Abstract

This article aims to present, analyze and evaluate a new equalizer architecture, inspired by the butterfly equalizer used in optical communication, based on Artificial Neural Networks (ANN) of the Multi-Layer Perceptron (MLP) type for nonlinear systems with two-dimensional modulation named the Butterfly Neural Equalizer (NE-Butterfly). The NE-Butterfly is intended to equalize any channel that has real or complex taps, whether linear or nonlinear. Simulation results are presented for different types of nonlinear fiber optic channels with complex and real taps, also containing inter symbolic interference and additive noise. The results are compared with other neural equalizers in the literature with the objective of validating the performance of the NE-Butterfly, which stands out as having the overall best performance against the ones it was compared to.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2018 (1)

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

2017 (3)

H. Wang, W. Zhou, and J. Yu, “Pam-4 signal delivery in one radio-over-fiber system,” Opt. Eng. 56, 106107 (2017).
[Crossref]

G. Kaur and G. Kaur, “Application of functional link artificial neural network for mitigating nonlinear effects in coherent optical ofdm,” Opt. Quantum Electron. 49, 227 (2017).
[Crossref]

H.-Y. Chen, N. Kaneda, J. Lee, J. Chen, and Y.-K. Chen, “Optical filter requirements in an eml-based single-sideband pam4 intensity-modulation and direct-detection transmission system,” Opt. Express 25, 5852–5860 (2017).
[Crossref] [PubMed]

2016 (2)

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, 21663–21673 (2016).
[Crossref] [PubMed]

S. T. Ahmad and K. P. Kumar, “Radial basis function neural network nonlinear equalizer for 16-qam coherent optical ofdm,” IEEE Photonics Tech. Lett. 28, 2507–2510 (2016).
[Crossref]

2015 (2)

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

S. Panda, P. K. Mohapatra, and S. P. Panigrahi, “A new training scheme for neural networks and application in non-linear channel equalization,” Appl. Soft Comput. 27, 47–52 (2015).
[Crossref]

2014 (3)

M. A. C. Fernandes, “Neural equalization applied to systems with bidimensional digital modulation,” Neural Comput. Appl. 25, 2057–2066 (2014).
[Crossref]

T. F. B. Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” WSEAS Trans. Commun. 13, 462–469 (2014).

G. Das, P. K. Pattnaik, and S. K. Padhy, “Artificial neural network trained by particle swarm optimization for non-linear channel equalization,” Expert Syst. Appl. 41, 3491–3496 (2014).
[Crossref]

2011 (1)

2010 (3)

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” Syst. Man Cybern. Part C: Appl. Rev. 40, 352–357 (2010).
[Crossref]

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

E. M. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Light. Technol. 28, 502 (2010).
[Crossref]

2008 (3)

2004 (1)

J. Wang and J. M. Kahn, “Performance of electrical equalizers in optically amplified ook and dpsk systems,” IEEE Photonics Tech. Lett. 16, 1397–1399 (2004).
[Crossref]

2002 (1)

T. Kim and T. Adali, “Fully complex multi-layer perceptron network for nonlinear signal processing,” J. VLSI Signal Process. 32, 29–43 (2002).
[Crossref]

1992 (3)

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization with neural networks: new multi-layer perceptron structures and their evaluation,” Acoust. Speech Signal Process. 2, 301–304 (1992).

N. Benvenuto and F. Piazza, “On the complex backpropagation algorithm,” Signal Process. 40, 967–969 (1992).

G. Georgiou and C. Koutsougeras, “Complex domain backpropagation,” Circuits Syst. II: Analog. Digit. Signal Process. 39, 330–334 (1992).
[Crossref]

1991 (3)

H. Leung and S. Haykin, “The complex backpropagation algorithm,” Signal Process. 39, 2101–2104 (1991).

G. Gibson, S. Siu, and C. Cowan, “The aplication of nonlinear structures to the reconstruction of binary signals,” Signal Process. 39, 1877–1884 (1991).

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization for pam and wam signals with neural networks,” Signals Syst. Comput. 1, 496–500 (1991).

1990 (1)

S. Chen, G. J. Gibson, C. F. N. Cowan, and P. M. Grant, “Adaptive equalisation of finite non-linear channels using multilayer perceptrons,” EURASIP Signal Process. J. 20, 107–119 (1990).
[Crossref]

Adali, T.

