- The singular exponent entropy:$${E}_{4}({P}_{{2}_{i}})={\displaystyle \sum _{i=1}^{i=N}{P}_{{2}_{i}}{e}^{1-{P}_{{2}_{i}}}}$$

**Figure 3.**Variations of four types of asynchronous delay-tap plot entropy (ADTPE) for six different modulation formats along with positive CD varying from 0 to 4000 ps/nm under different OSNR levels. The ADTPEs in the left, middle and right column correspond to 10-dB, 20-dB and 30-dB OSNRs, respectively.

## 3. Support Vector Machine for Modulation Format Classification

- The linear kernel function:$$K\left({x}_{i},{x}_{j}\right)=\gamma {x}_{i}^{T}{x}_{j}$$
- The polynomial kernel function:$$K\left({x}_{i},{x}_{j}\right)={\left(\gamma {x}_{i}^{T}{x}_{j}+r\right)}^{d}$$
- The RBF kernel:$$K\left({x}_{i},{x}_{j}\right)=\mathrm{exp}\left(-\gamma {\Vert {x}_{i}-{x}_{j}\Vert}^{2}\right)$$
- The sigmoid kernel function:$$K\left({x}_{i},{x}_{j}\right)=\mathrm{tanh}\left(\gamma {x}_{i}^{T}{x}_{j}+r\right)$$$$A=({C}_{+1}+{C}_{-1})/({C}_{+1}+{E}_{+1}+{C}_{-1}+{E}_{-1})$$

**Figure 5.**The structure of multiclass SVM comprised of fifteen sub-SVMs based on the one-versus-one algorithm.

## 4. The Structural Process of the Real-Time Modulation Format Recognition System and Database Formation

**Figure 6.**The structure of the real-time modulation format recognition system. PMD, polarization mode dispersion; SMF, single mode fiber; EDFA, erbium-doped fiber amplifier; VOA, variable optical attenuator; OBPF, optical band-pass filter; FDM, fixed dispersion module; PIN, positive intrinsic-negative diode; Async., asynchronous.

## 5. Results and Discussion

Kernel Function | Overall Accuracy (%) |
---|---|

Polynomial with 1-order (linear function) | 97.87 |

Polynomial with 2-order | 97.99 |

Polynomial with 3-order | 98.22 |

Polynomial with 4-order | 98.36 |

Polynomial with 5-order | 98.45 |

Polynomial with 6-order | 98.69 |

Polynomial with 7-order | 98.82 |

Polynomial with 8-order | 98.94 |

Polynomial with 9-order | 99.05 |

RBF | 97.88 |

Sigmoid | 97.54 |

Sub-SVM | Time (ms) |
---|---|

10-Gb RZ vs. 40-Gb NRZ-DPSK | 213 |

10-Gb RZ vs. 40-Gb DUO | 192 |

10-Gb RZ vs. 40-Gb RZ-DQPSK | 196 |

10-Gb RZ vs. 100-Gb PM-RZ-QPSK | 251 |

10-Gb RZ vs. 200-Gb PM-NRZ-16QAM | 191 |

40-Gb NRZ-DPSK vs. 40-Gb DUO | 183 |

40-Gb NRZ-DPSK vs. 40-Gb RZ-DQPSK | 203 |

40-Gb NRZ-DPSK vs. 100-Gb PM-RZ-QPSK | 189 |

40-Gb NRZ-DPSK vs. 200-Gb PM-NRZ-16QAM | 197 |

40-Gb DUO vs. 40-Gb RZ-DQPSK | 234 |

40-Gb DUO vs. 100-Gb PM-RZ-QPSK | 308 |

40-Gb DUO vs. 200-Gb PM-NRZ-16QAM | 250 |

40-Gb RZ-DQPSK vs. 100-Gb PM-RZ-QPSK | 187 |

40-Gb RZ-DQPSK vs. 200-Gb PM-NRZ-16QAM | 234 |

100-Gb PM-RZ-QPSK vs. 200-Gb PM-NRZ-16QAM | 332 |

Total time: 3360 |

**Table 3.**The recognition accuracies of the optical modulation format using multidimensional ADTPE and a multiclass SVM. The overall recognized accuracy is about 99.05%.

Actual Bit-Rate and Modulation Format | Recognized Accuracy of Optical Modulation Format | |||||
---|---|---|---|---|---|---|

10-Gb RZ | 40-Gb NRZ-DPSK | 40-Gb DUO | 40-Gb RZ-DQPSK | 100-Gb PM-RZ-QPSK | 200-Gb PM-NRZ-16QAM | |

10-Gb RZ | 100% | - | - | - | - | - |

40-Gb NRZ-DPSK | - | 97.67% | - | - | - | 2.73% |

40-Gb DUO | - | - | 100% | - | - | - |

40-Gb RZ-DQPSK | - | - | - | 99.72% | 0.34% | - |

100-Gb PM-RZ-QPSK | - | - | - | 0.27% | 99.66% | - |

200-Gb PM-NRZ-16QAM | - | 2.32% | - | - | - | 97.26% |

**Figure 8.**Recognized accuracy as a function of the proportion of the overall eigenvector for the SVM training.

**Table 4.**The correct recognition rates and time for more various bit rates and modulation formats using multidimensional ADTPE and SVM.

