Abstract

Linear and nonlinear impairments severely limit the transmission performance of high-speed visible light communication systems. Neural network-based equalizers have been applied to optical communication systems, which enables significantly improved system performance, such as transmission data rate and distance. In this paper, a memory-controlled deep long short-term memory (LSTM) neural network post-equalizer is proposed to mitigate both linear and nonlinear impairments in pulse amplitude modulation (PAM) based visible light communication (VLC) systems. Both 1.15-Gbps PAM4 and 0.9Gbps PAM8 VLC systems are successfully demonstrated, based on a single red-LED with bit error ratio (BER) below the hard decision forward error correction (HD-FEC) limit of 3.8 x 10−3. Compared with the traditional finite impulse response (FIR) based equalizer, the Q factor performance is improved by 1.2dB and the transmission distance is increased by one-third in the same experimental hardware setups. Compared with traditional nonlinear hybrid Volterra equalizers, the significant complexity and system performance advantages of using a LSTM-based equalizer is demonstrated. To the best of our knowledge, this is the first demonstration of using deep LSTM in VLC systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
    [Crossref]
  2. Y. Wang, N. Chi, Y. Wang, R. Li, X. Huang, C. Yang, and Z. Zhang, “High-speed quasi-balanced detection OFDM in visible light communication,” Opt. Express 21(23), 27558–27564 (2013).
    [Crossref] [PubMed]
  3. K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
    [Crossref]
  4. M. Zhang, M. Shi, F. Wang, J. Zhao, Y. Zhou, Z. Wang, and N. Chi, “4.05-Gb/s RGB LED-based VLC system utilizing PS-Manchester coded Nyquist PAM-8 modulation and hybrid time-frequency domain equalization.” Proc. OFC, W2A.42. LA (2017).
    [Crossref]
  5. I. Stefan, H. Elgala, and H. Haas, “Study of dimming and LED nonlinearity for ACO-OFDM based VLC systems,” in Wireless Communications and Networking Conference (WCNC). IEEE, 2012, pp. 990–994.
    [Crossref]
  6. N. Chi, M. Zhang, Y. Zhou, and J. Zhao, “3.375-Gb/s RGB-LED based WDM visible light communication system employing PAM-8 modulation with phase shifted Manchester coding,” Opt. Express 24(19), 21663–21673 (2016).
    [Crossref] [PubMed]
  7. Y. Wang, X. Huang, L. Tao, J. Shi, and N. Chi, “4.5-Gb/s RGB-LED based WDM visible light communication system employing CAP modulation and RLS based adaptive equalization,” Opt. Express 23(10), 13626–13633 (2015).
    [Crossref] [PubMed]
  8. G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE,” IEEE Photonics Technol. Lett. 25(16), 1597–1600 (2013).
    [Crossref]
  9. K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
    [Crossref]
  10. S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
    [Crossref]
  11. P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
    [Crossref]
  12. X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).
  13. J. Zhang, J. Yu, and H. Chien, EML-based IM/DD 400G (4× 112.5-Gbit/s) PAM-4 over 80 km SSMF based on linear pre-equalization and nonlinear LUT pre-distortion for inter-DCI applications. In Optical Fiber Communications Conference and Exhibition (OFC), 2017 (pp. 1–3).
  14. D. Angluin, “Queries and concept learning,” Mach. Learn. 2(4), 319–342 (1988).
    [Crossref]
  15. P. Domingos, “A few useful things to know about machine learning,” Commun. ACM 55(10), 78–87 (2012).
    [Crossref]
  16. J. Thrane, J. Wass, M. Piels, J. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightwave Technol. 35(4), 868–875 (2017).
    [Crossref]
  17. F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems.” Signal Processing in Photonic Communications. OSA, 2017.
  18. T. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photonics Technol. Lett. 29(23), 2091–2094 (2017).
    [Crossref]
  19. A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 1, 1097–1105 (2012).
  20. K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
    [Crossref] [PubMed]
  21. X. Huang, J. Shi, J. Li, Y. Wang, Y. Wang, and N. Chi, “750 Mbit/s visible light communications employing 64 QAM-OFDM based on amplitude equalization circuit,” presented at the Opt. Fiber Commun. Conf., 2015, Tu2G.1.
    [Crossref]

