Abstract

An improved digital backward propagation (DBP) is proposed to compensate inter-nonlinear effects and dispersion jointly in WDM systems based on an advanced perturbation technique (APT). A non-iterative weighted concept is presented to replace the iterative in analytical recursion expression, which can dramatically simplify the complexity and improve accuracy compared to the traditional perturbation technique (TPT). Furthermore, an analytical recursion expression of the output after backward propagation is obtained initially. Numerical simulations are executed for various parameters of the transmission system. The results indicate that the advanced perturbation technique will relax the step size requirements and reduce the oversampling factor when launch power is higher than −2 dBm. We estimate this technique will reduce computational complexity by a factor of around seven with respect to the conventional DBP.

© 2013 OSA

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References

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2012 (1)

2011 (6)

2010 (7)

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[Crossref]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed Transmission,” J. Lightwave Technol. 28(6), 939–951 (2010).
[Crossref]

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

R. Asif, C. Y. Lin, M. Holtmannspoetter, and B. Schmauss, “Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link,” Opt. Express 18(22), 22796–22807 (2010).
[Crossref] [PubMed]

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010).
[Crossref] [PubMed]

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (7)

2003 (2)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[Crossref] [PubMed]

J. Leibrich and W. Rosenkranz, “Efficient numerical simulation of multichannel WDM transmission systems limited by XPM,” IEEE Photon. Technol. Lett. 15(3), 395–397 (2003).
[Crossref]

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Adamczyk, O.

Asif, R.

Barros, D. J. F.

Bayvel, P.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[Crossref] [PubMed]

Behrens, C.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

Chen, X.

Chugtai, M. N.

Derevyanko, S. A.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[Crossref] [PubMed]

Dou, L.

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

Du, L. B.

Ellis, A. D.

Forzati, M.

Fürst, C.

Gavioli, G.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[Crossref]

Goldfarb, G.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of Fiber Impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[Crossref]

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. 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).
[Crossref] [PubMed]

Hellerbrand, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

Herath, V.

Herbst, S.

Hoffmann, S.

Holbein, L.

Holtmannspoetter, M.

Hoshida, T.

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

Ip, E.

Kahn, J. M.

Killey, R. I.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[Crossref] [PubMed]

Kim, I.

Korotkevich, A. O.

Lau, A. P.

Leibrich, J.

J. Leibrich and W. Rosenkranz, “Efficient numerical simulation of multichannel WDM transmission systems limited by XPM,” IEEE Photon. Technol. Lett. 15(3), 395–397 (2003).
[Crossref]

Li, G.

L. Zhu and G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express 20(13), 14362–14370 (2012).
[Crossref] [PubMed]

E. F. Mateo, X. Zhou, and G. Li, “Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems,” Opt. Express 19(2), 570–583 (2011).
[Crossref] [PubMed]

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
[Crossref] [PubMed]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 1(2), 144–152 (2009).
[Crossref]

E. F. Mateo and G. Li, “Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation,” Appl. Opt. 48(25), F6–F10 (2009).
[Crossref] [PubMed]

E. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express 16(20), 16124–16137 (2008).
[Crossref] [PubMed]

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of Fiber Impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[Crossref]

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. 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).
[Crossref] [PubMed]

Li, L.

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

Li, X.

Lin, C. Y.

Lin, L.

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

Lowery, A. J.

Lushnikov, P. M.

Makovejs, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

Mårtensson, J.

Mateo, E.

Mateo, E. F.

Millar, D. S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Mussolin, M.

Nakashima, H.

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

Noé, R.

Oda, S.

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

Peveling, R.

Pfau, T.

Poggiolini, P.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[Crossref]

Porrmann, M.

Rafique, D.

Rasmussen, J.

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

Rasmussen, J. C.

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

Rosenkranz, W.

J. Leibrich and W. Rosenkranz, “Efficient numerical simulation of multichannel WDM transmission systems limited by XPM,” IEEE Photon. Technol. Lett. 15(3), 395–397 (2003).
[Crossref]

Savory, S. J.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[Crossref]

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

Schmauss, B.

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Tanimura, T.

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

Tao, Z.

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

Taylor, M. G.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of Fiber Impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[Crossref]

Torrengo, E.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[Crossref]

Turitsyn, K. S.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[Crossref] [PubMed]

Turitsyn, S. K.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[Crossref] [PubMed]

Waegemans, R.

Watts, P.

Xiang, L.

Yaman, F.

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
[Crossref] [PubMed]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 1(2), 144–152 (2009).
[Crossref]

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. 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).
[Crossref] [PubMed]

Yan, M.

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

Yan, W.

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

Yurkevich, I. V.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[Crossref] [PubMed]

Zhang, X. P.

Zhao, J.

Zhou, X.

Zhu, L.

