## Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization |

Optics Express, Vol. 19, Issue 8, pp. 7756-7768 (2011)

http://dx.doi.org/10.1364/OE.19.007756

Acrobat PDF (1526 KB)

### Abstract

We present a novel investigation on the enhancement of phase noise in coherent optical transmission system due to electronic chromatic dispersion compensation. Two types of equalizers, including a time domain fiber dispersion finite impulse response (FD-FIR) filter and a frequency domain blind look-up (BLU) filter are applied to mitigate the chromatic dispersion in a 112-Gbit/s polarization division multiplexed quadrature phase shift keying (PDM-QPSK) transmission system. The bit-error-rate (BER) floor in phase estimation using an optimized one-tap normalized least-mean-square (NLMS) filter, and considering the equalization enhanced phase noise (EEPN) is evaluated analytically including the correlation effects. The numerical simulations are implemented and compared with the performance of differential QPSK demodulation system.

© 2011 OSA

## 1. Introduction

1. P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. **21**(12), 1862–1879 (1985). [CrossRef]

4. H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. Lightwave Technol. **26**(1), 158–167 (2008). [CrossRef]

4. H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. Lightwave Technol. **26**(1), 158–167 (2008). [CrossRef]

10. E. M. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol. **28**(4), 502–519 (2010). [CrossRef]

9. 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]

13. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express **17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

14. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express **16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

21. S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in *Proceeding of IEEE European Conference on Optical Communication* (Torino, Italy, 2010), paper Mo.1.C.2.

14. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express **16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

17. K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett. **36**(4), 585–587 (2011). [CrossRef] [PubMed]

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

20. I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express **18**(15), 16273–16278 (2010). [CrossRef] [PubMed]

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

25. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. **27**(16), 3721–3728 (2009). [CrossRef]

13. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express **17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

30. E. Vanin and G. Jacobsen, “Analytical estimation of laser phase noise induced BER floor in coherent receiver with digital signal processing,” Opt. Express **18**(5), 4246–4259 (2010). [CrossRef] [PubMed]

## 2. Principle of equalization enhanced phase noise

14. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express **16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

21. S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in *Proceeding of IEEE European Conference on Optical Communication* (Torino, Italy, 2010), paper Mo.1.C.2.

**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

*λ*is the central wavelength of the transmitted optical carrier wave,

*c*is the light speed in vacuum,

*D*is the chromatic dispersion coefficient of the transmission fiber,

*L*is the transmission fiber length,

## 3. Principle of normalized LMS filter for carrier phase estimation

### 3.1 Principle of normalized LMS filter

13. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express **17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

*n*represents the number of the symbol sequence,

**17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

### 3.2 BER floor of phase estimation using NLMS filter with EEPN

**17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

30. E. Vanin and G. Jacobsen, “Analytical estimation of laser phase noise induced BER floor in coherent receiver with digital signal processing,” Opt. Express **18**(5), 4246–4259 (2010). [CrossRef] [PubMed]

**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

^{−9}, we need to select a large value (76 MHz and 122 MHz) of the laser linewidth in Fig. 2(b), which may not be used in the practical case. It can be found clearly that the EEPN arises from the LO phase noise, because the BER floor does not change with the increment of fiber length when there is only phase fluctuation from the TX laser. Theoretical investigation demonstrates that the enhanced LO phase noise plays the dominant role in total phase fluctuation, when the accumulated fiber dispersion is larger than 700 ps/nm (about 45 km normal transmission fiber) [14

**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

16. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express **18**(16), 17239–17251 (2010). [CrossRef] [PubMed]

### 3.3 Optimization of the step size in NLMS filter

**17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

^{−3}) is around 1.8 dB.

^{−3}in the one-tap NLMS-CPE with the optimum step size are illustrated in Fig. 4(b). It is found that the OSNR penalty scales exponentially with the increment of the effective laser linewidth.

## 4. Simulation investigation of PDM-QPSK transmission system

^{16}bits. The central wavelength of the transmitter laser and the LO laser are both 1553.6 nm. The standard single mode fibers (SSMFs) with the CD coefficient equal to 16 ps/nm/km are employed in all the simulation work.

32. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. **26**(1), 64–72 (2008). [CrossRef]

33. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express **18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

34. 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]

35. 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]

## 5. Simulation results

### 5.1 Phase estimation considering EEPN with different CD equalization

### 5.2 Evaluation of BER floor in phase estimation with EEPN

## 6. Differential phase detection

### 6.1 Differential QPSK demodulation system

### 6.2 Correlation between EEPN and intrinsic LO phase noise

*ρ*is the correlation coefficient between the intrinsic LO laser phase noise and the EEPN, and we have the absolute value

*ρ*is usually a negative value.