2018 (1)

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

2017 (4)

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

J. Thrane, J. Wass, M. Piels, J. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightwave Technol. 35(4), 868–875 (2017).
[Crossref]

T. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photonics Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (4)

Y. Wang, X. Huang, L. Tao, J. Shi, and N. Chi, “4.5-Gb/s RGB-LED based WDM visible light communication system employing CAP modulation and RLS based adaptive equalization,” Opt. Express 23(10), 13626–13633 (2015).
[Crossref] [PubMed]

N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
[Crossref]

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

2013 (3)

P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
[Crossref]

Y. Wang, N. Chi, Y. Wang, R. Li, X. Huang, C. Yang, and Z. Zhang, “High-speed quasi-balanced detection OFDM in visible light communication,” Opt. Express 21(23), 27558–27564 (2013).
[Crossref] [PubMed]

G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE,” IEEE Photonics Technol. Lett. 25(16), 1597–1600 (2013).
[Crossref]

2012 (2)

P. Domingos, “A few useful things to know about machine learning,” Commun. ACM 55(10), 78–87 (2012).
[Crossref]

A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 1, 1097–1105 (2012).

1988 (1)

D. Angluin, “Queries and concept learning,” Mach. Learn. 2(4), 319–342 (1988).
[Crossref]

Angluin, D.

D. Angluin, “Queries and concept learning,” Mach. Learn. 2(4), 319–342 (1988).
[Crossref]

Bülow, H.

T. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photonics Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

Chi, N.

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

N. Chi, M. Zhang, Y. Zhou, and J. Zhao, “3.375-Gb/s RGB-LED based WDM visible light communication system employing PAM-8 modulation with phase shifted Manchester coding,” Opt. Express 24(19), 21663–21673 (2016).
[Crossref] [PubMed]

Y. Wang, X. Huang, L. Tao, J. Shi, and N. Chi, “4.5-Gb/s RGB-LED based WDM visible light communication system employing CAP modulation and RLS based adaptive equalization,” Opt. Express 23(10), 13626–13633 (2015).
[Crossref] [PubMed]

N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
[Crossref]

Y. Wang, N. Chi, Y. Wang, R. Li, X. Huang, C. Yang, and Z. Zhang, “High-speed quasi-balanced detection OFDM in visible light communication,” Opt. Express 21(23), 27558–27564 (2013).
[Crossref] [PubMed]

Diniz, J.

Domingos, P.

P. Domingos, “A few useful things to know about machine learning,” Commun. ACM 55(10), 78–87 (2012).
[Crossref]

Elgala, H.

I. Stefan, H. Elgala, and H. Haas, “Study of dimming and LED nonlinearity for ACO-OFDM based VLC systems,” in Wireless Communications and Networking Conference (WCNC). IEEE, 2012, pp. 990–994.
[Crossref]

Eriksson, T.

T. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photonics Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

Ghassemlooy, Z.

P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
[Crossref]

Greff, K.

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

Haas, H.

N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
[Crossref]

I. Stefan, H. Elgala, and H. Haas, “Study of dimming and LED nonlinearity for ACO-OFDM based VLC systems,” in Wireless Communications and Networking Conference (WCNC). IEEE, 2012, pp. 990–994.
[Crossref]

Haigh, P.

P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
[Crossref]

Hinton, G.

A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 1, 1097–1105 (2012).

Huang, X.

Jiang, Z.

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

Jones, R.

Kavehrad, M.

N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
[Crossref]

Koutník, J.

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

Krizhevsky, A.

A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 1, 1097–1105 (2012).

Leven, A.

T. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photonics Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

Li, R.

Liang, R.

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

Liang, S.

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

Little, T.

N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
[Crossref]

Lu, X.

