Abstract

We introduce a new system configuration to reduce the nonlinear phase noise (NLPN) by splitting the digital back propagation (DBP) between transmitter and receiver, asymmetrically, along with using mid-line optical phase conjugation (OPC). Our analytical results show that the variance of NLPN reduces by a factor of 16 compared to the standard configuration which is the dispersion uncompensated fiber optic link with full DBP at the receiver, i.e., the back propagation for the fiber spans is done entirely at the receiver. Numerical simulations show the same trend as predicted by the analytical model, and show about 2.6 dB and 2 dB improvement in Q-factor, for single channel and 5-channel WDM systems, respectively.

© 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. G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).
  2. S. Kumar and M. J. Deen, Fiber Optic Communications: Fundamentals and Applications (John Wiley & Sons, 2014).
    [Crossref]
  3. R.-J. Essiambre, G. Raybon, and B. Mikkelsen, “Pseudo-Linear Transmission Of High-Speed TDM Signals: 40 And 160 Gb/s,” in Optical Fiber Telecommunications IV-B, 4th ed., I. P. Kaminow and T. Li, eds. (Academic, 2002).
    [Crossref]
  4. S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, “Intrachannel nonlinear penalties in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8(3), 626–631 (2002).
    [Crossref]
  5. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15(23), 1351–1353 (1990).
    [Crossref] [PubMed]
  6. R.-J. Essiambre and P. J. Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” in 2005 European Conference on Optical Communication (IEEE, 2005), pp. 191–192.
  7. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [Crossref]
  8. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, Fatih Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008).
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    [Crossref]
  10. K. Ho, “Probability density of nonlinear phase noise,” J. Opt. Soc. Am. B: Opt. Phys. 20(9), 1875–1879 (2003).
    [Crossref]
  11. A. Mecozzi, “Probability density functions of the nonlinear phase noise,” Opt. Lett. 29(7), 673–675 (2004).
    [Crossref] [PubMed]
  12. S. Kumar, “Effect of dispersion on nonlinear phase noise in optical transmission systems,” Opt. Lett. 30(24), 3278–3280 (2005).
    [Crossref]
  13. S. Kumar, “Analysis of nonlinear phase noise in coherent fiber-optic systems based on phase shift keying,” J. Lightwave Technol. 27(21), 4722–4733 (2009).
    [Crossref]
  14. P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
    [Crossref]
  15. A. Demir, “Nonlinear phase noise in optical fiber communication systems,” J. Lightwave Technol. 25(8), 2002–2032 (2007).
    [Crossref]
  16. N. Ekanayake and H. Herath, “Effect of nonlinear phase noise on the performance of M-ary PSK signals in optical fiber links,” J. Lightwave Technol. 31(3), 447–454 (2013).
    [Crossref]
  17. Z. Xu, P. Y. Kam, and C. Yu, “Adaptive maximum likelihood sequence detection for QPSK coherent optical communication system,” IEEE Photonics Technol. Lett. 26(6), 583–586 (2014).
    [Crossref]
  18. X. Zhu and S. Kumar, “Nonlinear phase noise in coherent optical OFDM transmission systems,” Opt. Express 18(7), 7347–7360 (2010).
    [Crossref] [PubMed]
  19. C. Pan, H. Bülow, W. Idler, L. Schmalen, and F. Kschischang, “Optical nonlinear phase noise compensation for 9 × 32 -Gbaud PolDM-16 QAM transmission using a code-aided expectation-maximization algorithm,” J. Lightwave Technol. 33(17), 3679–3686 (2015).
    [Crossref]
  20. D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.
  21. D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
    [Crossref]
  22. D. Semrau, D. Lavery, L. Galdino, R. I. Killey, and P. Bayvel, “The impact of transceiver noise on digital nonlinearity compensation,” J. Lightwave Technol. 36(3), 695–702 (2018).
    [Crossref]
  23. A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4(2), 52–54 (1979).
    [Crossref] [PubMed]
  24. S. Watanabe, G. Ishikawa, T. Naito, and T. Chikama, “Generation of optical phase-conjugate waves and compensation for pulse shape distortion in a single-mode fiber,” J. Lightwave Technol. 12(12), 2139–2146(1994).
    [Crossref]
  25. S. Kumar and L. Liu, “Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems,” Opt. Express 15(5), 2166–2177 (2007).
    [Crossref] [PubMed]
  26. K. P. Ho, “Cross-Phase Modulation-Induced Nonlinear Phase Noise for Quadriphase-Shift-Keying Signals,” in Impact of Nonlinearities on Fiber Optic Communications, S. Kumar, ed. (Springer-Verlag, 2011).
    [Crossref]
  27. P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
    [Crossref]
  28. C. McKinstrie, S. Radic, and C. Xie, “Reduction of soliton phase jitter by in-line phase conjugation,” Opt. Lett. 28(17), 1519–1521 (2003).
    [Crossref] [PubMed]
  29. L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightwave Technol. 32(10), 1999–2002 (2014).
    [Crossref]
  30. R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.
  31. L. Galdino, D. Semrau, D. Lavery, G. Saavedra, C. B. Czegledi, E. Agrell, R. I. Killey, and P. Bayvel, “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express 25(4), 4564–4578 (2017).
    [Crossref] [PubMed]