T. Kim and T. Adali, “Fully complex multi-layer perceptron network for nonlinear signal processing,” J. VLSI Signal Process. 32, 29–43 (2002).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, vol. 22 of Wiley Series in Microwave and Optical Engineering (John Wiley and Sons, 2012), 4th ed.

Ahmad, S. T.

S. T. Ahmad and K. P. Kumar, “Radial basis function neural network nonlinear equalizer for 16-qam coherent optical ofdm,” IEEE Photonics Tech. Lett. 28, 2507–2510 (2016).
[Crossref]

Aldaya, I.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Algani, C.

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

Bae, H.-M.

A. C. Singer, N. R. Shanbhag, and H.-M. Bae, “Electronic dispersion compensation: An overview of optical communications systems,” IEEE Signal Process. Mag. 266, 110–130 (2008).
[Crossref]

Benvenuto, N.

N. Benvenuto and F. Piazza, “On the complex backpropagation algorithm,” Signal Process. 40, 967–969 (1992).

Bigo, S.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Billabert, A.-L.

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

Burse, K.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” Syst. Man Cybern. Part C: Appl. Rev. 40, 352–357 (2010).
[Crossref]

Chen, H.-Y.

Chen, J.

Chen, S.

S. Chen, G. J. Gibson, C. F. N. Cowan, and P. M. Grant, “Adaptive equalisation of finite non-linear channels using multilayer perceptrons,” EURASIP Signal Process. J. 20, 107–119 (1990).
[Crossref]

Chen, X.

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

Chen, Y.-K.

Chen, Z.

Chi, N.

Chung, W.-Z.

Cowan, C.

G. Gibson, S. Siu, and C. Cowan, “The aplication of nonlinear structures to the reconstruction of binary signals,” Signal Process. 39, 1877–1884 (1991).

C. Cowan, “Nonlinear adaptive equalization [multilayer perceptron],”,” in Sixth International Conference on Digital Processing Signals in Communications (IET,1991), pp. 1–5.

Cowan, C. F. N.

S. Chen, G. J. Gibson, C. F. N. Cowan, and P. M. Grant, “Adaptive equalisation of finite non-linear channels using multilayer perceptrons,” EURASIP Signal Process. J. 20, 107–119 (1990).
[Crossref]

Das, G.

G. Das, P. K. Pattnaik, and S. K. Padhy, “Artificial neural network trained by particle swarm optimization for non-linear channel equalization,” Expert Syst. Appl. 41, 3491–3496 (2014).
[Crossref]

de Sousa, T. F. B.

T. F. B. de Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” in 2013 SBMO/IEEE MTTS International Microwave and Optoelectronics Conference (IMOC) (IEEE2013).
[Crossref]

Diakité, M. L.

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

Doran, N. J.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Dupuy, J.-Y.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Emmaeinna, M.

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

Estaran, J.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Faci, S.

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

Fan, Y.

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

Fernandes, M. A. C.

M. A. C. Fernandes, “Neural equalization applied to systems with bidimensional digital modulation,” Neural Comput. Appl. 25, 2057–2066 (2014).
[Crossref]

T. F. B. Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” WSEAS Trans. Commun. 13, 462–469 (2014).

T. F. B. Sousa and M. A. C. Fernandes, “Bi-dimensional neural equalizer applied to optical receiver,” in 1st BRICS Congress on Computational Inteliigence and 11th Brazilian Congress on Computational Intelligence (IEEE, 2013).

T. F. B. de Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” in 2013 SBMO/IEEE MTTS International Microwave and Optoelectronics Conference (IMOC) (IEEE2013).
[Crossref]

Georgiou, G.

G. Georgiou and C. Koutsougeras, “Complex domain backpropagation,” Circuits Syst. II: Analog. Digit. Signal Process. 39, 330–334 (1992).
[Crossref]

Ghassemlooy, Z.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Giacoumidis, E.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Gibson, G.

G. Gibson, S. Siu, and C. Cowan, “The aplication of nonlinear structures to the reconstruction of binary signals,” Signal Process. 39, 1877–1884 (1991).

Gibson, G. J.

S. Chen, G. J. Gibson, C. F. N. Cowan, and P. M. Grant, “Adaptive equalisation of finite non-linear channels using multilayer perceptrons,” EURASIP Signal Process. J. 20, 107–119 (1990).
[Crossref]

Grant, P. M.