Appl. Opt. (1)

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

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[Crossref]

IEEE Photon. J. (2)

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 1(2), 144–152 (2009).
[Crossref]

IEEE Photon. Technol. Lett. (3)

J. Leibrich and W. Rosenkranz, “Efficient numerical simulation of multichannel WDM transmission systems limited by XPM,” IEEE Photon. Technol. Lett. 15(3), 395–397 (2003).
[Crossref]

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of Fiber Impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[Crossref]

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[Crossref]

J. Lightwave Technol. (3)

Nature (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Opt. Express (14)

E. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express 16(20), 16124–16137 (2008).
[Crossref] [PubMed]

T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noé, “Coherent optical communication: towards realtime systems at 40 Gbit/s and beyond,” Opt. Express 16(2), 866–872 (2008).
[Crossref] [PubMed]

E. Ip, A. P. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent Detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008).
[Crossref] [PubMed]

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010).
[Crossref] [PubMed]

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[Crossref] [PubMed]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. 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).
[Crossref] [PubMed]

R. Asif, C. Y. Lin, M. Holtmannspoetter, and B. Schmauss, “Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link,” Opt. Express 18(22), 22796–22807 (2010).
[Crossref] [PubMed]

D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011).
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D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011).
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L. Zhu and G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express 20(13), 14362–14370 (2012).
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D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express 19(10), 9453–9460 (2011).
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E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
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E. F. Mateo, X. Zhou, and G. Li, “Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems,” Opt. Express 19(2), 570–583 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[Crossref] [PubMed]

Other (8)

E. Ip and J. M. Kahn, “Nonlinear impairment compensation using backpropagation,” in Optical Fibre, New Developments (In-Tech, to be published).

R. Asif, C. Y. Lin, and B. Schmauss, Digital Backward Propagation: A Technique to Compensate Fiber Dispersion and Nonlinear Impairments (InTech-Book Publisher 2011).

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC (2011).

T. Hoshida, L. Dou, T. Tanimura, W. Yan, S. Oda, L. Li, H. Nakashima, M. Yan, Z. Tao, and J. C. Rasmussen, “Digital nonlinear compensation techniques for high-speed DWDM transmission systems,” in Proc.ECOC (2012).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

B. Schmauss, R. Asif, and C.-Y. Lin, “Recent advances in digital backward propagation algorithm for coherent transmission systems with higher order modulation formats,” in Proc. SPIE (2012)

L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. Rasmussen, “Implementation efficient non-linear equalizer based on correlated digital back-propagation,” in Proc. OFC (2011).

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proc. ECOC’ 11, Tu.3.A. (2011)

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Figures (5)

Fig. 1
Fig. 1

Block diagram for the implementation of the l th section using the develop perturbation technique.

Fig. 2
Fig. 2

Scheme of the WDM transmission system with coherent receiver.

Fig. 3
Fig. 3

(a) Q-factors as a function of step size for APT, C-DBP and TPT, (b) Q-factors versus a long fiber transmission distance for APT, C-DBP, TPT and only chromatic dispersion compensation with different step size.

Fig. 4
Fig. 4

Q-factors versus launch power per channel for both methods for γ = 1.46 and 3.5 (W.km)−1

Fig. 5
Fig. 5

(a) Q-factors versus launch power per channel for APT and C-DBP with oversampling factors of 2 and 4, (b) Q penalty for reduced oversampling factor for APT and C-DBP and (c) Q factor difference between APT and C-DBP for oversampling factors of 2 and 4.

Equations (12)

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E k z i β 2 2 2 E k t 2 + β 3 6 3 E k t 3 +iγ( | E k | 2 +2 qk | E q | 2 ) E k =G(z) E k ,
E ^ k (l) (ω,z)=exp( D ^ )[ E ^ k (l1) +iγ z z+h N L k (l1) (ω, z ) d z ],
D ^ = z z+h [G( z ) i β 2 ω 2 2 + i β 3 ω 3 6 ]d z ,
N L k (l1) =[( | φ k (l1) | 2 +2 qk | φ q (l1) | 2 ) φ k (l1) ]exp( D ^ ),
φ k (l1) = 1 [ E ^ k (l1) exp( D ^ )].
N L k (l1) (ω,z)=[ | φ k (l1) | 2 φ k (l1) ]exp( D ^ )[2 qk | φ q (l1) | 2 ] e i d qk zω [ φ k (l1) ]exp( D ^ ),
E ^ k out (ω,z)= E ^ k (0) exp(M D ^ )+iγ{exp(M D ^ ) z z+h N L k (0) (ω, z ) d z +exp((M1) D ^ ) z z+h N L k (1) (ω, z ) d z ++exp( D ^ ) z z+h N L k (M1) (ω, z ) )d z },
E ^ k (l) (ω,z)=exp( D ^ ){ E ^ k (l1) +iγh[ N L k (l1) (ω,z)+ N L k (l1) (ω,z+h) 2 ]}.
E ^ k (l) (ω,z)=exp( D ^ )[ E ^ k (l1) +iγh N L k (l1) (ω,z+εh)],
E ^ k out (ω,z)= E ^ k (0) exp(M D ^ )+iγh[exp(M D ^ ) N L k (0) (ω,εh) +exp((M1) D ^ ) N L k (1) (ω,εh)++exp( D ^ ) N L k (M1) (ω,εh)].
Nmu l DPT = L h DPT [2(s+p) log 2 (s+p)+3(s+p)+s]/s,
Nmu l CDBP = L h CDBP [2(s+p) log 2 (s+p)+2(s+p)+8s]/s,

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