*N*is the required tap number (or the necessary overlap) in the chromatic dispersion compensation filter, and

*T*is the sampling period in the transmission system. The tap number (or the necessary overlap) can be calculated by the fiber dispersion to be compensated [22

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

25. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. **27**(16), 3721–3728 (2009). [CrossRef]

9. 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]

16. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express **18**(16), 17239–17251 (2010). [CrossRef] [PubMed]

33. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express **18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

## 7. Conclusions

## Appendix: BER floor of phase estimation using one-tap NLMS filter

30. E. Vanin and G. Jacobsen, “Analytical estimation of laser phase noise induced BER floor in coherent receiver with digital signal processing,” Opt. Express **18**(5), 4246–4259 (2010). [CrossRef] [PubMed]

## References and links

1. | P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. |

2. | G. P. Agrawal, |

3. | J. G. Proakis, |

4. | H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. Lightwave Technol. |

5. | M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. |

6. | Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express |

7. | G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. |

8. | X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, and P. D. Magill, “High-spectral-efficiency 114-Gb/s transmission using PolMux-RZ-8PSK modulation format and single-ended digital coherent detection technique,” J. Lightwave Technol. |

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

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

11. | M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. |

12. | D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. |

13. | Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express |

14. | W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express |

15. | A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in |

16. | A. P. T. Lau, T. S. R. Shen, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express |

17. | K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett. |

18. | C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in |

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

20. | I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express |

21. | S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in |

22. | S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express |

23. | S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in |

24. | M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in |

25. | R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. |

26. | |

27. | S. Haykin, |

28. | S. Benedetto, E. Biglieri, and V. Castellani, |

29. | G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett. |

30. | E. Vanin and G. Jacobsen, “Analytical estimation of laser phase noise induced BER floor in coherent receiver with digital signal processing,” Opt. Express |

31. | S. J. Savory, “Digital signal processing options in long haul transmission,” in |

32. | C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. |

33. | T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express |

34. | 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. |

35. | F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 1, 2011

Revised Manuscript: March 31, 2011

Manuscript Accepted: March 31, 2011

Published: April 6, 2011

**Citation**

Tianhua Xu, Gunnar Jacobsen, Sergei Popov, Jie Li, Ari T. Friberg, and Yimo Zhang, "Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization," Opt. Express **19**, 7756-7768 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7756

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### References

- P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21(12), 1862–1879 (1985). [CrossRef]
- G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.
- J. G. Proakis, Digital communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap. 10.
- H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. Lightwave Technol. 26(1), 158–167 (2008). [CrossRef]
- M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]
- Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express 13(19), 7527–7534 (2005). [CrossRef] [PubMed]
- G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19(13), 969–971 (2007). [CrossRef]
- X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, and P. D. Magill, “High-spectral-efficiency 114-Gb/s transmission using PolMux-RZ-8PSK modulation format and single-ended digital coherent detection technique,” J. Lightwave Technol. 27(3), 146–152 (2009). [CrossRef]
- 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]
- E. M. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol. 28(4), 502–519 (2010). [CrossRef]
- M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009). [CrossRef]
- D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. 24(1), 12–21 (2006). [CrossRef]
- Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express 17(3), 1435–1441 (2009). [CrossRef] [PubMed]
- W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]
- A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in Proceedings of OptoElectronics and Communications Conference (Hong Kong, 2009), paper FQ3.
- A. P. T. Lau, T. S. R. Shen, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express 18(16), 17239–17251 (2010). [CrossRef] [PubMed]
- K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett. 36(4), 585–587 (2011). [CrossRef] [PubMed]
- C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT4.
- C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express 17(6), 4815–4823 (2009). [CrossRef] [PubMed]
- I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express 18(15), 16273–16278 (2010). [CrossRef] [PubMed]
- S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proceeding of IEEE European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.2.
- S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]
- S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.
- M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT1.
- R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009). [CrossRef]
- www.vpiphotonics.com
- S. Haykin, Adaptive filter theory 4th Edition (Prentice Hall, 2001).
- S. Benedetto, E. Biglieri, and V. Castellani, Digital transmission theory (Prentice-Hall, Inc., 1987), Chap.5.
- G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett. 46(10), 698–700 (2010). [CrossRef]
- E. Vanin and G. Jacobsen, “Analytical estimation of laser phase noise induced BER floor in coherent receiver with digital signal processing,” Opt. Express 18(5), 4246–4259 (2010). [CrossRef] [PubMed]
- S. J. Savory, “Digital signal processing options in long haul transmission,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2008), paper OTuO3.
- C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008). [CrossRef]
- T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [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]
- 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]

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