S. Chen, G. J. Gibson, C. F. N. Cowan, and P. M. Grant, “Adaptive equalisation of finite non-linear channels using multilayer perceptrons,” EURASIP Signal Process. J. 20, 107–119 (1990).
[Crossref]

Hauske, F. N.

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

Haykin, S.

H. Leung and S. Haykin, “The complex backpropagation algorithm,” Signal Process. 39, 2101–2104 (1991).

Haykin, S. S.

S. S. Haykin, Communication Systems(Wiley, 2001), 4th ed.

Ip, E. M.

E. M. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Light. Technol. 28, 502 (2010).
[Crossref]

Jarajreh, M. A.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Javidi, F.

F. Javidi and H. Khoshbin, “Performance of back-propagation and self organizing map neural equalizers for asymmetrically clipped optical ofdm,” in Iranian Conference on Electrical Engineering (ICEE, 2013).

Jorge, F.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Kabalan, A.

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

Kahn, J. M.

E. M. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Light. Technol. 28, 502 (2010).
[Crossref]

J. Wang and J. M. Kahn, “Performance of electrical equalizers in optically amplified ook and dpsk systems,” IEEE Photonics Tech. Lett. 16, 1397–1399 (2004).
[Crossref]

Kaneda, N.

Kaur, G.

G. Kaur and G. Kaur, “Application of functional link artificial neural network for mitigating nonlinear effects in coherent optical ofdm,” Opt. Quantum Electron. 49, 227 (2017).
[Crossref]

G. Kaur and G. Kaur, “Application of functional link artificial neural network for mitigating nonlinear effects in coherent optical ofdm,” Opt. Quantum Electron. 49, 227 (2017).
[Crossref]

Khoshbin, H.

F. Javidi and H. Khoshbin, “Performance of back-propagation and self organizing map neural equalizers for asymmetrically clipped optical ofdm,” in Iranian Conference on Electrical Engineering (ICEE, 2013).

Kim, K.-S.

Kim, S.-C.

Kim, T.

T. Kim and T. Adali, “Fully complex multi-layer perceptron network for nonlinear signal processing,” J. VLSI Signal Process. 32, 29–43 (2002).
[Crossref]

Konczykowska, A.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Koutsougeras, C.

G. Georgiou and C. Koutsougeras, “Complex domain backpropagation,” Circuits Syst. II: Analog. Digit. Signal Process. 39, 330–334 (1992).
[Crossref]

Krummrich, P. M.

M. Westhauser, C. Remmersmann, S. Pachnicke, and P. M. Krummrich, “Optical equalization of pmd-induced penalties in 112 gbit/s metro networks,” in Signal Processing in Photonic Communications (OSA, 2011).

Kumar, K. P.

S. T. Ahmad and K. P. Kumar, “Radial basis function neural network nonlinear equalizer for 16-qam coherent optical ofdm,” IEEE Photonics Tech. Lett. 28, 2507–2510 (2016).
[Crossref]

Kuschnerov, M.

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

Lankl, B.

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

Le, S. T.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Lee, J.

Lee, J.-H.

Leung, H.

H. Leung and S. Haykin, “The complex backpropagation algorithm,” Signal Process. 39, 2101–2104 (1991).

Li, M.

Li, Z.

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

Liu, B.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Luo, T.

T. Luo, “Digital equalization of fiber-optic transmission system impairments,” Master’s thesis, McMaster University (2011).

Mardoyan, H.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Mestre, M.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Mohapatra, P. K.

S. Panda, P. K. Mohapatra, and S. P. Panigrahi, “A new training scheme for neural networks and application in non-linear channel equalization,” Appl. Soft Comput. 27, 47–52 (2015).
[Crossref]

Nikias, C.

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization with neural networks: new multi-layer perceptron structures and their evaluation,” Acoust. Speech Signal Process. 2, 301–304 (1992).

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization for pam and wam signals with neural networks,” Signals Syst. Comput. 1, 496–500 (1991).

Pachnicke, S.

C. Remmersmann, M. Westhauser, and S. Pachnicke, “Equalization of first and second order pmd in 100 gbit/s polmux transmission using optical butterfly fir filters,” in Conference on Optic Engineers (OSA2010).

