## Estimating OSNR of equalised QPSK signals |

Optics Express, Vol. 19, Issue 26, pp. B661-B666 (2011)

http://dx.doi.org/10.1364/OE.19.00B661

Acrobat PDF (1048 KB)

### Abstract

We propose and demonstrate a technique to estimate the OSNR of an equalised QPSK signal based on the radial moments of the complex signal constellation. The technique is compared through simulation with maximum likelihood estimation and the effect of the block size used in the estimation is also assessed. The technique is verified experimentally and when combined with a single point calibration the OSNR of the input signal was estimated to within 0.5 dB.

© 2011 OSA

## 2. Theory

*z*, for an actual constellation point,

*R*e

*, with Gaussian noise variance,*

^{jθ}*σ*

^{2}, made up of ASE noise,

*R*and

*θ*are the radius and angle of the actual constellation point.

*θ*is unknown and so we treat this as a uniformly distributed random nuisance variable and remove it by integration [7]. Hence by substitution of

*r*= |

*z*|, we can write the likelihood as a univariate distribution of

*r*, where I

_{0}(.), is the modified Bessel function of the first kind. This is the well known Rician distribution [8, 9].

*R*and

*σ*of this distribution has been addressed in many fields using maximum likelihood estimation and the moments of the radial distribution with fixed point analysis [10

10. J. Sijbers, A. J. den Dekker, P. Scheunders, and D. V. Dyck, “Maximum-likelihood estimation of Rician distribution parameters,” IEEE Trans. Med. Imaging **17**, 357–361 (1998). [CrossRef] [PubMed]

12. C. G. Koay and P. J. Basser, “Analytically exact correction scheme for signal extraction from noisy magnitude MR signals,” J. Mag. Reson. **179**, 317–322 (2006). [CrossRef]

*r*

^{2}. From the Rician distribution we have where 𝔼{.} indicates the expectation value. These equations can be solved to calculate the electrical

*SNR*on either the I or Q signals given by

*R*and

*σ*of the distribution in Eq. (2) were also estimated by maximising the log likelihood [7, 10

10. J. Sijbers, A. J. den Dekker, P. Scheunders, and D. V. Dyck, “Maximum-likelihood estimation of Rician distribution parameters,” IEEE Trans. Med. Imaging **17**, 357–361 (1998). [CrossRef] [PubMed]

*OSNR*, is given by [5

_{dB}5. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express **16**, 753–791 (2008). [CrossRef] [PubMed]

*P*is the signal power,

_{s}*P*is the optical noise power measured in an optical bandwidth

_{ASE}*B*= 0.1 nm (≈12.5 GHz at 1550 nm) and

_{ref}*R*is the symbol rate.

_{s}## 3. Simulation

^{−1}PDM-QPSK transmission simulation was carried out for various levels of additive white Gaussian noise to emulate different OSNRs. In our simulation four shifted PRBS of length 2

^{15}– 1 were shaped using a root raised cosine filter before ideally modulating a carrier with a 1 MHz Lorentzian linewidth. The optical signal was transmitted through 10 km of standard single mode fibre before being received by an idealised coherent optical receiver with a local oscillator frequency offset of 10 MHz and zero linewidth. The received signal was equalised using a CMA adapted 17 tap FIR filter. The OSNR was calculated for the combined polarisation signals as a single data set, a total of 20000 data points, using Eqs. (4), (5) and (6). Figure 2 shows the estimated OSNR and the simulated OSNR, in 0.1 nm noise bandwidth for both the maximum likelihood and radial moments based techniques. The results show that the maximum likelihood and radial moments based techniques agree and both offer a bias free estimate of the OSNR over a wide range of OSNR.

*OSNR*- simulated

_{dB}*OSNR*) and standard deviation of the estimated

_{dB}*OSNR*for a various number of samples. In a digital optical coherent receiver the data is likely to be processed in parallel with a bus width > 100 such that by estimating the OSNR across this bus width the bias will be less than 0.1 dB.