2018 (1)

2017 (1)

2016 (1)

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

2015 (1)

2014 (2)

Z. Xu, P. Y. Kam, and C. Yu, “Adaptive maximum likelihood sequence detection for QPSK coherent optical communication system,” IEEE Photonics Technol. Lett. 26(6), 583–586 (2014).
[Crossref]

L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightwave Technol. 32(10), 1999–2002 (2014).
[Crossref]

2013 (1)

2010 (2)

X. Zhu and S. Kumar, “Nonlinear phase noise in coherent optical OFDM transmission systems,” Opt. Express 18(7), 7347–7360 (2010).
[Crossref] [PubMed]

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

2009 (1)

2008 (2)

2007 (2)

2005 (1)

2004 (1)

2003 (2)

K. Ho, “Probability density of nonlinear phase noise,” J. Opt. Soc. Am. B: Opt. Phys. 20(9), 1875–1879 (2003).
[Crossref]

C. McKinstrie, S. Radic, and C. Xie, “Reduction of soliton phase jitter by in-line phase conjugation,” Opt. Lett. 28(17), 1519–1521 (2003).
[Crossref] [PubMed]

2002 (1)

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, “Intrachannel nonlinear penalties in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8(3), 626–631 (2002).
[Crossref]

1996 (1)

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

1994 (2)

S. Watanabe, G. Ishikawa, T. Naito, and T. Chikama, “Generation of optical phase-conjugate waves and compensation for pulse shape distortion in a single-mode fiber,” J. Lightwave Technol. 12(12), 2139–2146(1994).
[Crossref]

A. Mecozzi, “Limits to the long haul coherent transmission set by the Kerr nonlinearity and noise of in-line amplifiers,” J. Lightwave Technol. 12(11), 1993–2000 (1994).
[Crossref]

1990 (1)

1979 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

Agrell, E.

Alvarado, A.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Bayvel, P.

D. Semrau, D. Lavery, L. Galdino, R. I. Killey, and P. Bayvel, “The impact of transceiver noise on digital nonlinearity compensation,” J. Lightwave Technol. 36(3), 695–702 (2018).
[Crossref]

L. Galdino, D. Semrau, D. Lavery, G. Saavedra, C. B. Czegledi, E. Agrell, R. I. Killey, and P. Bayvel, “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express 25(4), 4564–4578 (2017).
[Crossref] [PubMed]

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Bülow, H.

Chen, X.

Chikama, T.

S. Watanabe, G. Ishikawa, T. Naito, and T. Chikama, “Generation of optical phase-conjugate waves and compensation for pulse shape distortion in a single-mode fiber,” J. Lightwave Technol. 12(12), 2139–2146(1994).
[Crossref]

Chowdhury, D. Q.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, “Intrachannel nonlinear penalties in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8(3), 626–631 (2002).
[Crossref]

Cristiani, I.

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

Cui, Y.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Czegledi, C. B.

Deen, M. J.