M. Westhauser, C. Remmersmann, S. Pachnicke, and P. M. Krummrich, “Optical equalization of pmd-induced penalties in 112 gbit/s metro networks,” in Signal Processing in Photonic Communications (OSA, 2011).

Padhy, S. K.

G. Das, P. K. Pattnaik, and S. K. Padhy, “Artificial neural network trained by particle swarm optimization for non-linear channel equalization,” Expert Syst. Appl. 41, 3491–3496 (2014).
[Crossref]

Panda, S.

S. Panda, P. K. Mohapatra, and S. P. Panigrahi, “A new training scheme for neural networks and application in non-linear channel equalization,” Appl. Soft Comput. 27, 47–52 (2015).
[Crossref]

Panigrahi, S. P.

S. Panda, P. K. Mohapatra, and S. P. Panigrahi, “A new training scheme for neural networks and application in non-linear channel equalization,” Appl. Soft Comput. 27, 47–52 (2015).
[Crossref]

Park, J.-W.

Pattnaik, P. K.

G. Das, P. K. Pattnaik, and S. K. Padhy, “Artificial neural network trained by particle swarm optimization for non-linear channel equalization,” Expert Syst. Appl. 41, 3491–3496 (2014).
[Crossref]

Peng, M.

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization with neural networks: new multi-layer perceptron structures and their evaluation,” Acoust. Speech Signal Process. 2, 301–304 (1992).

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization for pam and wam signals with neural networks,” Signals Syst. Comput. 1, 496–500 (1991).

Piazza, F.

N. Benvenuto and F. Piazza, “On the complex backpropagation algorithm,” Signal Process. 40, 967–969 (1992).

Piyawanno, L.

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

Proakis, J.

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization with neural networks: new multi-layer perceptron structures and their evaluation,” Acoust. Speech Signal Process. 2, 301–304 (1992).

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization for pam and wam signals with neural networks,” Signals Syst. Comput. 1, 496–500 (1991).

J. Proakis, Digital Communications(McGraw-Hill Science/Engineering/Math, 2000).

Rao, L.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Remmersmann, C.

M. Westhauser, C. Remmersmann, S. Pachnicke, and P. M. Krummrich, “Optical equalization of pmd-induced penalties in 112 gbit/s metro networks,” in Signal Processing in Photonic Communications (OSA, 2011).

C. Remmersmann, M. Westhauser, and S. Pachnicke, “Equalization of first and second order pmd in 100 gbit/s polmux transmission using optical butterfly fir filters,” in Conference on Optic Engineers (OSA2010).

Rios-Müller, R.

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

Schmidt, E. D.

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

Shanbhag, N. R.

A. C. Singer, N. R. Shanbhag, and H.-M. Bae, “Electronic dispersion compensation: An overview of optical communications systems,” IEEE Signal Process. Mag. 266, 110–130 (2008).
[Crossref]

Shrivastava, S.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” Syst. Man Cybern. Part C: Appl. Rev. 40, 352–357 (2010).
[Crossref]

Singer, A. C.

A. C. Singer, N. R. Shanbhag, and H.-M. Bae, “Electronic dispersion compensation: An overview of optical communications systems,” IEEE Signal Process. Mag. 266, 110–130 (2008).
[Crossref]

Siu, S.

G. Gibson, S. Siu, and C. Cowan, “The aplication of nonlinear structures to the reconstruction of binary signals,” Signal Process. 39, 1877–1884 (1991).

Sousa, T. F. B.

T. F. B. Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” WSEAS Trans. Commun. 13, 462–469 (2014).

T. F. B. Sousa and M. A. C. Fernandes, “Bi-dimensional neural equalizer applied to optical receiver,” in 1st BRICS Congress on Computational Inteliigence and 11th Brazilian Congress on Computational Intelligence (IEEE, 2013).

Spinnler, B.

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

Tian, F.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Tian, Q.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Tsokanos, A.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

Ullah, R.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Wang, H.

H. Wang, W. Zhou, and J. Yu, “Pam-4 signal delivery in one radio-over-fiber system,” Opt. Eng. 56, 106107 (2017).
[Crossref]

Wang, J.

J. Wang and J. M. Kahn, “Performance of electrical equalizers in optically amplified ook and dpsk systems,” IEEE Photonics Tech. Lett. 16, 1397–1399 (2004).
[Crossref]

Wang, Y.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Westhauser, M.

