## Nonlinearity compensation using dispersion-folded digital backward propagation |

Optics Express, Vol. 20, Issue 13, pp. 14362-14370 (2012)

http://dx.doi.org/10.1364/OE.20.014362

Acrobat PDF (979 KB)

### Abstract

A computationally efficient dispersion-folded (D-folded) digital backward propagation (DBP) method for nonlinearity compensation of dispersion-managed fiber links is proposed. At the optimum power level of long-haul fiber transmission, the optical waveform evolution along the fiber is dominated by the chromatic dispersion. The optical waveform and, consequently, the nonlinear behavior of the optical signal repeat at locations of identical accumulated dispersion. Hence the DBP steps can be folded according to the accumulated dispersion. Experimental results show that for 6,084 km single channel transmission, the D-folded DBP method reduces the computation by a factor of 43 with negligible penalty in performance. Simulation of inter-channel nonlinearity compensation for 13,000 km wavelength-division multiplexing (WDM) transmission shows that the D-folded DBP method can reduce the computation by a factor of 37.

© 2012 OSA

## 1. Introduction

2. 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]

3. B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. **5**(10), 1250–1253 (1993). [CrossRef]

4. K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep. **3**(5), 292–339 (2006). [CrossRef]

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

6. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express **15**(5), 2120–2126 (2007). [CrossRef] [PubMed]

8. E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Express **19**(14), 13179–13184 (2011). [CrossRef] [PubMed]

9. J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature **411**(6841), 1007–1010 (2001). [CrossRef] [PubMed]

12. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. **28**(4), 662–701 (2010). [CrossRef]

14. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. **22**(3), 779–783 (2004). [CrossRef]

15. L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett. **22**(5), 320–322 (2010). [CrossRef]

16. K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. **18**(2), 403–405 (2006). [CrossRef]

19. 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]

20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. **21**(1), 61–68 (2003). [CrossRef]

20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. **21**(1), 61–68 (2003). [CrossRef]

28. L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett. **21**(5), 292–294 (2009). [CrossRef]

20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. **21**(1), 61–68 (2003). [CrossRef]

22. E. F. 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]

23. 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]

**21**(1), 61–68 (2003). [CrossRef]

24. Q. Zhang and M. I. Hayee, “Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems,” J. Lightwave Technol. **26**(2), 302–316 (2008). [CrossRef]

25. 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]

27. L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express **19**(7), 5953–5959 (2011). [CrossRef] [PubMed]

29. J. K. Fischer, C.-A. Bunge, and K. Petermann, “Equivalent single-span model for dispersion-managed fiber-optic transmission systems,” J. Lightwave Technol. **27**(16), 3425–3432 (2009). [CrossRef]

30. C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express **17**(6), 4815–4823 (2009). [CrossRef] [PubMed]

31. V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. **20**(17), 1473–1475 (2008). [CrossRef]

## 2. Dispersion-folded DBP method

33. 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]

27. L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express **19**(7), 5953–5959 (2011). [CrossRef] [PubMed]

## 3. Experimental results

^{23}-1 pseudo random bit sequence (PRBS). The single-polarization optical signal is launched into a recirculating loop controlled by two acousto-optic modulators (AOMs). The recirculating loop consists of two types of fibers: 82.6 km standard single mode fiber (SSMF) with 0.2 dB/km loss and 83 µm

^{2}effective area, and 11 km DCF with 0.46 dB/km loss and 20 µm

^{2}effective area. By optimizing the performance in the training experiments of EDC, the dispersion of the SSMF and the DCF are determined as 17.06 ps/nm/km and −123.35 ps/nm/km, respectively. The residual dispersion per span (RDPS) is 53 ps/nm. Two erbium doped fiber amplifiers (EDFAs) are used to completely compensate for the loss in the loop. An optical bandpass filter (BPF) is used to suppress the EDFA noise. At the receiver, the signal is mixed with the local oscillator from another external cavity laser in a 90° hybrid after the polarizations are aligned with a polarization controller (PC). The I and Q components of the received signal are detected using two photo-detectors (PDs). A real-time oscilloscope is used for analog-to-digital conversion and data acquisition at 40 Gsamples/s. The DSP is performed off-line with Matlab. Note that for realistic terrestrial systems, the parameters of the fiber spans may not be available with good accuracy. Attempts are being made at estimating the link parameters for conventional DBP [34]. Estimation of link parameters for D-folded DBP needs further investigation.

24. Q. Zhang and M. I. Hayee, “Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems,” J. Lightwave Technol. **26**(2), 302–316 (2008). [CrossRef]

**21**(1), 61–68 (2003). [CrossRef]

## 4. Simulation results

^{23}-1 PRBS sequences. Each PRBS generator is assigned with a unique random bit seed for de-correlation. The linewidth of the lasers is 100 kHz. The dispersion managed fiber link consists of 260 spans of the OFS UltraWave SLA/IDF Ocean Fiber combination. In each 50 km span, the SLA fiber with a large effective area is used near the EDFA, followed by the IDF fiber with inverse dispersion and dispersion slope. The loss, dispersion, relative dispersion slope and effective area of the SLA fiber are 0.188 dB/km, 19.5 ps/nm/km, 0.003/nm and 106 μm

^{2}, respectively. The corresponding parameters for the IDF fiber are 0.23 dB/km, −44 ps/nm/km, 0.003/nm and 31 μm

^{2}, respectively. The RDPS is determined by the proportion of SLA fiber to IDF fiber in each span. The noise figure of the EDFAs is 4.5 dB. After de-multiplexing and coherent detection, 8192 symbols from each channel are saved at a sampling rate of 56 Gsamples/s. Then the DSP is performed with Matlab.