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

Papakonstantinou, I.

P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
[Crossref]

Piels, M.

Qiao, L.

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

Qiu, P.

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

Rajbhandari, S.

P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
[Crossref]

Schmidhuber, J.

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

Shi, J.

Siuzdak, J.

G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE,” IEEE Photonics Technol. Lett. 25(16), 1597–1600 (2013).
[Crossref]

Srivastava, R. K.

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

Stefan, I.

I. Stefan, H. Elgala, and H. Haas, “Study of dimming and LED nonlinearity for ACO-OFDM based VLC systems,” in Wireless Communications and Networking Conference (WCNC). IEEE, 2012, pp. 990–994.
[Crossref]

Stepniak, G.

G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE,” IEEE Photonics Technol. Lett. 25(16), 1597–1600 (2013).
[Crossref]

Steunebrink, B. R.

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

Sutskever, I.

A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 1, 1097–1105 (2012).

Tao, L.

Thrane, J.

Wang, K.

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

Wang, Y.

Wass, J.

Yang, C.

Zhang, M.

Zhang, Z.

Zhao, J.

Zhou, W.

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

Zhou, Y.

Zibar, D.

Zwierko, P.

G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE,” IEEE Photonics Technol. Lett. 25(16), 1597–1600 (2013).
[Crossref]

Adv. Neural Inf. Process. Syst. (1)

A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 1, 1097–1105 (2012).

Commun. ACM (1)

P. Domingos, “A few useful things to know about machine learning,” Commun. ACM 55(10), 78–87 (2012).
[Crossref]

IEEE Commun. Mag. (1)

P. Haigh, Z. Ghassemlooy, S. Rajbhandari, and I. Papakonstantinou, “Visible light communications using organic light emitting diodes,” IEEE Commun. Mag. 51(8), 148–154 (2013).
[Crossref]

IEEE Photonics J. (3)

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

K. Wang, R. Liang, and P. Qiu, “Fluorescence Signal Generation Optimization by Optimal Filling of the High Numerical Aperture Objective Lens for High-Order Deep-Tissue Multiphoton Fluorescence Microscopy,” IEEE Photonics J. 7(6), 1–8 (2015).
[Crossref]

S. Liang, Z. Jiang, L. Qiao, X. Lu, and N. Chi, “Faster-Than-Nyquist precoded CAP modulation visible light communication system based on nonlinear weighted look-up table predistortion,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

IEEE Photonics Journal (1)

X. Lu, K. Wang, L. Qiao, W. Zhou, Y. Wang, and N. Chi, “Non-linear compensation of multi-cap VLC system employing clustering algorithm-based perception decision,” IEEE Photonics Journal,  9(5), 1-9 (2017).

IEEE Photonics Technol. Lett. (2)

G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of Volterra DFE,” IEEE Photonics Technol. Lett. 25(16), 1597–1600 (2013).
[Crossref]

T. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Photonics Technol. Lett. 29(23), 2091–2094 (2017).
[Crossref]

IEEE Trans. Neural Netw. Learn. Syst. (1)

K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “LSTM: A search space odyssey,” IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2222–2232 (2017).
[Crossref] [PubMed]

IEEE Wirel. Commun. (1)

N. Chi, H. Haas, M. Kavehrad, T. Little, and X. Huang, “Visible light communications: demand factors, benefits and opportunities,” IEEE Wirel. Commun. 22(2), 5–7 (2015).
[Crossref]

J. Lightwave Technol. (1)

Mach. Learn. (1)

D. Angluin, “Queries and concept learning,” Mach. Learn. 2(4), 319–342 (1988).
[Crossref]

Opt. Express (3)

Other (5)

M. Zhang, M. Shi, F. Wang, J. Zhao, Y. Zhou, Z. Wang, and N. Chi, “4.05-Gb/s RGB LED-based VLC system utilizing PS-Manchester coded Nyquist PAM-8 modulation and hybrid time-frequency domain equalization.” Proc. OFC, W2A.42. LA (2017).
[Crossref]

