Abstract

Modern spectrally efficient optical communication systems utilize polarization-multiplexed coherent transmission in complex modulation format. Coherent receivers used in these systems measure the amplitude and phase of the optical signals for both orthogonally polarized components carrying information. Knowledge of the amplitude and phase of the optical field, in combination with digital signal processing, gives the receiver an inherent metrology and performance monitoring capability. As the optical signal propagates from the transmitter over optical fiber to the receiver, a signal transformation and degradation is expected. The receiver observes the properties of the transmitted optical signal as degraded by the impairments of the transmission medium. The details of monitoring optical signal parameters and link impairments are the focus of this paper. The optical signal parameters include polarization state and residual carrier phase; optical link impairments include chromatic dispersion and polarization mode dispersion. Two distinct techniques are presented: one based on Stokes space analysis, and the other on Kalman filtering. The Stokes space techniques are modulation-format independent and do not require demodulation. The Kalman filtering provides optimal estimation of the physical quantities that describe the optical signal and the optical medium.

© 2012 IEEE

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  1. Optical Performance Monitoring: Advanced Techniques for Next-Generation Photonic Networks (Elsevier, 2010).
  2. R. A. Shafik, S. Rahman, A. H. M. R. Islam, "On the extended relationships among EVM, BER and SNR as performance metrics," Proc. IEEE Int. Conf. Electr. Comput. Eng. (2006) pp. 408-411.
  3. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, J. Leuthold, "Error vector magnitude as a performance measure for advanced modulation formats," IEEE Photon. Technol. Lett. 24, 61-63 (2012).
  4. F. N. Hauske, M. Kuschnerov, B. Spinnler, B. Lankl, "Optical performance monitoring in digital coherent receivers," J. Lightw. Technol. 27, 3623-3631 (2009).
  5. J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, B. Schmauss, "Performance monitoring using coherent receivers," Proc. Opt. Fiber Commun. Conf. (2009) pp. 22-26.
  6. E. Hecht, Optics (Addison-Wesley, 1987).
  7. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  8. C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, "Polarization dispersion and principal states in a 147-km undersea lightwave cable," J. Lightw. Technol. 6, 1185-1190 (1988).
  9. B. Szafraniec, B. Nebendahl, T. Marshall, "Polarization demultiplexing in stokes space," Opt. Exp. 18, 17928-17939 (2010).
  10. B. Szafraniec, "Performance monitoring and measurement techniques for coherent systems," Proc. Opt. Fiber Commun. Conf. (2012) pp. 4-8.
  11. F. Gardner, "A BPSK/QPSK timing-error detector for sampled receivers," IEEE Trans. Commun. COM-34, 423-429 (1986).
  12. H. Meyr, M. Moeneclaey, S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing (Wiley, 1998).
  13. F. N. Hauske, Z. Zhang, C. Li, C. Xie, Q. Xiong, "Precise, robust and least complexity CD estimation," Proc. Opt. Fiber Commun. Conf. (2011) pp. 6-10.
  14. R. C. Jones, "A new calculus for the treatment of optical systems," J. Opt. Soc. Amer. 31, 488-493 (1941).
  15. R. C. Jones, "A new calculus for the treatment of optical systems. VII. Properties of the N-matrices," J. Opt. Soc. Amer. 38, 671-683 (1948).
  16. D. M. Baney, B. Szafraniec, "Elementary matrix method for dispersion analysis in optical systems," J. Lightw. Technol. 28, 294-307 (2010).
  17. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series (MIT Press, 1949).
  18. R. E. Kalman, "A new approach to linear filtering and prediction problems," Trans. ASME—J. Basic Eng. 82(D), 35-45 (1960).
  19. R. G. Brown, P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering (Wiley, 1997).
  20. S. Haykin, Adaptive Filter Theory (Prentice-Hall, 2002).
  21. J. Treichler, B. Agee, "A new approach to multipath correction of constant modulus signals," IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 459-472 (1983).
  22. S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2008).
  23. T. Marshall, B. Szafraniec, B. Nebendahl, "Kalman filter carrier and polarization-state tracking," Opt. Lett. 35, 2203-2205 (2010).
  24. B. Szafraniec, T. Marshall, B. Nebendahl, Kalman filter based estimation and demodulation of complex signals Agilent Technologies Inc.Santa ClaraCA Appl. Note 5990-6409EN (2010).
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  27. J. Yu, X. Zhou, "Ultra-high-capacity DWDM transmission system for 100 G and beyond," IEEE Commun. Mag. 48, S56-S64 (2010).
  28. P. Boffi, P. Martelli, M. Cirigliano, M. Magarini, M. Martinelli, M. Bertolini, M. Pepe, D. Di Mola, G. Gavioli, "PDM-16QAM transmission performance over uncompensated fiber links," Opt. Exp. 19, 21898-21903 (2011).
  29. H. Zhang, Z. Tao, L. Liu, S. Oda, T. Hoshida, J. C. Rasmussen, "Polarization demultiplexing based on independent component analysis in optical coherent receivers," Proc. Eur. Conf. Opt. Commun. (2008) pp. 1-2.
  30. R. Bronson, Matrix Methods—An Introduction (Academic, 1970).