S. Kumar and M. J. Deen, Fiber Optic Communications: Fundamentals and Applications (John Wiley & Sons, 2014).
[Crossref]

Degiorgio, V.

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

Demir, A.

Ekanayake, N.

Essiambre, R.-J.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, “Pseudo-Linear Transmission Of High-Speed TDM Signals: 40 And 160 Gb/s,” in Optical Fiber Telecommunications IV-B, 4th ed., I. P. Kaminow and T. Li, eds. (Academic, 2002).
[Crossref]

R.-J. Essiambre and P. J. Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” in 2005 European Conference on Optical Communication (IEEE, 2005), pp. 191–192.

Fekete, D.

Galdino, L.

Goldfarb, G.

Gordon, J. P.

Herath, H.

Ho, K.

K. Ho, “Probability density of nonlinear phase noise,” J. Opt. Soc. Am. B: Opt. Phys. 20(9), 1875–1879 (2003).
[Crossref]

Ho, K. P.

K. P. Ho, “Cross-Phase Modulation-Induced Nonlinear Phase Noise for Quadriphase-Shift-Keying Signals,” in Impact of Nonlinearities on Fiber Optic Communications, S. Kumar, ed. (Springer-Verlag, 2011).
[Crossref]

Idler, W.

Ip, E.

Ishikawa, G.

S. Watanabe, G. Ishikawa, T. Naito, and T. Chikama, “Generation of optical phase-conjugate waves and compensation for pulse shape distortion in a single-mode fiber,” J. Lightwave Technol. 12(12), 2139–2146(1994).
[Crossref]

Ives, D.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

Kahn, J. M.

Kam, P. Y.

Z. Xu, P. Y. Kam, and C. Yu, “Adaptive maximum likelihood sequence detection for QPSK coherent optical communication system,” IEEE Photonics Technol. Lett. 26(6), 583–586 (2014).
[Crossref]

Killey, R.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Killey, R. I.

Kim, I.

Kschischang, F.

Kschischang, F. R.

Kumar, S.

Lavery, D.

D. Semrau, D. Lavery, L. Galdino, R. I. Killey, and P. Bayvel, “The impact of transceiver noise on digital nonlinearity compensation,” J. Lightwave Technol. 36(3), 695–702 (2018).
[Crossref]

L. Galdino, D. Semrau, D. Lavery, G. Saavedra, C. B. Czegledi, E. Agrell, R. I. Killey, and P. Bayvel, “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express 25(4), 4564–4578 (2017).
[Crossref] [PubMed]

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Li, G.

Li, X.

Li, Z.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Liga, G.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

Liu, J.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Liu, L.

Maher, R.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Marazzi, L.

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

Martinelli, M.

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

Mateo, E.

Mauro, J. C.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, “Intrachannel nonlinear penalties in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8(3), 626–631 (2002).
[Crossref]

McKinstrie, C.

Mecozzi, A.

A. Mecozzi, “Probability density functions of the nonlinear phase noise,” Opt. Lett. 29(7), 673–675 (2004).
[Crossref] [PubMed]

A. Mecozzi, “Limits to the long haul coherent transmission set by the Kerr nonlinearity and noise of in-line amplifiers,” J. Lightwave Technol. 12(11), 1993–2000 (1994).
[Crossref]

Menyak, C. R.

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Mikkelsen, B.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, “Pseudo-Linear Transmission Of High-Speed TDM Signals: 40 And 160 Gb/s,” in Optical Fiber Telecommunications IV-B, 4th ed., I. P. Kaminow and T. Li, eds. (Academic, 2002).
[Crossref]

Millar, D.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Minzioni, P.

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

Mollenauer, L. F.

Naito, T.

S. Watanabe, G. Ishikawa, T. Naito, and T. Chikama, “Generation of optical phase-conjugate waves and compensation for pulse shape distortion in a single-mode fiber,” J. Lightwave Technol. 12(12), 2139–2146(1994).
[Crossref]

Pan, C.

Parsons, K.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th4D.5.

Pepper, D. M.

Pusino, V.

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

Radic, S.