Modulation Formats | Time (ms) | Correct Recognition Accuracy of Modulation Formats (%) |
---|---|---|

10-Gb RZ | 264 | 99.69 |

20-Gb RZ | 231 | 96.32 |

10-Gb NRZ | 259 | 99.84 |

40-Gb PM-RZ-QPSK | 172 | 93.99 |

100-Gb PM-RZ-QPSK | 164 | 94.69 |

40-Gb PM-NRZ-QPSK | 186 | 99.1 |

100-Gb PM-NRZ-QPSK | 191 | 98.71 |

100-Gb PM-NRZ-QAM | 267 | 99.23 |

200-Gb PM-NRZ-QAM | 196 | 98.59 |

10-Gb NRZ-DPSK | 165 | 100 |

40-Gb NRZ-DPSK | 397 | 99.6 |

40-Gb NRZ-QPSK | 161 | 99.15 |

40-Gb RZ-QPSK | 193 | 99.37 |

20-Gb DUO | 166 | 99.1 |

40-Gb DUO | 179 | 95.78 |

Overall accuracy: 98.21 |

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- ITU-T. Interfaces for the Optical TRANSPORT Network (OTN). Available online: https://www.itu.int/rec/T-REC-G.709-200912-S/en (accessed on 13 January 2016).
- Wei, W.; Wang, C.; Yu, J. Cognitive Optical Networks: Key Drivers, Enabling Techniques, and Adaptive Bandwidth Services. IEEE Commun. Mag.
**2012**, 50, 106–113. [Google Scholar] [CrossRef] - Prakasaml, P.; Madheswaran, M. Automatic Modulation Identification of QPSK and GMSK Using Wavelet Transformfor Adaptive Demodulator in SDR. In Proceedings of the International Conference on Signal Processing, Communications and Networking, Chennai, India, 22–24 February 2007; pp. 507–511.
- Sajjad, A.G.; Ijaz, M.Q.; Aziz, M.A.; Tanveer, A.C. Classification of Digital Modulated Signals Using Linear Discriminant Analysis on Faded Channel. World Appl. Sci. J.
**2014**, 29, 1220–1227. [Google Scholar] - Fu, K.; Qu, J.F.; Chai, Y.; Dong, Y. Classification of Seizure Based on the Time-Frequency Image of EEG Signals Using HHT and SVM. Biomed. Signal Process. Control
**2014**, 13, 15–22. [Google Scholar] [CrossRef] - Chen, M.; Zhu, Q. Cooperative Automatic modulation recognition in cognitive radio. J. China Univ. Posts Telecommun.
**2010**, 17, 46–52. [Google Scholar] [CrossRef] - Hu, Y.Q.; Liu, J.; Tan, X.H. Digital modulation recognition based on instantaneous information. J. China Univ. Posts Telecommun.
**2010**, 17, 52–59. [Google Scholar] [CrossRef] - Eric, J.A.; Denis, M.L.; Johnson, W.R.; McKenna, T.P. Blind Optical Modulation Formats Identification from Physical Layer Characteristics. J. Lightwave Technol.
**2014**, 32, 1501–1509. [Google Scholar] - Eugen, L.; Wilfried, L. Modulation formats for 100 G and beyond. Opt. Fiber Technol.
**2011**, 17, 377–386. [Google Scholar] - Khan, F.N.; Zhou, Y.D.; Lau, A.P.T.; Lu, C. Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks. Opt. Express
**2012**, 20, 12422–12431. [Google Scholar] [CrossRef] [PubMed] - Khan, F.N.; Zhou, Y.D.; Sui, Q.; Lau, A.P.T. Non-data-aided joint bit-rate and modulation format identification for next-generation heterogeneous optical networks. Opt. Fiber Technol.
**2014**, 20, 68–74. [Google Scholar] [CrossRef] - Burges, C.J. A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov.
**1998**, 2, 121–167. [Google Scholar] [CrossRef] - Hsu, C.W.; Lin, C.J. A simple decomposition method for support vector machine. Mach. Learn.
**2002**, 46, 219–314. [Google Scholar] [CrossRef] - Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning, 2nd ed.; Springer-Verlag: New York, NY, USA, 2008. [Google Scholar]
- VPIphotonics. Available online: https://www.VPIphotonics.com (accessed on 15 January 2016).
- Pan, Z.; Yu, C.; Willner, E.A. Optical performance monitoring for the next generation optical communication networks. Opt. Fiber Technol.
**2010**, 16, 20–45. [Google Scholar] [CrossRef] - Dods, S.D.; Anderson, T.B.; Clarke, K.; Bakaul, M.; Kowalczyk, A. Asynchronous Sampling for Optical Performance Monitoring. In Proceedings of the Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Anaheim, CA, USA, 25–29 March 2007.
- Chen, J.K.; Dou, Y.H.; Wang, Z.H.; Li, G.Q. A Novel Method for PD Feature Extraction of Power Cable with Renyi Entropy. Entropy