2012

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, J. Leuthold, "Error vector magnitude as a performance measure for advanced modulation formats," IEEE Photon. Technol. Lett. 24, 61-63 (2012).

2011

P. Boffi, P. Martelli, M. Cirigliano, M. Magarini, M. Martinelli, M. Bertolini, M. Pepe, D. Di Mola, G. Gavioli, "PDM-16QAM transmission performance over uncompensated fiber links," Opt. Exp. 19, 21898-21903 (2011).

2010

T. Marshall, B. Szafraniec, B. Nebendahl, "Kalman filter carrier and polarization-state tracking," Opt. Lett. 35, 2203-2205 (2010).

J. Yu, X. Zhou, "Ultra-high-capacity DWDM transmission system for 100 G and beyond," IEEE Commun. Mag. 48, S56-S64 (2010).

B. Szafraniec, B. Nebendahl, T. Marshall, "Polarization demultiplexing in stokes space," Opt. Exp. 18, 17928-17939 (2010).

D. M. Baney, B. Szafraniec, "Elementary matrix method for dispersion analysis in optical systems," J. Lightw. Technol. 28, 294-307 (2010).

2009

F. N. Hauske, M. Kuschnerov, B. Spinnler, B. Lankl, "Optical performance monitoring in digital coherent receivers," J. Lightw. Technol. 27, 3623-3631 (2009).

2008

S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2008).

1988

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, "Polarization dispersion and principal states in a 147-km undersea lightwave cable," J. Lightw. Technol. 6, 1185-1190 (1988).

1986

F. Gardner, "A BPSK/QPSK timing-error detector for sampled receivers," IEEE Trans. Commun. COM-34, 423-429 (1986).

1983

J. Treichler, B. Agee, "A new approach to multipath correction of constant modulus signals," IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 459-472 (1983).

1960

R. E. Kalman, "A new approach to linear filtering and prediction problems," Trans. ASME—J. Basic Eng. 82(D), 35-45 (1960).

1948

R. C. Jones, "A new calculus for the treatment of optical systems. VII. Properties of the N-matrices," J. Opt. Soc. Amer. 38, 671-683 (1948).

1941

R. C. Jones, "A new calculus for the treatment of optical systems," J. Opt. Soc. Amer. 31, 488-493 (1941).

IEEE Commun. Mag.

J. Yu, X. Zhou, "Ultra-high-capacity DWDM transmission system for 100 G and beyond," IEEE Commun. Mag. 48, S56-S64 (2010).

IEEE Photon. Technol. Lett.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, J. Leuthold, "Error vector magnitude as a performance measure for advanced modulation formats," IEEE Photon. Technol. Lett. 24, 61-63 (2012).

IEEE Trans. Acoust. Speech Signal Process.

J. Treichler, B. Agee, "A new approach to multipath correction of constant modulus signals," IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 459-472 (1983).

IEEE Trans. Commun.

