# LED Nonlinearity Estimation and Compensation in VLC Systems Using Probabilistic Bayesian Learning

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

## 3. PBL-Based LED Nonlinearity Estimation and Compensation in VLC

#### 3.1. PBL Regression

#### 3.2. LED Nonlinearity Estimation and Compensation Using PBL Regression

## 4. Simulation Setup

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Komine, T.; Nakagawa, M. Fundamental analysis for visible-light communication system using LED lights. IEEE Trans. Consum. Electron.
**2004**, 50, 100–107. [Google Scholar] [CrossRef] - Jovicic, A.; Li, J.; Richardson, T. Visible light communication: Opportunities, challenges and the path to market. IEEE Commun. Mag.
**2013**, 51, 26–32. [Google Scholar] [CrossRef] - Pathak, P.H.; Feng, X.; Hu, P.; Mohapatra, P. Visible light communication, networking, and sensing: A survey, potential and challenges. IEEE Commun. Surv. Tutor.
**2015**, 17, 2047–2077. [Google Scholar] [CrossRef] - Wu, D.; Zhong, W.D.; Ghassemlooy, Z.; Chen, C. Short-range visible light ranging and detecting system using illumination light emitting diodes. IET Optoelectron.
**2016**, 10, 94–99. [Google Scholar] [CrossRef] - Deng, X.; Mardanikorani, S.; Wu, Y.; Arulandu, K.; Chen, B.; Khalid, A.M.; Linnartz, J.P.M. Mitigating LED nonlinearity to enhance visible light communications. IEEE Trans. Commun.
**2018**, 66, 5593–5607. [Google Scholar] [CrossRef] - Rajbhandari, S.; Chun, H.; Faulkner, G.; Cameron, K.; Jalajakumari, A.V.; Henderson, R.; Tsonev, D.; Ijaz, M.; Chen, Z.; Haas, H.; et al. High-speed integrated visible light communication system: Device constraints and design considerations. IEEE J. Sel. Areas Commun.
**2015**, 33, 1750–1757. [Google Scholar] [CrossRef] - Elgala, H.; Mesleh, R.; Haas, H.; Pricope, B. OFDM visible light wireless communication based on white LEDs. In Proceedings of the IEEE 65th Vehicular Technology Conference (VTC Spring), Dublin, Ireland, 22–25 April 2007; pp. 2185–2189. [Google Scholar]
- Marshoud, H.; Kapinas, V.M.; Karagiannidis, G.K.; Muhaidat, S. Non-orthogonal multiple access for visible light communications. IEEE Photonics Technol. Lett.
**2015**, 28, 51–54. [Google Scholar] [CrossRef] - Chen, C.; Zhong, W.D.; Yang, H.; Du, P. On the performance of MIMO-NOMA-based visible light communication systems. IEEE Photonics Technol. Lett.
**2017**, 30, 307–310. [Google Scholar] [CrossRef] - Yang, Y.; Chen, C.; Zhang, W.; Deng, X.; Du, P.; Yang, H.; Zhong, W.D.; Chen, L. Secure and private NOMA VLC using OFDM with two-level chaotic encryption. Opt. Express
**2018**, 26, 34031–34042. [Google Scholar] [CrossRef][Green Version] - Chen, C.; Zhong, W.D.; Yang, H.; Du, P.; Yang, Y. Flexible-rate SIC-free NOMA for downlink VLC based on constellation partitioning coding. IEEE Wirel. Commun. Lett.
**2019**, 8, 568–571. [Google Scholar] [CrossRef] - Zeng, L.; O’Brien, D.C.; Le Minh, H.; Faulkner, G.E.; Lee, K.; Jung, D.; Oh, Y.; Won, E.T. High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting. IEEE J. Sel. Areas Commun.
**2009**, 27, 1654–1662. [Google Scholar] [CrossRef] - Chen, C.; Zhong, W.D.; Wu, D. On the coverage of multiple-input multiple-output visible light communications. IEEE/OSA J. Opt. Commun. Netw.
**2017**, 9, D31–D41. [Google Scholar] [CrossRef] - Chen, C.; Zhong, W.D.; Wu, D. Indoor OFDM visible light communications employing adaptive digital pre-frequency domain equalization. In Proceedings of the Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, USA, 5–10 June 2016. paper JTh2A. [Google Scholar]
- Le Minh, H.; O’Brien, D.; Faulkner, G.; Zeng, L.; Lee, K.; Jung, D.; Oh, Y.; Won, E.T. 100-Mb/s NRZ visible light communications using a postequalized white LED. IEEE Photonics Technol. Lett.
