## Statistical moments-based OSNR monitoring for coherent optical systems |

Optics Express, Vol. 20, Issue 16, pp. 17711-17721 (2012)

http://dx.doi.org/10.1364/OE.20.017711

Acrobat PDF (1610 KB)

### Abstract

We present a novel statistical moments-based method for optical signal-to-noise ratio (OSNR) monitoring in polarization-multiplexed (pol-mux) coherent optical systems. This technique only requires the knowledge of the envelope of the equalized signal before phase correction, which can be achieved by using any two arbitrary statistical moments, and it is suitable for both constant and non-constant modulus modulation formats. The proposed estimation method is experimentally demonstrated for 10-Gbaud pol-mux coherent systems using QPSK and 16-QAM. Additionally, numerical simulations are carried out to demonstrate 20-Gbaud systems using 16-QAM and 64-QAM. The results show that the OSNR can be estimated accurately over a wide range of values for QPSK, 16-QAM or 64-QAM systems up to 1920-km long and with up to 50-ps all-order polarization mode dispersion. By setting a proper reference value for calibration, the proposed algorithm also shows good tolerance when the received signal is not well compensated.

© 2012 OSA

## 1. Introduction

1. J. Yu and X. Zhou, “Ultra-high-capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. **48**(3), S56–S64 (2010). [CrossRef]

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

3. K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. **48**(7), 62–69 (2010). [CrossRef]

4. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. **22**(1), 294–304 (2004). [CrossRef]

17. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE Sel. Top. Quantum Electron. **16**(5), 1180–1192 (2010). [CrossRef]

18. M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express **19**(13), 12789–12798 (2011). [CrossRef] [PubMed]

## 2. Statistical moments-based OSNR estimator

*m*different amplitudes,

*p*

_{1},

*k*equalized symbol,

^{th}*i*moment of the Ricean distribution in terms of parameters

^{th}*η*and

*σ*as [20]:where:

*m*different PSK sub-systems; for example, PSK partitioning for 16-QAM and 64-QAM is shown as colored rings in Fig. 1. Therefore, the moments of the signal envelope are

*m*Ricean distributions, one for each ring [21

21. G. Ping and C. Tepedelenlioglu, “SNR estimation for nonconstant modulus constellations,” IEEE Trans. Signal Process. **53**(3), 865–870 (2005). [CrossRef]

*i*moment of the equalized signal, given by

^{th}*η*≤ 30 dB with, say, a step size 0.01 dB. However, there exists a simpler approach when (2, 4) is chosen for (

*SNR*which is the SNR value measured by the back-to-back transmission without the ASE noise, after taking the noise reference bandwidth into account [12]. The OSNR estimator can then be described as:where

_{RF}## 3. Experimental demonstration

22. A. V. Tran, C. Zhu, C. C. Do, S. Chen, T. Anderson, D. Hewitt, and E. Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. **24**(11), 885–887 (2012). [CrossRef]

23. 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]

*TS*1 and

*TS*2 for the X polarization and

*TS*3 and

*TS*4 for the Y polarization. These symbols were chosen to be orthogonal to each other, as shown at the bottom of Fig. 3(a). Their spectra were scheduled according to the Alamouti coding matrix [24], where (.)* denotes the complex conjugate operation.

22. A. V. Tran, C. Zhu, C. C. Do, S. Chen, T. Anderson, D. Hewitt, and E. Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. **24**(11), 885–887 (2012). [CrossRef]

## 4. Simulation results

*η*

_{2,4}was used for all simulations unless specified. The system was set to have 20-Gbaud, which supports 160-Gb/s for a pol-mux 16-QAM system, and the DSP algorithm was the same as that in the experiments except that the length of the equalizer was adjusted according to the bit rate and different fiber impairments. Moreover, we investigated a much wider OSNR range of 1 - 23 dB. The standard deviations of the estimation errors after several trials were used to evaluate the performance.

