Abstract

In polarization multiplexing based coherent optical transmission, two main kinds of impairements have to be counter-acted: 1) the inter-symbol interference generated by the chromatic dispersion and the polarization mode dispersion and 2) the frequency offset. Usually adaptive approaches are carried out to mitigate them. Since the channel is very slowly time-varying, we propose to combat these impairements by using block-wise methods. Therefore, we introduce two new algorithms: the first one is a block-wise version of blind time equalizer (such as CMA), and the second one estimates the frequency offset in block-wise way. These algorithms are suitable for PSK and QAM constellations. By simulation investigations, we show that they outperform the standard approach in terms of convergence speed only at a moderate expense of computational load. We also experimentally evaluate their performance using 8-PSK real data traces and off-line processing which takes into account other physical impairments such as phase noise and non-linear effects.

© 2011 IEEE

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  1. X. Zhou, J. Yu, "Multi-level, multi-dimensional coding for high-speed and high-spectral-efficiency optical transmission," J. Lightw. Technol. 27, 3641-3653 (2009).
  2. M. Seimetz, "High spectral efficiency phase and quadrature amplitude modulation for optical fiber transmission—Configurations, trends, and reach," Proc. ECOC209 .
  3. M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, M. Yoshida, "256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz," IEEE Photon. Technol. Lett. 22, 185-187 (2010).
  4. C. Fludger, "Coherent equalisation and POLMUX-RZ-DQPSK for robust 100-GE transmission," J. Lightw. Technol. 26, 64-72 (2008).
  5. P. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, B. Zhu, "Generation and 1 200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator," Proc. ECOC'2010 pp. 1-3.
  6. K. Fukuchi, "112 Gb/s optical transponder with PM-QPSK and coherent detection employing parallel FPGA-based real-time digital signal processing, FEC and 100 GbE ethernet interface," Proc. ECOC'2010 .
  7. C. Fludger, J. C. Geyer, T. Duthel, S. Wiese, C. Schulien, "Real-time prototypes for digital coherent receivers," Proc. OFC'2010 .
  8. H. Sun, K.-T. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (2008).
  9. E. M. Ip, J. M. Kahn, "Fiber impairment compensation using coherent detection and digital signal processing," J. Lightw. Technol. 28, 502-518 (2010).
  10. J. Renaudier, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver," J. Lightw. Technol. 26, 36-42 (2008).
  11. M. Seimetz, "Performance of coherent optical square 16-QAM systems based on IQ-transmitters and homodyne receivers with digital phase estimation," Proc. OSA/NFOEC'2006 .
  12. K. Kikuchi, "Electronic post-compenation for non-linear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Exp. 16, 889-896 (2008).
  13. J. Renaudier, "Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks," J. Lightw. Technol. 21, 1816-1818 (2009).
  14. S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2005).
  15. H. Louchet, K. Kuzmin, A. Richter, "Improved DSP algorithms for coherent 16-QAM transmission," Proc. ECOC'2008 .
  16. I. Fatadin, S. Savory, D. Ives, "Blind equalization and carrier phase recovery in a 16-QAM optical coherent system," J. Lightw. Technol. 17, 3042-3049 (2009).