Raghavan, S.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, “Intrachannel nonlinear penalties in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8(3), 626–631 (2002).
[Crossref]

Raybon, G.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, “Pseudo-Linear Transmission Of High-Speed TDM Signals: 40 And 160 Gb/s,” in Optical Fiber Telecommunications IV-B, 4th ed., I. P. Kaminow and T. Li, eds. (Academic, 2002).
[Crossref]

Saavedra, G.

Savory, S. J.

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

Schmalen, L.

Semrau, D.

Wai, P. K. A.

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Wang, D.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Wang, H.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Watanabe, S.

S. Watanabe, G. Ishikawa, T. Naito, and T. Chikama, “Generation of optical phase-conjugate waves and compensation for pulse shape distortion in a single-mode fiber,” J. Lightwave Technol. 12(12), 2139–2146(1994).
[Crossref]

Winzer, P. J.

R.-J. Essiambre and P. J. Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” in 2005 European Conference on Optical Communication (IEEE, 2005), pp. 191–192.

Xie, C.

Xu, Z.

Z. Xu, P. Y. Kam, and C. Yu, “Adaptive maximum likelihood sequence detection for QPSK coherent optical communication system,” IEEE Photonics Technol. Lett. 26(6), 583–586 (2014).
[Crossref]

Yaman, Fatih

Yang, Y.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Yariv, A.

Yu, C.

Z. Xu, P. Y. Kam, and C. Yu, “Adaptive maximum likelihood sequence detection for QPSK coherent optical communication system,” IEEE Photonics Technol. Lett. 26(6), 583–586 (2014).
[Crossref]

Zhang, L. M.

Zhang, M.

D. Wang, M. Zhang, Z. Li, Y. Cui, J. Liu, Y. Yang, and H. Wang, “Nonlinear decision boundary created by a machine learning-based classifier to mitigate nonlinear phase noise,” in 2015 European Conference on Optical Communication (IEEE, 2015), pp. 1–3.

Zhu, X.

IEEE J. Sel. Top. Quantum Electron. (1)

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, “Intrachannel nonlinear penalties in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8(3), 626–631 (2002).
[Crossref]

IEEE Photonics J. (1)

P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, and V. Degiorgio, “Study of the Gordon-Mollenauer effect and of the optical-phase-conjugation compensation method in phase-modulated optical communication systems,” IEEE Photonics J. 2(3), 284–291 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (2)

Z. Xu, P. Y. Kam, and C. Yu, “Adaptive maximum likelihood sequence detection for QPSK coherent optical communication system,” IEEE Photonics Technol. Lett. 26(6), 583–586 (2014).
[Crossref]

D. Lavery, D. Ives, G. Liga, A. Alvarado, S. J. Savory, and P. Bayvel, “The benefit of split nonlinearity compensation for single-channel optical fiber communications,” IEEE Photonics Technol. Lett. 28(617), 1803–1806 (2016).
[Crossref]

J. Lightwave Technol. (10)

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Figures (11)

Fig. 1
Fig. 1 Close-up representation of a fiber-optic communication link. TF= Transmission fiber.
Fig. 2
Fig. 2 Scheme 1: Full DBP at the receiver. The standard configuration. TF stands for transmission fiber, and VF stands for the virtual fiber.
Fig. 3
Fig. 3 Scheme 2: DBP split between transmitter and receiver. TF = transmission fiber, VF = virtual fiber.
Fig. 4
Fig. 4 Scheme 3: Full DBP at the receiver with OPC set-up. OPC = optical phase conjugation, DPC = digital phase conjugation, TF = transmission fiber.
Fig. 5
Fig. 5 Noise source located at mL has an image at point (Nm)L, from which the distance to the end of the line is mL.
Fig. 6
Fig. 6 Scheme 4: Fiber optic system with a mid-point OPC and asymmetric DBP. OPC = optical phase conjugation, DPC = digital phase conjugation, TF = transmission fiber.
Fig. 7
Fig. 7 Multiplication factor profile. Multiplication factor M(m) is the strength of NLPN originated at the point mL. N = 120.
Fig. 8
Fig. 8 Q-factor performance comparison of the four schemes, for single channel systems.
Fig. 9
Fig. 9 Maximum achievable reach for single channel systems. The forward error correction (FEC) limit is 4.7 × 10−3, (i.e. Q = 8.29 dB) [29].
Fig. 10
Fig. 10 Q-factor performance comparison of the four schemes, for WDM system with 5 channels.
Fig. 11
Fig. 11 Maximum achievable reach for 5 channel WDM systems. The forward error correction (FEC) limit is 4.7 × 10−3, (i.e. Q = 8.29 dB) [29].