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

^{−20}m

^{2}/W. As can be seen in Fig. 9 , without extra non-linear compensation, the estimation performance decreases as the launched power becomes larger, this is due to the increasing non-Gaussian characteristic of the equalized signal caused by the fiber non-linearity. The estimation error is more than 1 dB when the launched power is ≥ 4 dBm.

18. M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express **19**(13), 12789–12798 (2011). [CrossRef] [PubMed]

## 5. Conclusions

## Acknowledgments

## References and links

1. | J. Yu and X. Zhou, “Ultra-high-capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. |

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

3. | K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. |

4. | D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. |

5. | W. Chen, R. S. Tucker, X. Yi, W. Shieh, and J. Evans, “Optical signal-to-noise ratio monitoring using uncorrelated beat noise,” IEEE Photon. Technol. Lett. |

6. | Y. C. Chung, “Polarization-nulling method for monitoring OSNR in WDM networks,” in Optical Fiber Communication Conference (OFC), paper OThP3 (2006). |

7. | T. S. R. Shen, A. P. T. Lau, and G. N. Liu, “OSNR monitoring for higher order modulation formats using asynchronous amplitude histogram,” IEEE Photon. Technol. Lett. |

8. | S. D. Dods, T. B. Anderson, K. Clarke, M. Bakaul, and A. Kowalczyk, “Asynchronous sampling for optical performance monitoring,” in Optical Fiber Communication Conference (OFC), paper OMM5 (2007). |

9. | J. A. Jargon, X. Wu, H. Y. Choi, Y. C. Chung, and A. E. Willner, “Optical performance monitoring of QPSK data channels by use of neural networks trained with parameters derived from asynchronous constellation diagrams,” Opt. Express |

10. | F. N. Khan, A. P. T. Lau, C. Lu, and P. K. A. Wai, “Joint OSNR and chromatic dispersion monitoring using empirical moments of asynchronously sampled signal amplitudes,” Opto-Electronics and Communications Conference, Paper 6B4_5 (2011). |

11. | M. S. Faruk and K. Kikuchi, “Monitoring of optical signal-to-noise ratio using statistical moments of adaptive-equalizer output in coherent optical receivers,” Opto-Electronics and Communications Conference, 233–234 (2011). |

12. | D. J. Ives, B. C. Thomasen, R. Maher, and S. Savory, “Estimating OSNR of equalised QPSK signals,” in European Conference and Exhibition on Optical Communication (ECOC), OThH5 (2011). |

13. | W. Shieh, R. S. Tucker, W. Chen, X. Yi, and G. Pendock, “Optical performance monitoring in coherent optical OFDM systems,” Opt. Express |

14. | F. N. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, B. Lankl, T. Duthel, C. R. S. Fludger, D. van den Borne, E. D. Schmidt, and B. Spinnler, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Proc. Fiber Commun. Conf., paper OthW2 (2008). |

15. | M. P. Dlubek, A. J. Phillips, and E. C. Larkins, “Optical signal quality metric based on statistical moments and Laguerre expansion,” Opt. Quantum Electron. |

16. | B. Porat and B. Friedlander, “Blind equalization of digital communication channels using high-order moments,” IEEE Trans. Signal Process. |

17. | B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE Sel. Top. Quantum Electron. |

18. | M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express |

19. | J. J. K. O. Ruanaidh and W. J. Fitzgerald, |

20. | G. L. Stuber, |

21. | G. Ping and C. Tepedelenlioglu, “SNR estimation for nonconstant modulus constellations,” IEEE Trans. Signal Process. |

22. | A. V. Tran, C. Zhu, C. C. Do, S. Chen, T. Anderson, D. Hewitt, and E. Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. |

23. | 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. |

24. | S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Commun. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 23, 2012

Revised Manuscript: July 5, 2012

Manuscript Accepted: July 5, 2012

Published: July 19, 2012

**Citation**

Chen Zhu, An V. Tran, Simin Chen, Liang B. Du, Cuong C. Do, Trevor Anderson, Arthur J. Lowery, and Efstratios Skafidas, "Statistical moments-based OSNR monitoring for coherent optical systems," Opt. Express **20**, 17711-17721 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17711