  17. M. Selmi, P. Ciblat, Y. Jaouen, C. Gosset, "Pseudo-Newton based equalization algorithms for QAM coherent optical systems," Proc. OFC'2010 .
  18. H. Bulow, "PMD mitigation techniques and their effectiveness in installed fiber," Proc. OFC'2000 pp. 110-112.
  19. E. Ip, A. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Exp. 16, 753-791 (2008).
  20. S. Salaun, F. Neddam, J. Poirrier, B. Rayguenes, M. Moignard, "Fast SOP variation measurements on WDM systems are OPMDC fast enough?," Proc. ECOC'2009 .
  21. J. Armstrong, "OFDM for optical communications," J. Lightw. Technol. 27, 189-204 (2009).
  22. A. Barbieri, "OFDM versus single-carrier transmission for 100 Gbps optical communication," J. Lightw. Technol. 28, 2537-2551 (2010).
  23. R. Kudo, "Two-stage overlap frequency domain equalization for long-haul optical systems," Proc. OFC'2009 .
  24. S. Houcke, A. Chevreuil, "Characterization of the undesirable global minima of Godard criterion: Case of non circular symmetric complex signals," IEEE Trans. Signal Process. 54, 1917-1922 (2006).
  25. D. Tse, P. Viswanath, Fundamentals of Wireless Communication (Cambridge Univ. Press, 2005).
  26. D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28, (1980).
  27. V. Zarzoso, P. Comon, "Optimal step-size constant modulus algorithm," IEEE Trans. Commun. 56, 10-13 (2008).
  28. L. Mazet, P. Ciblat, P. Loubaton, "Fractionally spaced blind equalization: CMA versus second order based methods," Proc. SPAWC'1999 .
  29. Y. Wang, E. Serpedin, P. Ciblat, "Optimal blind carrier recovery for M-PSK burst transmissions," IEEE Trans. Commun. 51, 1571-1581 (2003).
  30. Y. Wang, E. Serpedin, P. Ciblat, "Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for general QAM modulations," IEEE Trans. Wireless Commun. 2, 1040-1054 (2003).
  31. A. J. Viterbi, A. M. Viterbi, "Non-linear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).
  32. U. Mengali, A. N. D'Andrea, Synchronization Techniques for Digital Receivers (Plenum Press, 1997).
  33. P. Ciblat, M. Ghogho, "Blind NLLS carrier frequency offset estimation for QAM, PSK, and PAM modulations: Performance at low SNR," IEEE Trans. Commun. 54, 1725-1730 (2006).
  34. D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightw. Technol. 24, 12-21 (2006).
  35. L. He, M. G. Amin, C. Reed, R. C. Malkemes, "A hybrid adaptive blind equalization algorithm for QAM signals in wireless communications," IEEE Trans. Signal Process. 52, 2058-2069 (2004).
  36. E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).
  37. S. J. Savory, "Digital coherent optical receivers: Algorithms and subsystems," IEEE J. Sel. Topics Quantum Electron. 16, 1164-1179 (2010).
  38. X. Chongjin, S. Chandrasekhar, "Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver," Proc. OFC'2010 .
  39. A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, L. Raptis, "Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers," IEEE Photon. Technol. Lett. 22, 45-47 (2010).
  40. G. Colavolpe, "Robust multilevel coherent optical systems with linear processing at the receiver," J. Lightw. Technol. 27, 2357-2369 (2009).
  41. T. Foggi, G. Colavolpe, G. Prati, "Stop-and-go algorithm for blind equalization in QAM single-carrier coherent optical systems," IEEE Photon. Lett. 22, 1838-1840 (2010).
  42. M. Seimetz, L. Molle, M. Gruner, D.-D. Gro, R. Freund, "Transmission reach attainable for single-polarization and PolMux coherent star 16QAM systems in comparison to 8PSK and QPSK at 10 Gbaud," Proc. OFC'2009 .