**2015**, 17, 7698–7712. [Google Scholar] [CrossRef] - Wang, S.H.; Yang, X.J.; Zhang, Y.D.; Phillips, P.; Yang, J.F.; Yuan, T.F. Identification of Green, Oolong and Black Teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine. Entropy
**2015**, 17, 6663–6682. [Google Scholar] [CrossRef] - Wang, S.H.; Zhang, Y.D.; Ji, G.L.; Yang, J.Q.; Wu, J.G.; Wei, L. Fruit Classification by Wavelet-Entropy and Feedforward Neural Network Trained by Fitness-Scaled Chaotic ABC and Biogeography-Based Optimization. Entropy
**2015**, 17, 5711–5728. [Google Scholar] [CrossRef] - Avci, E. Selecting of the optimal feature subset and kernel parameters in digital modulation classification by using hybrid genetic algorithm–support vector machines: HGASVM. Expert Syst. Appl.
**2009**, 36, 1391–1402. [Google Scholar] [CrossRef] - Avci, E.; Avci, D. Using combination of support vector machines for automatic analog modulation recognition. Expert Syst. Appl.
**2009**, 36, 3956–3964. [Google Scholar] [CrossRef] - Zhang, L.; Tian, F.; Nie, H.; Dang, L.; Li, G.; Ye, Q.; Kadri, C. Classification of multiple indoor air contaminants by an electronic nose and a hybrid support vector machine. Sens. Actuators B Chem.
**2012**, 174, 114–125. [Google Scholar] [CrossRef] - Zhang, L.; Tian, F.C. A new kernel discriminant analysis framework for electronic nose recognition. Anal. Chimica Acta
**2014**, 816, 8–17. [Google Scholar] [CrossRef] [PubMed] - Peng, X.; Zhang, L.; Tian, F.; Zhang, D. A novel sensor feature extraction based on kernel entropy component analysis for discrimination of indoor air contaminants. Sens. Actuators A Phys.
**2015**, 234, 143–149. [Google Scholar] [CrossRef] - Pontil, M.; Veri, A. Support vector machines for 3-d object recognition. IEEE Trans. Pattern Anal. Mach. Intell.
**1998**, 20, 637–646. [Google Scholar] [CrossRef] - Yao, Y.; Frasconi, P.; Pontil, M. Fingerprint Classification with Combinations of Support Vector Machines. In Audio- and Video-Based Biometric Person Authentication; Springer-Verlag: Berlin/Heidelberg, Germany, 2001; pp. 253–258. [Google Scholar]
- Christianini, N.; Shawe-Taylor, J. An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Zhang, Y.D.; Dong, Z.C.; Phillips, P.; Wang, S.H.; Ji, G.L.; Yang, J.Q. Exponential wavelet iterative shrinkage thresholding algorithm for compressed sensing magnetic resonance imaging. Inform. Sci.
**2015**, 322, 115–132. [Google Scholar] [CrossRef] - Hamja, A.; Uddin, M.S.; Sultana, J.; Islam, M.M.; Iqbal, S. DSP Aided Chromatic Dispersion Reckoning in Single Carrier High Speed Coherent Optical Communications. In Proceedings of the International Conference on Electrical Information and Communication Technology (EICT), Khulna, Bangladesh, 13–15 February 2014.
- Li, G.F. Recent advances in coherent optical communication. Adv. Opt. Photon.
**2009**, 1, 279–307. [Google Scholar] [CrossRef] - Savory, S.J. Digital filters for coherent optical receivers. Opt. Express
**2008**, 16, 804–817. [Google Scholar] [CrossRef] [PubMed]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wei, J.; Huang, Z.; Su, S.; Zuo, Z.
Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition. *Entropy* **2016**, *18*, 30.
https://doi.org/10.3390/e18010030

**AMA Style**

Wei J, Huang Z, Su S, Zuo Z.
Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition. *Entropy*. 2016; 18(1):30.
https://doi.org/10.3390/e18010030

**Chicago/Turabian Style**

Wei, Junyu, Zhiping Huang, Shaojing Su, and Zhen Zuo.
2016. "Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition" *Entropy* 18, no. 1: 30.
https://doi.org/10.3390/e18010030