## Relative phase noise estimation and mitigation in Raman amplified coherent optical communication system |

Optics Express, Vol. 22, Issue 2, pp. 1257-1266 (2014)

http://dx.doi.org/10.1364/OE.22.001257

Acrobat PDF (2296 KB)

### Abstract

The interplay between the stochastic intensity fluctuation of Raman pump laser and cross-phase modulation (XPM) effect in transmission optical fiber leads to additional phase noise, namely, relative phase noise (RPN) of signal in multi-level modulated coherent optical communication system. Both theoretical analysis and quantitative simulation have been performed to investigate the characteristics and impact of RPN. Being low-pass in nature, RPN is different from XPM induced phase noise in PSK/OOK hybrid system, and has not been considered yet. The noise power of RPN can accumulate incoherently along transmission links. With a proper signal model, we study the impact of RPN to the coherent optical communication system through Monte Carlo simulation. RPN will cause more cycle slips in Viterbi-and-Viterbi (V-V) phase estimation (PE), and the quantitative analysis of cycle slip probability is carried out. When using sliding window V-V without any optimization, the Q factor penalty of RPN on DQPSK signal can be as large as around 5 dB in strong RPN condition. However, it can be reduced by over 3 dB when using an optimal block size or optimal averaging weights.

© 2014 Optical Society of America

## 1. Introduction

1. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics **1**(2), 279–307 (2009). [CrossRef]

2. 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]

3. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express **17**(2), 703–715 (2009). [CrossRef] [PubMed]

4. T. Tanimura, S. Oda, M. Yuki, H. Zhang, L. Li, Z. Tao, H. Nakashima, T. Hoshida, K. Nakamura, and J. C. Rasmussen, “Non-linearity tolerance of direct detection and coherent receivers for 43 Gb/s RZ-DQPSK signals with co-propagating 11.1 Gb/s NRZ signals over NZ-DSF,” in *Tech. Digest of the Conference on Optical Fiber Communication* (2008), paper OTuM4. [CrossRef]

5. Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express **17**(16), 13860–13868 (2009). [CrossRef] [PubMed]

8. J. Cheng, M. Tang, S. Fu, P. P. Shum, and D. Liu, “Relative phase noise induced impairment in M-ary phase-shift-keying coherent optical communication system using distributed fiber Raman amplifier,” Opt. Lett. **38**(7), 1055–1057 (2013). [CrossRef] [PubMed]

## 2. Relative phase noise and signal model

### 2.1 Relative phase noise

*d*accounts for the group-velocity mismatch between the pump and signal. Since

8. J. Cheng, M. Tang, S. Fu, P. P. Shum, and D. Liu, “Relative phase noise induced impairment in M-ary phase-shift-keying coherent optical communication system using distributed fiber Raman amplifier,” Opt. Lett. **38**(7), 1055–1057 (2013). [CrossRef] [PubMed]

10. C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to signal RIN transfer in Raman fiber amplifiers,” J. Lightwave Technol. **19**(8), 1140–1148 (2001). [CrossRef]

5. Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express **17**(16), 13860–13868 (2009). [CrossRef] [PubMed]

^{2}, fiber dispersion is 16 ps/nm/km and channel spacing between PSK and OOK signal is 100 GHz. As shown here, counter-pumping RPN changes so slow that can be treated as a constant in a block window of PE algorithm, thus will not affect phase tracking performance. Nonetheless, although co-pumping RPN changes slower than XPM induced phase noise in PSK/OOK hybrid system, it changes faster than laser phase noise, and will probably induce non-negligible system impairment. Therefore, in this paper, we ignore counter-pumping RPN and deal with co-pumping RPN only.

### 2.2 Signal model

*k-*th symbol interval

## 3. Probability of cycle slips induced by RPN

11. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. **27**(7), 901–914 (2009). [CrossRef]

^{−18}[11

11. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. **27**(7), 901–914 (2009). [CrossRef]

*A*and

*B*are constants. The fitted curve is also included in Fig. 3, from which we can see that the 10

^{−18}cycle slip probability occurs at

^{2}. It is rather a low threshold, which is equivalent to noise power after transmission of 4 spans of 100 km typical SMF, where 22.4 dB Raman on-off gain is provided in each span, with a co-pumping pump laser of 800 mW power and −120 dB/Hz pump RIN. Also, because RPN can accumulate span by span incoherently, even if pump laser has fairly low RIN, it is always possible to reach the threshold in long-haul transmission. Once the threshold is reached, differential logical detection is better to be deployed.