**2009**, 21, 1063–1065. [Google Scholar] [CrossRef] - Ying, K.; Yu, Z.; Baxley, R.J.; Qian, H.; Chang, G.K.; Zhou, G.T. Nonlinear distortion mitigation in visible light communications. IEEE Wirel. Commun.
**2015**, 22, 36–45. [Google Scholar] [CrossRef] - Stepniak, G.; Siuzdak, J.; Zwierko, P. Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE. IEEE Photonics Technol. Lett.
**2013**, 25, 1597–1600. [Google Scholar] [CrossRef] - Mitra, R.; Bhatia, V. Chebyshev polynomial-based adaptive predistorter for nonlinear LED compensation in VLC. IEEE Photonics Technol. Lett.
**2016**, 28, 1053–1056. [Google Scholar] [CrossRef] - Liang, S.; Jiang, Z.; Qiao, L.; Lu, X.; Chi, N. Faster-than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion. IEEE Photonics J.
**2018**, 10, 1–9. [Google Scholar] [CrossRef] - Lu, H.; Jin, J.; Wang, J. Alleviation of LED nonlinearity impact in visible light communication using companding and predistortion. IET Commun.
**2019**, 13, 818–821. [Google Scholar] [CrossRef] - Mitra, R.; Bhatia, V. Adaptive sparse dictionary-based kernel minimum symbol error rate post-distortion for nonlinear LEDs in visible light communications. IEEE Photonics J.
**2016**, 8, 1–13. [Google Scholar] [CrossRef] - Deng, X.; Mardanikorani, S.; Arulandu, K.; Linnartz, J.P.M. Novel Post-distortion to Mitigate LED Nonlinearity in High-speed Visible Light Communications. In Proceedings of the IEEE Globecom Workshops (GC Wkshps), Abu Dhabi, UAE, 9–13 December 2018; pp. 1–6. [Google Scholar]
- Wang, Y.; Tao, L.; Huang, X.; Shi, J.; Chi, N. Enhanced performance of a high-speed WDM CAP64 VLC system employing Volterra series-based nonlinear equalizer. IEEE Photonics J.
**2015**, 7, 1–7. [Google Scholar] [CrossRef] - Lu, X.; Wang, K.; Qiao, L.; Zhou, W.; Wang, Y.; Chi, N. Nonlinear compensation of multi-CAP VLC system employing clustering algorithm based perception decision. IEEE Photonics J.
**2017**, 9, 1–9. [Google Scholar] [CrossRef] - Ma, J.; He, J.; Shi, J.; Zhou, Z.; Deng, R. Nonlinear Compensation Based on K-Means Clustering Algorithm for Nyquist PAM-4 VLC System. IEEE Photonics Technol. Lett.
**2019**, 31, 935–938. [Google Scholar] [CrossRef] - Lu, X.; Lu, C.; Yu, W.; Qiao, L.; Liang, S.; Lau, A.P.T.; Chi, N. Memory-controlled deep LSTM neural network post-equalizer used in high-speed PAM VLC system. Opt. Express
**2019**, 27, 7822–7833. [Google Scholar] [CrossRef] [PubMed][Green Version] - Miao, P.; Zhu, B.; Qi, C.; Jin, Y.; Lin, C. A Model-Driven Deep Learning Method for LED Nonlinearity Mitigation in OFDM-based Optical Communications. IEEE Access
**2019**, 7, 71436–71446. [Google Scholar] [CrossRef] - Nguyen, T.; Mhatli, S.; Giacoumidis, E.; Van Compernolle, L.; Wuilpart, M.; Mégret, P. Fiber nonlinearity equalizer based on support vector classification for coherent optical OFDM. IEEE Photonics J.
**2016**, 8, 1–9. [Google Scholar] [CrossRef] - Lake, B.M.; Salakhutdinov, R.; Tenenbaum, J.B. Human-level concept learning through probabilistic program induction. Science
**2015**, 350, 1332–1338. [Google Scholar] [CrossRef][Green Version] - Tipping, M.E. Sparse Bayesian learning and the relevance vector machine. J. Mach. Learn. Res.
**2001**, 1, 211–244. [Google Scholar] - Chen, C.; Zhong, W.D.; Zhao, L. Sparse Bayesian RVM regression based channel estimation for IM/DD OFDM-VLC systems with reduced training overhead. In Proceedings of the IEEE International Conference on Communications Workshops (ICC Workshops), Paris, France, 21–25 May 2017; pp. 162–167. [Google Scholar]
- Zhao, L.; Wang, L.; Yang, L.; Zoubir, A.M.; Bi, G. The race to improve radar imagery: An overview of recent progress in statistical sparsity-based techniques. IEEE Signal Process. Mag.
**2016**, 33, 85–102. [Google Scholar] [CrossRef] - Zhao, L.; Wang, L.; Bi, G.; Zhang, L.; Zhang, H. Robust frequency-hopping spectrum estimation based on sparse Bayesian method. IEEE Trans. Wirel. Commun.
**2014**, 14, 781–793. [Google Scholar] [CrossRef] - Li, J.; Huang, Z.; Liu, X.; Ji, Y. Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems. Opt. Express
**2015**, 23, 611–619. [Google Scholar] [CrossRef] - Tipping, M.E.; Faul, A.C. Fast marginal likelihood maximisation for sparse Bayesian models. In Proceedings of the 9th International Workshop on Artificial Intelligence and Statistics, Key West, FL, USA, 3–6 January 2003; pp. 1–13. [Google Scholar]
- Aggarwal, P.; Kabra, T.; Ahmad, R.; Bohara, V.A.; Srivastava, A. Adaptive learning architecture-based predistorter for nonlinear VLC system. Photonics Netw. Commun.
**2019**, 1–12. [Google Scholar] [CrossRef]