I. Stefan, H. Elgala, and H. Haas, “Study of dimming and LED nonlinearity for ACO-OFDM based VLC systems,” in Wireless Communications and Networking Conference (WCNC). IEEE, 2012, pp. 990–994.
[Crossref]

J. Zhang, J. Yu, and H. Chien, EML-based IM/DD 400G (4× 112.5-Gbit/s) PAM-4 over 80 km SSMF based on linear pre-equalization and nonlinear LUT pre-distortion for inter-DCI applications. In Optical Fiber Communications Conference and Exhibition (OFC), 2017 (pp. 1–3).

F. Khan, C. Lu, and A. Lau, “Machine learning methods for optical communication systems.” Signal Processing in Photonic Communications. OSA, 2017.

X. Huang, J. Shi, J. Li, Y. Wang, Y. Wang, and N. Chi, “750 Mbit/s visible light communications employing 64 QAM-OFDM based on amplitude equalization circuit,” presented at the Opt. Fiber Commun. Conf., 2015, Tu2G.1.
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Back-to-back transfer curve of PAM8 data of VLC system.
Fig. 2
Fig. 2 Diagram of LSTM.
Fig. 3
Fig. 3 Structure of LSTM based equalizer.
Fig. 4
Fig. 4 Flow chart of training and equalization.
Fig. 5
Fig. 5 Experimental setup.
Fig. 6
Fig. 6 Training convergence curve of LSTM.
Fig. 7
Fig. 7 a) Q factor (dB) comparison of LSTM and LMS + DDLMS. b) Constellation of the best working conditions of the LMS + DDLMS equalizer. b) Constellation of the best working conditions of the LMS + Volterra equalizer. d) Probability distribution of every symbols for the best working conditions of the LSTM equalizer and e) Constellations without equalizer.
Fig. 8
Fig. 8 BER comparison of LSTM and LMS + DDLMS of a) PAM4 and b) PAM8 VLC systems under different baud rate, respectively.
Fig. 9
Fig. 9 Transmission distance comparison with LSTM and LMS + DDLMS in PAM8 VLC systems versus different bitrates: a) 750Mbit/s; b) 900Mbit/s.
Fig. 10
Fig. 10 Measured BER versus bias currents and input signal Vpp.
Fig. 11
Fig. 11 Q factor performance curve of pseudo-random and random sequence.
Fig. 12
Fig. 12 Q factor performance curve of training sequence length.

Tables (1)

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Table 1 Complexity Comparison of Equalizersa

Equations (11)

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y(n)= i=0 N1 w i x(ni)
y(n)= k 1 =0 N 1 1 w k 1 (n)x(n k 1 ) + k 1 =0 N 2 1 k 2 = k 1 N 2 1 w k 1 k 2 (n)x(n k 1 ) x(n k 2 ) + k 1 =0 N 3 1 k 2 = k 1 N 3 1 k 3 = k 2 N 3 1 w k 1 k 2 k 3 (n)x(n k 1 ) x(n k 2 ) x(n k 3 )+... + k 1 =0 N p 1 ... k p = k p1 N p 1 w k 1 ... k p (n)x(n k 1 ) ...x(n k p )
y(n)=f( X n ) =g{h[ i=0 N w i x(ni) +b]}
X n = X T = [x(n),x(n1),...,x(0)] T
S(n)={ X n ,y(n)}
P(y= L i )= e X T w i k=1 K e X T w k
g()= i=0 NoL P(y= L i ) L i ¯
H Y train (Y)= i Y i trian log( P X train (y= L i )) = i Y i trian log( e X T w i k=1 K e X T w k )
batc h k ={ S n , S n+1 ,..., S n+m }=[ { X n ,y(n) } ... { X n+m ,y(n+m) } ]
P(y= L i |ybatc h k )> P X train (y= L j )= e X T w i k=1 K e X T w k
batc h k '=r(batc h k )=random{ S n , S n+1 ,..., S n+m }

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