2010

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, M. Yoshida, "256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz," IEEE Photon. Technol. Lett. 22, 185-187 (2010).

E. M. Ip, J. M. Kahn, "Fiber impairment compensation using coherent detection and digital signal processing," J. Lightw. Technol. 28, 502-518 (2010).

A. Barbieri, "OFDM versus single-carrier transmission for 100 Gbps optical communication," J. Lightw. Technol. 28, 2537-2551 (2010).

S. J. Savory, "Digital coherent optical receivers: Algorithms and subsystems," IEEE J. Sel. Topics Quantum Electron. 16, 1164-1179 (2010).

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, L. Raptis, "Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers," IEEE Photon. Technol. Lett. 22, 45-47 (2010).

T. Foggi, G. Colavolpe, G. Prati, "Stop-and-go algorithm for blind equalization in QAM single-carrier coherent optical systems," IEEE Photon. Lett. 22, 1838-1840 (2010).

2009

G. Colavolpe, "Robust multilevel coherent optical systems with linear processing at the receiver," J. Lightw. Technol. 27, 2357-2369 (2009).

X. Zhou, J. Yu, "Multi-level, multi-dimensional coding for high-speed and high-spectral-efficiency optical transmission," J. Lightw. Technol. 27, 3641-3653 (2009).

J. Armstrong, "OFDM for optical communications," J. Lightw. Technol. 27, 189-204 (2009).

J. Renaudier, "Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks," J. Lightw. Technol. 21, 1816-1818 (2009).

I. Fatadin, S. Savory, D. Ives, "Blind equalization and carrier phase recovery in a 16-QAM optical coherent system," J. Lightw. Technol. 17, 3042-3049 (2009).

2008

E. Ip, A. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Exp. 16, 753-791 (2008).

J. Renaudier, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver," J. Lightw. Technol. 26, 36-42 (2008).

K. Kikuchi, "Electronic post-compenation for non-linear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Exp. 16, 889-896 (2008).

C. Fludger, "Coherent equalisation and POLMUX-RZ-DQPSK for robust 100-GE transmission," J. Lightw. Technol. 26, 64-72 (2008).

H. Sun, K.-T. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (2008).

V. Zarzoso, P. Comon, "Optimal step-size constant modulus algorithm," IEEE Trans. Commun. 56, 10-13 (2008).

2007

E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).

2006

P. Ciblat, M. Ghogho, "Blind NLLS carrier frequency offset estimation for QAM, PSK, and PAM modulations: Performance at low SNR," IEEE Trans. Commun. 54, 1725-1730 (2006).

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightw. Technol. 24, 12-21 (2006).

S. Houcke, A. Chevreuil, "Characterization of the undesirable global minima of Godard criterion: Case of non circular symmetric complex signals," IEEE Trans. Signal Process. 54, 1917-1922 (2006).

2005

S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2005).

2004

L. He, M. G. Amin, C. Reed, R. C. Malkemes, "A hybrid adaptive blind equalization algorithm for QAM signals in wireless communications," IEEE Trans. Signal Process. 52, 2058-2069 (2004).

2003

Y. Wang, E. Serpedin, P. Ciblat, "Optimal blind carrier recovery for M-PSK burst transmissions," IEEE Trans. Commun. 51, 1571-1581 (2003).

Y. Wang, E. Serpedin, P. Ciblat, "Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for general QAM modulations," IEEE Trans. Wireless Commun. 2, 1040-1054 (2003).

1983

A. J. Viterbi, A. M. Viterbi, "Non-linear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).

1980

D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28, (1980).

IEEE Photon. Lett.

T. Foggi, G. Colavolpe, G. Prati, "Stop-and-go algorithm for blind equalization in QAM single-carrier coherent optical systems," IEEE Photon. Lett. 22, 1838-1840 (2010).

IEEE Photon. Technol. Lett.

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, L. Raptis, "Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers," IEEE Photon. Technol. Lett. 22, 45-47 (2010).

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, M. Yoshida, "256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz," IEEE Photon. Technol. Lett. 22, 185-187 (2010).

IEEE Trans. Signal Process.

L. He, M. G. Amin, C. Reed, R. C. Malkemes, "A hybrid adaptive blind equalization algorithm for QAM signals in wireless communications," IEEE Trans. Signal Process. 52, 2058-2069 (2004).

IEEE J. Sel. Topics Quantum Electron.

S. J. Savory, "Digital coherent optical receivers: Algorithms and subsystems," IEEE J. Sel. Topics Quantum Electron. 16, 1164-1179 (2010).

IEEE Trans. Commun.

Y. Wang, E. Serpedin, P. Ciblat, "Optimal blind carrier recovery for M-PSK burst transmissions," IEEE Trans. Commun. 51, 1571-1581 (2003).

IEEE Trans. Commun.

D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28, (1980).

V. Zarzoso, P. Comon, "Optimal step-size constant modulus algorithm," IEEE Trans. Commun. 56, 10-13 (2008).

P. Ciblat, M. Ghogho, "Blind NLLS carrier frequency offset estimation for QAM, PSK, and PAM modulations: Performance at low SNR," IEEE Trans. Commun. 54, 1725-1730 (2006).

IEEE Trans. Inf. Theory

A. J. Viterbi, A. M. Viterbi, "Non-linear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).

IEEE Trans. Signal Process.

S. Houcke, A. Chevreuil, "Characterization of the undesirable global minima of Godard criterion: Case of non circular symmetric complex signals," IEEE Trans. Signal Process. 54, 1917-1922 (2006).

IEEE Trans. Wireless Commun.