F. Gardner, "A BPSK/QPSK timing-error detector for sampled receivers," IEEE Trans. Commun. COM-34, 423-429 (1986).

J. Lightw. Technol.

D. M. Baney, B. Szafraniec, "Elementary matrix method for dispersion analysis in optical systems," J. Lightw. Technol. 28, 294-307 (2010).

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, "Polarization dispersion and principal states in a 147-km undersea lightwave cable," J. Lightw. Technol. 6, 1185-1190 (1988).

J. Opt. Soc. Amer.

R. C. Jones, "A new calculus for the treatment of optical systems. VII. Properties of the N-matrices," J. Opt. Soc. Amer. 38, 671-683 (1948).

J. Lightw. Technol.

F. N. Hauske, M. Kuschnerov, B. Spinnler, B. Lankl, "Optical performance monitoring in digital coherent receivers," J. Lightw. Technol. 27, 3623-3631 (2009).

J. Opt. Soc. Amer.

R. C. Jones, "A new calculus for the treatment of optical systems," J. Opt. Soc. Amer. 31, 488-493 (1941).

Opt. Exp.

B. Szafraniec, B. Nebendahl, T. Marshall, "Polarization demultiplexing in stokes space," Opt. Exp. 18, 17928-17939 (2010).

S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2008).

P. Boffi, P. Martelli, M. Cirigliano, M. Magarini, M. Martinelli, M. Bertolini, M. Pepe, D. Di Mola, G. Gavioli, "PDM-16QAM transmission performance over uncompensated fiber links," Opt. Exp. 19, 21898-21903 (2011).

Opt. Lett.

Trans. ASME—J. Basic Eng.

R. E. Kalman, "A new approach to linear filtering and prediction problems," Trans. ASME—J. Basic Eng. 82(D), 35-45 (1960).

Other

R. G. Brown, P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering (Wiley, 1997).

S. Haykin, Adaptive Filter Theory (Prentice-Hall, 2002).

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series (MIT Press, 1949).

H. Meyr, M. Moeneclaey, S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing (Wiley, 1998).

F. N. Hauske, Z. Zhang, C. Li, C. Xie, Q. Xiong, "Precise, robust and least complexity CD estimation," Proc. Opt. Fiber Commun. Conf. (2011) pp. 6-10.

B. Szafraniec, "Performance monitoring and measurement techniques for coherent systems," Proc. Opt. Fiber Commun. Conf. (2012) pp. 4-8.

Optical Performance Monitoring: Advanced Techniques for Next-Generation Photonic Networks (Elsevier, 2010).

R. A. Shafik, S. Rahman, A. H. M. R. Islam, "On the extended relationships among EVM, BER and SNR as performance metrics," Proc. IEEE Int. Conf. Electr. Comput. Eng. (2006) pp. 408-411.

J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, B. Schmauss, "Performance monitoring using coherent receivers," Proc. Opt. Fiber Commun. Conf. (2009) pp. 22-26.

E. Hecht, Optics (Addison-Wesley, 1987).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

H. Zhang, Z. Tao, L. Liu, S. Oda, T. Hoshida, J. C. Rasmussen, "Polarization demultiplexing based on independent component analysis in optical coherent receivers," Proc. Eur. Conf. Opt. Commun. (2008) pp. 1-2.

R. Bronson, Matrix Methods—An Introduction (Academic, 1970).

B. Szafraniec, T. Marshall, B. Nebendahl, Kalman filter based estimation and demodulation of complex signals Agilent Technologies Inc.Santa ClaraCA Appl. Note 5990-6409EN (2010).

G. Welch, G. Bishop, An introduction to the Kalman filter Dept. Comput. Sci., Univ. North Carolina,Chapel Hill Tech. Rep. TR 95-041 (2006).

J. Renaudier, O. Bertran-Pardo, M. Salsi, H. Mardoyan, P. Tran, G. Charlet, S. Bigo, "Will 100 Gb/s resist higher bit rates?," Proc. Eur. Conf. Opt. Commun. (2011) pp. 18-22.

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