Tables (1)

Tables Icon

Table 1 Reach decrease in WDM systems compared to single channel case.

Equations (31)

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q ( 0 , t ) = A f ( t ) ,
q ( L + , t ) = A f ( t ) e j γ | f ( t ) | 2 L e f f A 2 + n 1 ( t ) ,
n 1 ( t ) = δ A 1 f ( t ) e j θ n 1 ( t ) .
q ( L + , t ) = ( A + δ A 1 ) f ( t ) e j γ | f ( t ) | 2 L e f f A 2 + j θ n 1 ( t ) ,
q ( 2 L , t ) = ( A + δ A 1 ) f ( t ) e α L / 2 + j θ n 1 ( t ) e j γ | f ( t ) | 2 [ A 2 L e f f + ( A + δ A 1 ) 2 L e f f ] .
q ( 2 L , t ) ( A + δ A 1 ) f ( t ) e α L / 2 + j θ n 1 ( t ) e j γ | f ( t ) | 2 L e f f [ 2 A 2 + 2 A δ A 1 ] .
q ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) + j K ( t ) [ N A 2 + 2 A m = 1 N ( N m ) δ A m ] ,
θ n ( t ) = i = 1 N θ n i ( t ) ,
K ( t ) = γ | f ( t ) | 2 L e f f .
q b ( L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) + j K ( t ) [ ( N 1 ) A 2 + 2 A m = 1 N ( N m 1 ) δ A m ] .
q b ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) j 2 A K ( t ) ( m = 1 N m δ A m ) .
δ ϕ N L 1 = 2 A K ( t ) ( m = 1 N M ( m ) δ A m ) .
σ N L 1 2 = δ ϕ N L 1 2 = ( 2 A K ( t ) ) 2 δ A 2 ( m = 1 N m 2 ) ,
σ N L 1 2 ( 2 A K ( t ) ) 2 N 3 .
q b ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j δ ϕ N L 2 ( t ) + j θ n ( t ) ,
δ ϕ N L 2 ( t ) = 2 A K ( t ) m = 1 N M ( m ) δ A m ,
M ( m ) = N 2 m .
σ N L 2 2 ( 2 A K ( t ) ) 2 ( N 3 4 ) .
q ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) + j 2 A K ( t ) [ m = 1 N 2 m δ A m + m = N 2 + 1 N ( N m ) δ A m ] .
q b ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) + δ ϕ N L 3 ( t ) ,
δ ϕ N L 3 = 2 A K ( t ) [ m = 1 N M ( m ) δ A m ] ,
M ( m ) = { m if 1 m N 2 m N . if N 2 + 1 m N
σ N L 3 2 ( 2 A K ( t ) ) 2 ( N 3 4 ) .
q ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) + j K ( t ) A 2 X N + j 2 A K ( t ) [ m = 1 N 2 m δ A m + m = N 2 + 1 N ( N m ) δ A m ] .
q b ( N L + , t ) = ( A + m = 1 N δ A m ) f ( t ) e j θ n ( t ) + δ ϕ N L 4 ( t ) ,
δ ϕ N L 4 = 2 A K ( t ) [ m = 1 N M ( m ) δ A m ] ,
M ( m ) = { N X m if 1 m N 2 m N ( 1 X ) . if N 2 + 1 m N
σ N L 4 2 ( X ) = ( 2 A K ( t ) ) 2 δ A 2 [ m = 1 N M 2 ( m ) ] ,
δ A 2 = δ A i 2 ,   i = 1 , 2 , , N .
σ N L 4 2 ( 2 A K ( t ) ) 2 ( N 3 16 ) .
Q = 20 l o g 10 ( 2 e r f c i n v [ 2. B E R ] ) ,

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