35. L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. **46**(16), 1140–1141 (2010). [CrossRef]

23. 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]

## 5. Conclusion

## Appendix: calculation of the computational load

28. L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett. **21**(5), 292–294 (2009). [CrossRef]

**21**(1), 61–68 (2003). [CrossRef]

^{10}which is practical for the current electronic technology. By using 11 overlap-add filtering operators with

## References and links

1. | G. P. Agrawal, |

2. | P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature |

3. | B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. |

4. | K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep. |

5. | E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express |

6. | S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express |

7. | H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express |

8. | E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Express |

9. | J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature |

10. | E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightwave Technol. |

11. | A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. |

12. | R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. |

13. | L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise statistics monitoring,” in Proc. ECOC’09, Paper P3.16 (2009). |

14. | K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. |

15. | L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett. |

16. | K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. |

17. | X. Li, X. Chen, G. Goldfarb, E. F. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express |

18. | E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol. |

19. | 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. |

20. | O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. |

21. | S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver.” in Proc. OFC’09, Paper OThR6 (2009). |

22. | E. F. 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 |

23. | 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 |

24. | Q. Zhang and M. I. Hayee, “Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems,” J. Lightwave Technol. |

25. | 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 |

26. | 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 |

27. | L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express |

28. | L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett. |

29. | J. K. Fischer, C.-A. Bunge, and K. Petermann, “Equivalent single-span model for dispersion-managed fiber-optic transmission systems,” J. Lightwave Technol. |

30. | C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express |

31. | V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. |

32. | 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). |

33. | J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. |

34. | T. Tanimura, T. Hoshida, T. Tanaka, L. Li, S. Oda, H. Nakashima, Z. Tao, and J. C. Rasmussen, “Semi-blind nonlinear equalization in coherent multi-span transmission system with inhomogeneous span parameters,” in Proc. OFC’10, OMR6 (2010). |

35. | L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

(190.4370) Nonlinear optics : Nonlinear optics, fibers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 27, 2012

Revised Manuscript: May 18, 2012

Manuscript Accepted: May 25, 2012

Published: June 12, 2012

**Citation**

Likai Zhu and Guifang Li, "Nonlinearity compensation using dispersion-folded digital backward propagation," Opt. Express **20**, 14362-14370 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14362

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### References

- G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Elsevier, 2001).
- P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001). [CrossRef] [PubMed]
- B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett.5(10), 1250–1253 (1993). [CrossRef]
- K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006). [CrossRef]
- E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008). [CrossRef] [PubMed]
- S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007). [CrossRef] [PubMed]
- H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express16(2), 873–879 (2008). [CrossRef] [PubMed]
- E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Express19(14), 13179–13184 (2011). [CrossRef] [PubMed]
- J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature411(6841), 1007–1010 (2001). [CrossRef] [PubMed]
- E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightwave Technol.24(12), 4697–4710 (2006). [CrossRef]
- A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol.28(4), 423–433 (2010). [CrossRef]
- R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol.28(4), 662–701 (2010). [CrossRef]
- L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise statistics monitoring,” in Proc. ECOC’09, Paper P3.16 (2009).
- K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol.22(3), 779–783 (2004). [CrossRef]
- L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett.22(5), 320–322 (2010). [CrossRef]
- K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006). [CrossRef]
- X. Li, X. Chen, G. Goldfarb, E. F. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16(2), 880–888 (2008). [CrossRef] [PubMed]
- E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol.28(4), 502–519 (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]
- O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol.21(1), 61–68 (2003). [CrossRef]
- S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver.” in Proc. OFC’09, Paper OThR6 (2009).
- E. F. 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. Express16(20), 16124–16137 (2008). [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. Express18(14), 15144–15154 (2010). [CrossRef] [PubMed]
- Q. Zhang and M. I. Hayee, “Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems,” J. Lightwave Technol.26(2), 302–316 (2008). [CrossRef]
- L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express18(16), 17075–17088 (2010). [CrossRef] [PubMed]
- 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. Express19(10), 9453–9460 (2011). [CrossRef] [PubMed]
- L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express19(7), 5953–5959 (2011). [CrossRef] [PubMed]
- L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett.21(5), 292–294 (2009). [CrossRef]
- J. K. Fischer, C.-A. Bunge, and K. Petermann, “Equivalent single-span model for dispersion-managed fiber-optic transmission systems,” J. Lightwave Technol.27(16), 3425–3432 (2009). [CrossRef]
- C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17(6), 4815–4823 (2009). [CrossRef] [PubMed]
- V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008). [CrossRef]
- 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).
- 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]
- T. Tanimura, T. Hoshida, T. Tanaka, L. Li, S. Oda, H. Nakashima, Z. Tao, and J. C. Rasmussen, “Semi-blind nonlinear equalization in coherent multi-span transmission system with inhomogeneous span parameters,” in Proc. OFC’10, OMR6 (2010).
- L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett.46(16), 1140–1141 (2010). [CrossRef]

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