## Chromatic dispersion compensation in coherent transmission system using digital filters |

Optics Express, Vol. 18, Issue 15, pp. 16243-16257 (2010)

http://dx.doi.org/10.1364/OE.18.016243

Acrobat PDF (1994 KB)

### Abstract

We present a comparative analysis of three popular digital filters for chromatic dispersion compensation: a time-domain least mean square adaptive filter, a time-domain fiber dispersion finite impulse response filter, and a frequency-domain blind look-up filter. The filters are applied to equalize the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying transmission system. The characteristics of these filters are compared by evaluating their applicability for different fiber lengths, their usability for dispersion perturbations, and their computational complexity. In addition, the phase noise tolerance of these filters is also analyzed.

© 2010 OSA

## 1. Introduction

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

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

6. Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express **13**(19), 7527–7534 (2005). [CrossRef] [PubMed]

13. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. **27**(16), 3614–3622 (2009). [CrossRef]

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

8. A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s receiver with digital equaliser using maximum likelihood sequence estimation,” in *Proceeding of IEEE European Conference on Optical Communication* (Stockholm, Sweden, 2004), paper Th4.1.5.

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

13. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. **27**(16), 3614–3622 (2009). [CrossRef]

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

13. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. **27**(16), 3614–3622 (2009). [CrossRef]

15. T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. **283**(6), 963–967 (2010). [CrossRef]

## 2. Digital signal processing modules in coherent receiver

16. 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]

## 3. Principle and structures of three digital filters for CD equalization

### 3.1 Least mean square adaptive filter

*n*represents the number of sample sequence,

*μ*is a key real coefficient called step size. The tap weights vector

*μ*needs to satisfy the condition of

*μ*is chosen to be very small, then the algorithm converges very slowly. A large value of

*μ*could lead to a faster convergence, but the algorithm will be less stable and safe, because sometimes the step size

*μ*may be larger than

*μ*is to make it change with the time-dependent largest eigenvalue

### 3.2 Fiber dispersion FIR filter

**16**(2), 804–817 (2008). [CrossRef] [PubMed]

*D*is the fiber chromatic dispersion coefficient,

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

*z*is the fiber length in the transmission channel,

*T*is the sampling period,

*x*.

15. T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. **283**(6), 963–967 (2010). [CrossRef]

**16**(2), 804–817 (2008). [CrossRef] [PubMed]

*T*as

**16**(2), 804–817 (2008). [CrossRef] [PubMed]

**16**(2), 804–817 (2008). [CrossRef] [PubMed]

18. M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. **22**, 314–316 (2010). [CrossRef]

18. M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. **22**, 314–316 (2010). [CrossRef]

*x*.

**16**(2), 804–817 (2008). [CrossRef] [PubMed]

### 3.3 Blind look-up filter

**27**(16), 3614–3622 (2009). [CrossRef]

15. T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. **283**(6), 963–967 (2010). [CrossRef]

**27**(16), 3614–3622 (2009). [CrossRef]

22. 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]

22. 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]

*N*is the FFT-size of the frequency domain equalizer.

_{FFT}## 4. Principle of equalization for polarization dependent impairments and phase noise

### 4.1 Adaptive PMD and polarization rotation equalization

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

### 4.2 Normalized LMS filter for phase estimation

16. 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]

## 5. 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.

16. 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]

26. 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]

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

## 6. Simulation results

### 6.1 Static chromatic dispersion equalization

^{−3}can be observed. This phenomenon contradicts with our previous result [15

**283**(6), 963–967 (2010). [CrossRef]

^{A}= 9) analyzed by anti-aliasing or the tap number (N

^{P}= 7) determined by pulse broadening.

*p*of time window to evaluate the precision of time window approximation, which is given by

*T*. In order to broaden the time window, we need to raise the Nyquist frequency correspondingly. The Nyquist frequency is defined as half of the sampling frequency of the system, and this means we need to increase the sampling rate in the ADC modules. With sampling rate being increased, the Nyquist frequency are also raised, meanwhile, the sample period

*T*is reduced, which allows the broadened continuous time window to be digitalized more precisely.