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### References

- J. Yu and X. Zhou, “Ultra-high-capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag.48(3), S56–S64 (2010). [CrossRef]
- S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008). [CrossRef] [PubMed]
- K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010). [CrossRef]
- D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol.22(1), 294–304 (2004). [CrossRef]
- W. Chen, R. S. Tucker, X. Yi, W. Shieh, and J. Evans, “Optical signal-to-noise ratio monitoring using uncorrelated beat noise,” IEEE Photon. Technol. Lett.17(11), 2484–2486 (2005). [CrossRef]
- Y. C. Chung, “Polarization-nulling method for monitoring OSNR in WDM networks,” in Optical Fiber Communication Conference (OFC), paper OThP3 (2006).
- T. S. R. Shen, A. P. T. Lau, and G. N. Liu, “OSNR monitoring for higher order modulation formats using asynchronous amplitude histogram,” IEEE Photon. Technol. Lett.22, 1632–1634 (2010).
- S. D. Dods, T. B. Anderson, K. Clarke, M. Bakaul, and A. Kowalczyk, “Asynchronous sampling for optical performance monitoring,” in Optical Fiber Communication Conference (OFC), paper OMM5 (2007).
- J. A. Jargon, X. Wu, H. Y. Choi, Y. C. Chung, and A. E. Willner, “Optical performance monitoring of QPSK data channels by use of neural networks trained with parameters derived from asynchronous constellation diagrams,” Opt. Express18(5), 4931–4938 (2010). [CrossRef] [PubMed]
- F. N. Khan, A. P. T. Lau, C. Lu, and P. K. A. Wai, “Joint OSNR and chromatic dispersion monitoring using empirical moments of asynchronously sampled signal amplitudes,” Opto-Electronics and Communications Conference, Paper 6B4_5 (2011).
- M. S. Faruk and K. Kikuchi, “Monitoring of optical signal-to-noise ratio using statistical moments of adaptive-equalizer output in coherent optical receivers,” Opto-Electronics and Communications Conference, 233–234 (2011).
- D. J. Ives, B. C. Thomasen, R. Maher, and S. Savory, “Estimating OSNR of equalised QPSK signals,” in European Conference and Exhibition on Optical Communication (ECOC), OThH5 (2011).
- W. Shieh, R. S. Tucker, W. Chen, X. Yi, and G. Pendock, “Optical performance monitoring in coherent optical OFDM systems,” Opt. Express15(2), 350–356 (2007). [CrossRef] [PubMed]
- F. N. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, B. Lankl, T. Duthel, C. R. S. Fludger, D. van den Borne, E. D. Schmidt, and B. Spinnler, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Proc. Fiber Commun. Conf., paper OthW2 (2008).
- M. P. Dlubek, A. J. Phillips, and E. C. Larkins, “Optical signal quality metric based on statistical moments and Laguerre expansion,” Opt. Quantum Electron.40(8), 561–575 (2008). [CrossRef]
- B. Porat and B. Friedlander, “Blind equalization of digital communication channels using high-order moments,” IEEE Trans. Signal Process.39(2), 522–526 (1991). [CrossRef]
- B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE Sel. Top. Quantum Electron.16(5), 1180–1192 (2010). [CrossRef]
- M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express19(13), 12789–12798 (2011). [CrossRef] [PubMed]
- J. J. K. O. Ruanaidh and W. J. Fitzgerald, Numerical Bayesian Methods applied to Signal Processing (Springer-Verlag, 1995).
- G. L. Stuber, Principles of Mobile Communication (Norwell, MA: Kluwer, 1996).
- G. Ping and C. Tepedelenlioglu, “SNR estimation for nonconstant modulus constellations,” IEEE Trans. Signal Process.53(3), 865–870 (2005). [CrossRef]
- A. V. Tran, C. Zhu, C. C. Do, S. Chen, T. Anderson, D. Hewitt, and E. Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett.24(11), 885–887 (2012). [CrossRef]
- 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]
- S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Commun.16, 1451–1458 (1998).

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