**Figure 1.**Block diagram of an OFDM-based nonlinear VLC system using PBL-based LED nonlinearity estimation (est.) and compensation (comp.).

**Figure 4.**Normalized signal amplitude vs. normalized input current for (

**a**) MI = 0.6 and (

**b**) MI = 0.8.

Parameter | Value |
---|---|

Semi-angle at half power of LED | ${60}^{\circ}$ |

LED output optical power | 10 W |

Gain of optical filter | 0.9 |

Refractive index of optical lens | 1.5 |

Half-angle FOV of optical lens | ${72}^{\circ}$ |

Active area of PD | 16 ${\mathrm{mm}}^{2}$ |

Responsivity of PD | 0.53 A/W |

Vertical distance between LED and PD | 2 m |

Horizontal offset between LED and PD | 2 m |

Modulation bandwidth | 20 MHz |

QAM constellation order | 16 |

Raw data rate | 80 Mbit/s |

Size of FFT/IFFT | 512 |

Number of data subcarriers | 128 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, C.; Deng, X.; Yang, Y.; Du, P.; Yang, H.; Zhao, L.
LED Nonlinearity Estimation and Compensation in VLC Systems Using Probabilistic Bayesian Learning. *Appl. Sci.* **2019**, *9*, 2711.
https://doi.org/10.3390/app9132711

**AMA Style**

Chen C, Deng X, Yang Y, Du P, Yang H, Zhao L.
LED Nonlinearity Estimation and Compensation in VLC Systems Using Probabilistic Bayesian Learning. *Applied Sciences*. 2019; 9(13):2711.
https://doi.org/10.3390/app9132711

**Chicago/Turabian Style**

Chen, Chen, Xiong Deng, Yanbing Yang, Pengfei Du, Helin Yang, and Lifan Zhao.
2019. "LED Nonlinearity Estimation and Compensation in VLC Systems Using Probabilistic Bayesian Learning" *Applied Sciences* 9, no. 13: 2711.
https://doi.org/10.3390/app9132711