_{N}

^{A}/T

_{W}

^{A}) using FD-FIR filter is shown in Fig. 9(b), where a significant improvement can also be found. Meanwhile, we find that the FD-FIR filter performs better when the value of T

_{N}

^{A}/T

_{W}

^{A}is around 1.0, which is consistent with our preceding analysis.

18. M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. **22**, 314–316 (2010). [CrossRef]

22. 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]

### 6.2 Dynamic chromatic dispersion equalization

### 6.3 Computational complexity of the three filters

*C*,

_{LMS}*C*and

_{FD-FIR}*C*are the computational complexity of the three filters respectively,

_{BLU}*L*is the filter length for CD equalization,

_{CD}*M*is the number of points in signal constellation,

*n*is the oversampling ratio in samples per symbol,

_{SC}*N*is the length of FFT operation in the BLU filter. In the 112-Gbit/s NRZ-PDM-QPSK transmission system with a 2 Sa/Sy sampling rate at the ADC modules, we have

_{FFT}*M*= 4 and

*n*= 2 in the above formulas.

_{SC}### 6.4 Phase noise compensation

^{−3}, which is much better than FD-FIR and BLU filters (above 10

^{−2}). Meanwhile, we find the phase noise compensation using the one-tap NLMS equalizer can achieve a satisfactory performance with a small penalty from the back-to-back result for all the three filters. More detailed investigation of the phase noise influence is in progress and will be presented in a separate publication.

## 7. Conclusions

## 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. | E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. |

8. | A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s receiver with digital equaliser using maximum likelihood sequence estimation,” in |

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

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

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

12. | 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 |

13. | M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. |

14. | |

15. | T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. |

16. | 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. | S. Haykin, |

18. | M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. |

19. | A. V. Oppenheim, R. W. Schafer, and R. John, Buck, |

20. | J. G. Proakis, and D. G. Manolakis, |

21. | R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in |

22. | 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. |

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

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

25. | K. Kikuchi, and S. Y. Kim, “Investigation of nonlinear impairment effects on optical quadrature phase-shift keying signals transmitted through a long-haul system,” in |

26. | 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. |

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

28. | B. Spinnler, F. N. Hauske, and M. Kuschnerov, “Adaptive equalizer complexity in coherent optical receivers,” in |

29. | B. Spinnler, “Complexity of algorithms for digital coherent receivers,” in |

**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: June 2, 2010

Revised Manuscript: July 8, 2010

Manuscript Accepted: July 9, 2010

Published: July 16, 2010

**Citation**

Tianhua Xu, Gunnar Jacobsen, Sergei Popov, Jie Li, Evgeny Vanin, Ke Wang, Ari T. Friberg, and Yimo Zhang, "Chromatic dispersion compensation in coherent transmission system using digital filters," Opt. Express **18**, 16243-16257 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-16243

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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]
- E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. 25(8), 2033–2043 (2007). [CrossRef]
- A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.
- 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]
- 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.
- M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. 27(16), 3614–3622 (2009). [CrossRef]
- www.vpiphotonics.com
- T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010). [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]
- S. Haykin, Adaptive filter theory 4th Edition (Prentice Hall, 2001).
- M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010). [CrossRef]
- A. V. Oppenheim, R. W. Schafer, and R. John, Buck, Discrete-time signal processing 2nd Edition (Prentice Hall, 1999).
- J. G. Proakis, and D. G. Manolakis, Digital signal processing 4th Edition (Prentice Hall, 2006).
- R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT3.
- 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]
- C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, G. D. Khoe, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008). [CrossRef]
- 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.
- K. Kikuchi, and S. Y. Kim, “Investigation of nonlinear impairment effects on optical quadrature phase-shift keying signals transmitted through a long-haul system,” in Proceedings of IEEE Laser and Electro-Optics Society Summer Topical Meetings (Acapulco, Mexico, 2008), pp. 131–132.
- 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 Photonics J. 1(2), 144–152 (2009). [CrossRef]
- B. Spinnler, F. N. Hauske, and M. Kuschnerov, “Adaptive equalizer complexity in coherent optical receivers,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.4.
- B. Spinnler, “Complexity of algorithms for digital coherent receivers,” in Proceeding of IEEE European Conference on Optical Communication (Vienna, Austria, 2009), paper 7.3.6.

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