C. Remmersmann, M. Westhauser, and S. Pachnicke, “Equalization of first and second order pmd in 100 gbit/s polmux transmission using optical butterfly fir filters,” in Conference on Optic Engineers (OSA2010).

M. Westhauser, C. Remmersmann, S. Pachnicke, and P. M. Krummrich, “Optical equalization of pmd-induced penalties in 112 gbit/s metro networks,” in Signal Processing in Photonic Communications (OSA, 2011).

Xiao, F.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Xin, X.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Xu, A.

Yadav, R.

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” Syst. Man Cybern. Part C: Appl. Rev. 40, 352–357 (2010).
[Crossref]

Yu, J.

H. Wang, W. Zhou, and J. Yu, “Pam-4 signal delivery in one radio-over-fiber system,” Opt. Eng. 56, 106107 (2017).
[Crossref]

Zhang, F.

Zhang, L.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Zhang, M.

Zhang, Q.

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

Zhao, J.

Zhou, W.

H. Wang, W. Zhou, and J. Yu, “Pam-4 signal delivery in one radio-over-fiber system,” Opt. Eng. 56, 106107 (2017).
[Crossref]

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

Zhou, X.

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

Zhou, Y.

Zhu, H.

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

Acoust. Speech Signal Process. (1)

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization with neural networks: new multi-layer perceptron structures and their evaluation,” Acoust. Speech Signal Process. 2, 301–304 (1992).

Appl. Soft Comput. (1)

S. Panda, P. K. Mohapatra, and S. P. Panigrahi, “A new training scheme for neural networks and application in non-linear channel equalization,” Appl. Soft Comput. 27, 47–52 (2015).
[Crossref]

Circuits Syst. II: Analog. Digit. Signal Process. (1)

G. Georgiou and C. Koutsougeras, “Complex domain backpropagation,” Circuits Syst. II: Analog. Digit. Signal Process. 39, 330–334 (1992).
[Crossref]

EURASIP Signal Process. J. (1)

S. Chen, G. J. Gibson, C. F. N. Cowan, and P. M. Grant, “Adaptive equalisation of finite non-linear channels using multilayer perceptrons,” EURASIP Signal Process. J. 20, 107–119 (1990).
[Crossref]

Expert Syst. Appl. (1)

G. Das, P. K. Pattnaik, and S. K. Padhy, “Artificial neural network trained by particle swarm optimization for non-linear channel equalization,” Expert Syst. Appl. 41, 3491–3496 (2014).
[Crossref]

IEEE Photonics Tech. Lett. (2)

S. T. Ahmad and K. P. Kumar, “Radial basis function neural network nonlinear equalizer for 16-qam coherent optical ofdm,” IEEE Photonics Tech. Lett. 28, 2507–2510 (2016).
[Crossref]

J. Wang and J. M. Kahn, “Performance of electrical equalizers in optically amplified ook and dpsk systems,” IEEE Photonics Tech. Lett. 16, 1397–1399 (2004).
[Crossref]

IEEE Photonics Technol. Lett. (1)

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical ofdm,” IEEE Photonics Technol. Lett. 27, 387–390 (2015).
[Crossref]

IEEE Signal Process. Mag. (1)

A. C. Singer, N. R. Shanbhag, and H.-M. Bae, “Electronic dispersion compensation: An overview of optical communications systems,” IEEE Signal Process. Mag. 266, 110–130 (2008).
[Crossref]

J. Light. Technol. (2)

Y. Fan, X. Chen, X. Zhou, W. Zhou, H. Zhu, and Z. Li, “Vco clock synchronization loop combined with dispersion equalization in optical coherent receivers,” J. Light. Technol. 17, 122 (2010).

E. M. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Light. Technol. 28, 502 (2010).
[Crossref]

J. Opt. Soc. Korea (2)

J. VLSI Signal Process. (1)

T. Kim and T. Adali, “Fully complex multi-layer perceptron network for nonlinear signal processing,” J. VLSI Signal Process. 32, 29–43 (2002).
[Crossref]

Neural Comput. Appl. (1)

M. A. C. Fernandes, “Neural equalization applied to systems with bidimensional digital modulation,” Neural Comput. Appl. 25, 2057–2066 (2014).
[Crossref]

Opt. Eng. (2)

F. Xiao, B. Liu, L. Zhang, X. Xin, Q. Zhang, Q. Tian, F. Tian, Y. Wang, L. Rao, R. Ullah, and et al., “Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication,” Opt. Eng. 57, 026107 (2018).

