## Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems |

Optics Express, Vol. 20, Issue 15, pp. 17183-17191 (2012)

http://dx.doi.org/10.1364/OE.20.017183

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### Abstract

Using numerical simulations, the impact of nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal on polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems at 42.8 (112)-Gbit/s is investigated over dispersion-managed (DM) link. Both symbol-aligned and symbol-interleaved formats are considered and compared. We find that for symbol-aligned PM-QPSK systems, the impact of NSNI on system performance seems rather weak due to the strong inter-channel cross-polarization modulation (XPolM). However, when the symbol-interleaved format is used, in which the XPolM is suppressed significantly, the system performance is seriously degraded by NSNI, especially at low bit-rate. Results of 1000-km transmission employing standard single-mode fiber (SSMF) over DM link show that for 42.8-Gbit/s coherent PM-QPSK systems, the nonlinear threshold (NLT) will decrease from 5.8dBm to 0.6dBm due to the nonlinear signal-noise interactions when symbol-interleaved RZ format is used.

© 2012 OSA

## 1. Introduction

1. J. Yu, X. Zhou, M.-F. Huang, D. Qian, P. N. Ji, T. Wang, and P. Magill, “400Gb/s (4 x 100Gb/s) orthogonal PDM-RZ-QPSK DWDM signal transmission over 1040km SMF-28,” Opt. Express **17**(20), 17928–17933 (2009). [CrossRef] [PubMed]

2. G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. B. Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4-bit/s capacity over 2550km using PDM QPSK modulation format and coherent receiver,” J. Lightwave Technol. **27**(3), 153–157 (2009). [CrossRef]

3. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1164–1179 (2010). [CrossRef]

4. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol. **26**(1), 36–42 (2008). [CrossRef]

5. C. Xie, “Interchannel nonlinearities in coherent polarization division-multiplexed quadrature-phase-shift-keying systems,” IEEE Photon. Technol. Lett. **21**(5), 274–276 (2009). [CrossRef]

6. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. J. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16x100Gb/s transmission over installed fiber with different dispersion maps,” IEEE Photon. Technol. Lett. **22**(6), 371–373 (2010). [CrossRef]

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

8. Y.-H. Wang and I. Lyubomirsky, “Impact of DP-QPSK pulse shape in nonlinear 100G transmission,” J. Lightwave Technol. **28**(18), 2750–2756 (2010). [CrossRef]

14. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

## 2. System model

^{2}/km, and nonlinear coefficient

## 3. Results and discussions

^{−3}after 1000-km transmission for the system with and without NSNI. The pulse shapes studied include NRZ and 50% duty cycle RZ. The launch power per channel is defined as the input power per the single wavelength and the OSNR penalty is measured with reference to the system at back-to-back (b2b) operation. The nonlinear threshold (NLT) for the four analyzed system configurations is also displayed in Table 2 . When considering NSNI along the transmission link, the NLT is obtained based on the algorithm presented in [14

14. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

^{−3}.

8. Y.-H. Wang and I. Lyubomirsky, “Impact of DP-QPSK pulse shape in nonlinear 100G transmission,” J. Lightwave Technol. **28**(18), 2750–2756 (2010). [CrossRef]

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

15. C. Xie, “Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems,” Chin. Opt. Lett. **8**(9), 844–851 (2010). [CrossRef]

15. C. Xie, “Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems,” Chin. Opt. Lett. **8**(9), 844–851 (2010). [CrossRef]

^{−4}, 3.14 × 10

^{−3}, 2.77 × 10

^{−3}and 4.61 × 10

^{−3}, respectively.

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

17. M. N. Chughtai, M. Forzati, J. Mårtensson, and D. Rafique, “Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels,” Opt. Express **20**(7), 8155–8160 (2012). [CrossRef] [PubMed]

17. M. N. Chughtai, M. Forzati, J. Mårtensson, and D. Rafique, “Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels,” Opt. Express **20**(7), 8155–8160 (2012). [CrossRef] [PubMed]

## 4. Conclusions

## Appendix: Calculation of the OSNR penalty when considering NSNI for nonlinear transmission

^{−3}. So we need to calculate the required OSNR at BER=10

^{−3}in this case. The procedure for the measurement of the OSNR penalty when considering NSNI is detailed here:

- 1. Measure the required OSNR (OSNR
_{b2b}) at back-to-back operation that gives BER=10^{−3}. - 2. For each given transmitted power P
_{in}, we vary noise figure (NF) of inline EDFA so that BER=10^{−3}is obtained at NF_{0}after nonlinear transmission. The required OSNR (OSNR_{R}) at BER=10^{−3}can be obtained OSNR_{R}=P_{in}/P_{ASE}, being P_{ASE}the cumulated ASE power at the end of the link, generated from the inline EDFAs. P_{ASE}can be obtained from NF_{0}. - 3. The OSNR penalty at the given launch power is obtained OSNR
_{penalty}=OSNR_{R}-OSNR_{b2b}.