^{2}and 0.158 rad

^{2}for optimized block size PE and optimized averaging weights PE, respectively.

## 4. RPN estimation and mitigation

*L*symbols to obtain the estimated phase. The sliding window implementation estimates the carrier phase symbol by symbol. Two optimized algorithms are then presented to give an improved performance. Parameters used in the simulation are listed in Table 1.

12. G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express **14**(18), 8043–8053 (2006). [CrossRef] [PubMed]

*L*to

*L*are used to estimate the carrier phase at time 0, the optimal averaging weights

## 5. Conclusion

## Acknowledgments

## References and links

1. | G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics |

2. | 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. |

3. | S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express |

4. | T. Tanimura, S. Oda, M. Yuki, H. Zhang, L. Li, Z. Tao, H. Nakashima, T. Hoshida, K. Nakamura, and J. C. Rasmussen, “Non-linearity tolerance of direct detection and coherent receivers for 43 Gb/s RZ-DQPSK signals with co-propagating 11.1 Gb/s NRZ signals over NZ-DSF,” in |

5. | Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express |

6. | L. Li, Z. Tao, S. Oda, T. Tanimura, M. Yuki, T. Hoshida, and J. C. Rasmussen, “Adaptive optimization for digital carrier phase estimation in optical coherent receivers,” in |

7. | 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 |

8. | J. Cheng, M. Tang, S. Fu, P. P. Shum, and D. Liu, “Relative phase noise induced impairment in M-ary phase-shift-keying coherent optical communication system using distributed fiber Raman amplifier,” Opt. Lett. |

9. | G. P. Agrawal, |

10. | C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to signal RIN transfer in Raman fiber amplifiers,” J. Lightwave Technol. |

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

12. | G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(230.4480) Optical devices : Optical amplifiers

**ToC Category:**

Optical Communications

**History**

Original Manuscript: October 1, 2013

Revised Manuscript: December 29, 2013

Manuscript Accepted: January 6, 2014

Published: January 13, 2014

**Citation**

Jingchi Cheng, Ming Tang, Songnian Fu, Perry Ping Shum, Deming Liu, Meng Xiang, Zhenhua Feng, and Dawei Yu, "Relative phase noise estimation and mitigation in Raman amplified coherent optical communication system," Opt. Express **22**, 1257-1266 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1257

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### References

- G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009). [CrossRef]
- D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. 24(1), 12–21 (2006). [CrossRef]
- S. Zhang, P. Y. Kam, J. Chen, C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express 17(2), 703–715 (2009). [CrossRef] [PubMed]
- T. Tanimura, S. Oda, M. Yuki, H. Zhang, L. Li, Z. Tao, H. Nakashima, T. Hoshida, K. Nakamura, and J. C. Rasmussen, “Non-linearity tolerance of direct detection and coherent receivers for 43 Gb/s RZ-DQPSK signals with co-propagating 11.1 Gb/s NRZ signals over NZ-DSF,” in Tech. Digest of the Conference on Optical Fiber Communication (2008), paper OTuM4. [CrossRef]
- Z. Tao, W. Yan, S. Oda, T. Hoshida, J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17(16), 13860–13868 (2009). [CrossRef] [PubMed]
- L. Li, Z. Tao, S. Oda, T. Tanimura, M. Yuki, T. Hoshida, and J. C. Rasmussen, “Adaptive optimization for digital carrier phase estimation in optical coherent receivers,” in Digest IEEE/LEOS Summer Topical Meetings, Acapulco, Mexico, Jul. 2008, pp. 121–122, paper TuC3.3.
- 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. European Conference on Optical Communications (2009), paper P3.16.
- J. Cheng, M. Tang, S. Fu, P. P. Shum, D. Liu, “Relative phase noise induced impairment in M-ary phase-shift-keying coherent optical communication system using distributed fiber Raman amplifier,” Opt. Lett. 38(7), 1055–1057 (2013). [CrossRef] [PubMed]
- G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2000).
- C. R. S. Fludger, V. Handerek, R. J. Mears, “Pump to signal RIN transfer in Raman fiber amplifiers,” J. Lightwave Technol. 19(8), 1140–1148 (2001). [CrossRef]
- M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009). [CrossRef]
- G. Goldfarb, G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14(18), 8043–8053 (2006). [CrossRef] [PubMed]

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