H. Wang, W. Zhou, and J. Yu, “Pam-4 signal delivery in one radio-over-fiber system,” Opt. Eng. 56, 106107 (2017).
[Crossref]

Opt. Express (3)

Opt. Quantum Electron. (1)

G. Kaur and G. Kaur, “Application of functional link artificial neural network for mitigating nonlinear effects in coherent optical ofdm,” Opt. Quantum Electron. 49, 227 (2017).
[Crossref]

Signal Process. (3)

H. Leung and S. Haykin, “The complex backpropagation algorithm,” Signal Process. 39, 2101–2104 (1991).

G. Gibson, S. Siu, and C. Cowan, “The aplication of nonlinear structures to the reconstruction of binary signals,” Signal Process. 39, 1877–1884 (1991).

N. Benvenuto and F. Piazza, “On the complex backpropagation algorithm,” Signal Process. 40, 967–969 (1992).

Signals Syst. Comput. (1)

M. Peng, C. Nikias, and J. Proakis, “Adaptive equalization for pam and wam signals with neural networks,” Signals Syst. Comput. 1, 496–500 (1991).

Syst. Man Cybern. Part C: Appl. Rev. (1)

K. Burse, R. Yadav, and S. Shrivastava, “Channel equalization using neural networks: A review,” Syst. Man Cybern. Part C: Appl. Rev. 40, 352–357 (2010).
[Crossref]

WSEAS Trans. Commun. (1)

T. F. B. Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” WSEAS Trans. Commun. 13, 462–469 (2014).

Other (13)

C. Remmersmann, M. Westhauser, and S. Pachnicke, “Equalization of first and second order pmd in 100 gbit/s polmux transmission using optical butterfly fir filters,” in Conference on Optic Engineers (OSA2010).

F. Javidi and H. Khoshbin, “Performance of back-propagation and self organizing map neural equalizers for asymmetrically clipped optical ofdm,” in Iranian Conference on Electrical Engineering (ICEE, 2013).

M. Emmaeinna, S. Faci, A.-L. Billabert, A. Kabalan, C. Algani, and M. L. Diakité, “Performance analysis of radio-over-fiber based on phase-modulation and direct-detection for the future 5g network,” in), 2018 20th International Conference on Transparent Optical Networks (ICTON), (IEEE, 2018), pp. 1–4.

G. P. Agrawal, Fiber-Optic Communication Systems, vol. 22 of Wiley Series in Microwave and Optical Engineering (John Wiley and Sons, 2012), 4th ed.

M. Westhauser, C. Remmersmann, S. Pachnicke, and P. M. Krummrich, “Optical equalization of pmd-induced penalties in 112 gbit/s metro networks,” in Signal Processing in Photonic Communications (OSA, 2011).

T. Luo, “Digital equalization of fiber-optic transmission system impairments,” Master’s thesis, McMaster University (2011).

M. Kuschnerov, F. N. Hauske, L. Piyawanno, B. Spinnler, E. D. Schmidt, and B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” ECOC2008 (2008).

C. Cowan, “Nonlinear adaptive equalization [multilayer perceptron],”,” in Sixth International Conference on Digital Processing Signals in Communications (IET,1991), pp. 1–5.

S. S. Haykin, Communication Systems(Wiley, 2001), 4th ed.

J. Proakis, Digital Communications(McGraw-Hill Science/Engineering/Math, 2000).

J. Estaran, R. Rios-Müller, M. Mestre, F. Jorge, H. Mardoyan, A. Konczykowska, J.-Y. Dupuy, and S. Bigo, “Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate im/dd systems,” in), Proceedings of ECOC 2016 42nd European Conference on Optical Communication (VDE, 2016), pp. 1–3.

T. F. B. de Sousa and M. A. C. Fernandes, “Multilayer perceptron equalizer for optical communication systems,” in 2013 SBMO/IEEE MTTS International Microwave and Optoelectronics Conference (IMOC) (IEEE2013).
[Crossref]

T. F. B. Sousa and M. A. C. Fernandes, “Bi-dimensional neural equalizer applied to optical receiver,” in 1st BRICS Congress on Computational Inteliigence and 11th Brazilian Congress on Computational Intelligence (IEEE, 2013).