_{dB}## 4. Experimental results

^{−1}PDM-QPSK signal. The signal was noise loaded with ASE noise before being detected with a coherent optical receiver with balanced detection. The combined linewidth of the transmitter laser and local oscillator was < 1MHz. The signal was sampled using a 50 GSa.s

^{−1}real time scope before off line DSP was carried out using MATLAB®. The OSNR was then calculated using Eqs. (4) and (6). The actual OSNR was measured using an OSA for comparison. Figure 3 shows the estimated OSNR vs the OSA measured OSNR both for a 0.1 nm reference bandwidth.

## 5. Discussion

*SNR*is given by where

^{−21}. Figure 3 shows the corrected and uncorrected OSNR estimates from the coherent receiver and the OSNR measured using the OSA. It can be seen that the single point calibration brings the estimated OSNR closer to the OSA measured OSNR. Figure 5 shows the difference between the coherent receiver estimated OSNR and the OSA measured OSNR after calibration vs the OSA measured OSNR and shows that the coherent receiver estimated OSNR was within 0.5 dB of the OSA measured OSNR.

## 6. Conclusion

## Acknowledgments

## References and links

1. | 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. |

2. | H. Y. Choi, Y. Takushima, and Y. C. Chung, “Optical performance monitoring technique using asynchronous amplitude and phase histograms,” Opt. Express |

3. | S. D. Dods and T. B. Anderson, “Optical performance monitoring technique using delay tap asynchronous waveform sampling,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, (OFC/NFOEC) (2006). [CrossRef] |

4. | 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 |

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

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

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

8. | S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. |

9. | S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. |

10. | J. Sijbers, A. J. den Dekker, P. Scheunders, and D. V. Dyck, “Maximum-likelihood estimation of Rician distribution parameters,” IEEE Trans. Med. Imaging |

11. | K. K. Talukdar and W. D. Lawing, “Estimation of the parameters of the Rice distribution,” J. Acoust. Soc. Am. |

12. | C. G. Koay and P. J. Basser, “Analytically exact correction scheme for signal extraction from noisy magnitude MR signals,” J. Mag. Reson. |

13. | International Telecommunication Union, “Forward error correction for high bit-rate DWDM submarine systems,” ITU-T recommendation G.975.1 (2004). |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Subsystems for Optical Networks

**History**

Original Manuscript: October 3, 2011

Revised Manuscript: November 15, 2011

Manuscript Accepted: November 19, 2011

Published: December 2, 2011

**Virtual Issues**

European Conference on Optical Communication 2011 (2011) *Optics Express*

**Citation**

David J. Ives, Benn C. Thomsen, Robert Maher, and Seb J. Savory, "Estimating OSNR of equalised QPSK signals," Opt. Express **19**, B661-B666 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-26-B661

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### References

- 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).
- H. Y. Choi, Y. Takushima, and Y. C. Chung, “Optical performance monitoring technique using asynchronous amplitude and phase histograms,” Opt. Express17, 23953–23958 (2009). [CrossRef]
- S. D. Dods and T. B. Anderson, “Optical performance monitoring technique using delay tap asynchronous waveform sampling,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, (OFC/NFOEC) (2006). [CrossRef]
- 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, 4931–4938 (2010). [CrossRef] [PubMed]
- E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16, 753–791 (2008). [CrossRef] [PubMed]
- S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top Quantum Electron.16, 1164–1179 (2010). [CrossRef]
- J. J. K. O. Ruanaidh and W. J. Fitzgerald, Numerical Bayesian Methods Applied to Signal Processing (Springer-Verlag, 1995).
- S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J.23, 282–332 (1944).
- S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J.24, 46–156 (1945).
- J. Sijbers, A. J. den Dekker, P. Scheunders, and D. V. Dyck, “Maximum-likelihood estimation of Rician distribution parameters,” IEEE Trans. Med. Imaging17, 357–361 (1998). [CrossRef] [PubMed]
- K. K. Talukdar and W. D. Lawing, “Estimation of the parameters of the Rice distribution,” J. Acoust. Soc. Am.89, 1193–1197 (1991). [CrossRef]
- C. G. Koay and P. J. Basser, “Analytically exact correction scheme for signal extraction from noisy magnitude MR signals,” J. Mag. Reson.179, 317–322 (2006). [CrossRef]
- International Telecommunication Union, “Forward error correction for high bit-rate DWDM submarine systems,” ITU-T recommendation G.975.1 (2004).

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