## Acknowledgments

## References and links

1. | J. Yu, X. Zhou, M.-F. Huang, D. Qian, P. N. Ji, T. Wang, and P. Magill, “400Gb/s (4 x 100Gb/s) orthogonal PDM-RZ-QPSK DWDM signal transmission over 1040km SMF-28,” Opt. Express |

2. | G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. B. Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4-bit/s capacity over 2550km using PDM QPSK modulation format and coherent receiver,” J. Lightwave Technol. |

3. | S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. |

4. | J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol. |

5. | C. Xie, “Interchannel nonlinearities in coherent polarization division-multiplexed quadrature-phase-shift-keying systems,” IEEE Photon. Technol. Lett. |

6. | G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. J. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16x100Gb/s transmission over installed fiber with different dispersion maps,” IEEE Photon. Technol. Lett. |

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

8. | Y.-H. Wang and I. Lyubomirsky, “Impact of DP-QPSK pulse shape in nonlinear 100G transmission,” J. Lightwave Technol. |

9. | A. Bononi, P. Serena and N. Rossi, “Modeling of signal-noise interactions in nonlinear fiber transmission with different modulation formats,” ECOC2009 (2009), paper 10.4.6. |

10. | A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?,” ECOC2010 (2010), paper Th.10.E.1. |

11. | P. Serena, A. Orlandini, and A. Bononi, “Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise,” J. Lightwave Technol. |

12. | A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” J. Lightwave Technol. |

13. | K.-P. Ho, “Probability density of nonlinear phase noise,” J. Opt. Soc. Am. B |

14. | A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. |

15. | C. Xie, “Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems,” Chin. Opt. Lett. |

16. | O. Vassilieva, T. Hoshida, J. C. Rasmussen, and T. Naito, “Symbol rate dependence of XPM-induced phase noise penalty on QPSK-based modulation format,” ECOC2008 (2008), paper We.1.E.4. |

17. | M. N. Chughtai, M. Forzati, J. Mårtensson, and D. Rafique, “Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels,” Opt. Express |

18. | H. Kim, “Nonlinear phase noise in phase-coded transmission,” OFC2005 (2005), paper OThO3. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: April 18, 2012

Revised Manuscript: June 14, 2012

Manuscript Accepted: July 1, 2012

Published: July 12, 2012

**Citation**

Xiaogang Yi, Yan Li, Jian Wu, Kun Xu, and Jintong Lin, "Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems," Opt. Express **20**, 17183-17191 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-17183

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### References

- J. Yu, X. Zhou, M.-F. Huang, D. Qian, P. N. Ji, T. Wang, and P. Magill, “400Gb/s (4 x 100Gb/s) orthogonal PDM-RZ-QPSK DWDM signal transmission over 1040km SMF-28,” Opt. Express17(20), 17928–17933 (2009). [CrossRef] [PubMed]
- G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. B. Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4-bit/s capacity over 2550km using PDM QPSK modulation format and coherent receiver,” J. Lightwave Technol.27(3), 153–157 (2009). [CrossRef]
- S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron.16(5), 1164–1179 (2010). [CrossRef]
- J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol.26(1), 36–42 (2008). [CrossRef]
- C. Xie, “Interchannel nonlinearities in coherent polarization division-multiplexed quadrature-phase-shift-keying systems,” IEEE Photon. Technol. Lett.21(5), 274–276 (2009). [CrossRef]
- G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. J. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16x100Gb/s transmission over installed fiber with different dispersion maps,” IEEE Photon. Technol. Lett.22(6), 371–373 (2010). [CrossRef]
- C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17(6), 4815–4823 (2009). [CrossRef] [PubMed]
- Y.-H. Wang and I. Lyubomirsky, “Impact of DP-QPSK pulse shape in nonlinear 100G transmission,” J. Lightwave Technol.28(18), 2750–2756 (2010). [CrossRef]
- A. Bononi, P. Serena and N. Rossi, “Modeling of signal-noise interactions in nonlinear fiber transmission with different modulation formats,” ECOC2009 (2009), paper 10.4.6.
- A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?,” ECOC2010 (2010), paper Th.10.E.1.
- P. Serena, A. Orlandini, and A. Bononi, “Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise,” J. Lightwave Technol.24(5), 2026–2037 (2006). [CrossRef]
- A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” J. Lightwave Technol.25(10), 3008–3016 (2007). [CrossRef]
- K.-P. Ho, “Probability density of nonlinear phase noise,” J. Opt. Soc. Am. B20(9), 1875–1879 (2003). [CrossRef]
- A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol.16(2), 73–85 (2010). [CrossRef]
- C. Xie, “Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems,” Chin. Opt. Lett.8(9), 844–851 (2010). [CrossRef]
- O. Vassilieva, T. Hoshida, J. C. Rasmussen, and T. Naito, “Symbol rate dependence of XPM-induced phase noise penalty on QPSK-based modulation format,” ECOC2008 (2008), paper We.1.E.4.
- M. N. Chughtai, M. Forzati, J. Mårtensson, and D. Rafique, “Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels,” Opt. Express20(7), 8155–8160 (2012). [CrossRef] [PubMed]
- H. Kim, “Nonlinear phase noise in phase-coded transmission,” OFC2005 (2005), paper OThO3.

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