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Figures (11)

Fig. 1
Fig. 1 Simplified digital communication system model.
Fig. 2
Fig. 2 Non-linear optical channel model.
Fig. 3
Fig. 3 Adaptive equalizer scheme.
Fig. 4
Fig. 4 NE-Butterfly model.
Fig. 5
Fig. 5 Neural equalizer architecture.
Fig. 6
Fig. 6 NE-Butterfly training scheme.
Fig. 7
Fig. 7 Performance curves for 4-QAM system (without channel coding) using the optical channel model for Channel 1.
Fig. 8
Fig. 8 Performance curves for 4-QAM system (without channel coding) using the optical channel model for Channel 2.
Fig. 9
Fig. 9 Performance curves for 4-QAM system (without channel coding) using the optical channel model for Channel 3.
Fig. 10
Fig. 10 Performance curves for 4-QAM system (without channel coding) using the optical channel model for Channel 4.
Fig. 11
Fig. 11 Performance curves for 4-QAM system (without channel coding) using the optical channel model for Channel 5.

Tables (1)

Tables Icon

Table 1 Channel taps for the different channels used in the simulations.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

x ( t ) = f t ( n = a ( n ) p ( t n T s ) ) ,
p ( t ) = { 1 for  0 t < T s 0 for  t < 0 or t T s ,
H C D ( f ) = e ( j π D L f 2 λ 2 c ) ,
H P M D ( f , τ , β ) = β e ( j π f τ ) ,
h x ( t ) = F 1 ( H C D ( f ) H P M D ( f , τ x , β x ) ) = β x k = 0 N 1 ρ k δ ( t τ k τ x )
h y ( t ) = F 1 ( H C D ( f ) H P M D ( f , τ y , β y ) ) = β y k = 0 N 1 ρ k δ ( t τ k τ y )
r ( t ) = | u x ( t ) + n x ( t ) | 2 + | u y ( t ) + n y ( t ) | 2 ,
u x ( t ) = β x k = 0 N 1 ρ k x ( t τ k τ x )
u y ( t ) = β y k = 0 N 1 ρ k x ( t τ k τ y ) .
r ( t ) = | β x k = 0 N 1 ρ k x ( t τ k τ x ) + n x ( t ) | 2 + | β y k = 0 N 1 ρ k x ( t τ k τ y ) + n y ( t ) | 2 ,
a ˜ I ( n ) = a ˜ I I ( n ) + a ˜ I Q ( n )
a ˜ I I ( n ) = i = 0 K 1 ( w i 1 ( n ) ) I I tanh ( j = 0 P 1 ( w i j 0 ( n ) ) I I r I ( n j ) ) ,
a ˜ I Q ( n ) = i = 0 K 1 ( w i 1 ( n ) ) I Q tanh ( j = 0 P 1 ( w i j 0 ( n ) ) I Q r Q ( n j ) )
a ˜ Q ( n ) = a ˜ Q I ( n ) + a ˜ Q Q ( n )
a ˜ Q I ( n ) = i = 0 K 1 ( w i 1 ( n ) ) Q I tanh ( j = 0 P 1 ( w i j 0 ( n ) ) Q I r I ( n j ) ) ,
a ˜ Q Q ( n ) = i = 0 K 1 ( w i 1 ( n ) ) Q Q tanh ( j = 0 P 1 ( w i j 0 ( n ) ) Q Q r Q ( n j ) )
d m i n = 2 M 1
e I ( n ) = t r I ( n d ) a ˜ I ( n )
e Q ( n ) = t r Q ( n d ) a ˜ Q ( n ) ,
e I ( n ) = a ^ I ( n ) a ˜ I ( n )
e Q ( n ) = a ^ Q ( n ) a ˜ Q ( n ) .
h x ( t ) = β x { a δ ( t ) + b δ ( t T s ) + c δ ( t 2 T s ) + d δ ( t 3 T s ) + e δ ( t 4 T s ) + f δ ( t 5 T s ) + g δ ( t T s ) }
h y ( t ) = β y { a δ ( t ) + b δ ( t T s ) + c δ ( t 2 T s ) + d δ ( t 3 T s ) + e δ ( t 4 T s ) + f δ ( t 5 T s ) + g δ ( t T s ) } ,