Y. Wang, E. Serpedin, P. Ciblat, "Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for general QAM modulations," IEEE Trans. Wireless Commun. 2, 1040-1054 (2003).

J. Lightw. Technol.

A. Barbieri, "OFDM versus single-carrier transmission for 100 Gbps optical communication," J. Lightw. Technol. 28, 2537-2551 (2010).

E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).

C. Fludger, "Coherent equalisation and POLMUX-RZ-DQPSK for robust 100-GE transmission," J. Lightw. Technol. 26, 64-72 (2008).

J. Lightw. Technol.

I. Fatadin, S. Savory, D. Ives, "Blind equalization and carrier phase recovery in a 16-QAM optical coherent system," J. Lightw. Technol. 17, 3042-3049 (2009).

J. Lightw. Technol.

J. Renaudier, "Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks," J. Lightw. Technol. 21, 1816-1818 (2009).

X. Zhou, J. Yu, "Multi-level, multi-dimensional coding for high-speed and high-spectral-efficiency optical transmission," J. Lightw. Technol. 27, 3641-3653 (2009).

E. M. Ip, J. M. Kahn, "Fiber impairment compensation using coherent detection and digital signal processing," J. Lightw. Technol. 28, 502-518 (2010).

J. Renaudier, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver," J. Lightw. Technol. 26, 36-42 (2008).

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightw. Technol. 24, 12-21 (2006).

G. Colavolpe, "Robust multilevel coherent optical systems with linear processing at the receiver," J. Lightw. Technol. 27, 2357-2369 (2009).

J. Armstrong, "OFDM for optical communications," J. Lightw. Technol. 27, 189-204 (2009).

Opt. Exp.

S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2005).

H. Sun, K.-T. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (2008).

K. Kikuchi, "Electronic post-compenation for non-linear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Exp. 16, 889-896 (2008).

E. Ip, A. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Exp. 16, 753-791 (2008).

Other

S. Salaun, F. Neddam, J. Poirrier, B. Rayguenes, M. Moignard, "Fast SOP variation measurements on WDM systems are OPMDC fast enough?," Proc. ECOC'2009 .

M. Selmi, P. Ciblat, Y. Jaouen, C. Gosset, "Pseudo-Newton based equalization algorithms for QAM coherent optical systems," Proc. OFC'2010 .

H. Bulow, "PMD mitigation techniques and their effectiveness in installed fiber," Proc. OFC'2000 pp. 110-112.

H. Louchet, K. Kuzmin, A. Richter, "Improved DSP algorithms for coherent 16-QAM transmission," Proc. ECOC'2008 .

M. Seimetz, "Performance of coherent optical square 16-QAM systems based on IQ-transmitters and homodyne receivers with digital phase estimation," Proc. OSA/NFOEC'2006 .

M. Seimetz, "High spectral efficiency phase and quadrature amplitude modulation for optical fiber transmission—Configurations, trends, and reach," Proc. ECOC209 .

P. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, B. Zhu, "Generation and 1 200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator," Proc. ECOC'2010 pp. 1-3.

K. Fukuchi, "112 Gb/s optical transponder with PM-QPSK and coherent detection employing parallel FPGA-based real-time digital signal processing, FEC and 100 GbE ethernet interface," Proc. ECOC'2010 .

C. Fludger, J. C. Geyer, T. Duthel, S. Wiese, C. Schulien, "Real-time prototypes for digital coherent receivers," Proc. OFC'2010 .

U. Mengali, A. N. D'Andrea, Synchronization Techniques for Digital Receivers (Plenum Press, 1997).

X. Chongjin, S. Chandrasekhar, "Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver," Proc. OFC'2010 .

R. Kudo, "Two-stage overlap frequency domain equalization for long-haul optical systems," Proc. OFC'2009 .

D. Tse, P. Viswanath, Fundamentals of Wireless Communication (Cambridge Univ. Press, 2005).

L. Mazet, P. Ciblat, P. Loubaton, "Fractionally spaced blind equalization: CMA versus second order based methods," Proc. SPAWC'1999 .

M. Seimetz, L. Molle, M. Gruner, D.-D. Gro, R. Freund, "Transmission reach attainable for single-polarization and PolMux coherent star 16QAM systems in comparison to 8PSK and QPSK at 10 Gbaud," Proc. OFC'2009 .

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