Abstract

We analytically studied the block length effect (BLE) of decision-aided maximum likelihood (DA ML) carrier phase estimation in coherent optical phase-modulated systems. The results agree well with the trends found using extensive Monte Carlo simulations. In order to eliminate the BLE and accurately recover the carrier phase, an adaptive decision-aided (DA) receiver is proposed that does not require knowledge of the statistical characteristics of the carrier phase, or any parameter to be preset. The simulation results show that using the adaptive DA receiver, the maximum tolerance ratio of the linewidth per laser to symbol rate $(\Delta \nu T)$ at a bit error rate $({\rm BER}) = 10^{- 4}$ has been increased to $2.5 \times 10^{- 4}, 4.1 \times 10^{- 5}$, and $9.5 \times 10^{- 6}$, respectively, for quadrature-, 8- and 16-phase-shift keying formats. The ratio $(\Delta \nu T)$ of the adaptive DA receiver in 16 quadrature amplitude modulation (QAM) is decreased to $2 \times 10^{- 5}$ due to the constellation penalty from $2.5 \times 10^{- 5}$ by using DA ML with optimum memory length, though it consistently performs well without optimizing any parameters as in DA ML. The phase error variance of the adaptive DA receiver is also analytically investigated. In addition, an analog-to-digital converter with bit resolution higher than 4 bits is shown to be sufficient to implement our adaptive DA receiver.

© 2010 IEEE

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  1. A. H. Gnauck, P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightw. Technol. 23, 115-130 (2005).
  2. C. Xu, X. Liu, X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).
  3. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).
  4. R. No'e, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).
  5. E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).
  6. S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Transmission of 42.8 Gbit/s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation," Proc. OFC Paper OTuA1 (2007).
  7. T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S. K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
  8. A. J. Viterbi, A. N. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).
  9. 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).
  10. M. Seimetz, "Laser linewidth limitations for optical systems with high-order modulation employing feed-forward digital carrier phase estimation," Proc. OFC/NFOEC 2008, Paper OTuM2 .
  11. S. Zhang, P. Y. Kam, C. Yu, J. Chen, "Laser linewidth tolerance of decision-aided maximum likelihood phase estimation in coherent optical $M$-ary PSK and QAM systems," IEEE Photon. Technol. Lett. 21, 1075-1077 (2009).
  12. F. Rice, M. Rice, B. Cowley, "A new algorithm for 16 QAM carrier phase estimation using QPSK partitioning," Digital Signal Process. 12, 77-86 (2002).
  13. H. Louchet, K. Kuzmin, A. Richter, "Improved DSP algorithms for coherent 16- QAM transmission," Proc. ECOC (2008).
  14. M. G. Taylor, "Accurate digital phase estimation for coherent detection using a parallel digital processor," Proc. ECOC (2005) pp. 263-264.
  15. E. Ip, J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightw. Technol. 25, 2675-2692 (2007).
  16. L. M. Pessoa, H. M. Salgado, I. Darwazeh, "Joint mitigation of optical impairments and phase estimation in coherent optical systems," Proc. IEEE LEOS Summer Topical Meetings (2008) pp. 169-170.
  17. P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).
  18. S. Zhang, P. Y. Kam, J. Chen, C. Yu, "Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system," Opt. Exp. 17, 703-715 (2009).
  19. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, K. Kikuchi, "Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver," Opt. Exp. 17, 1435-1441 (2009).
  20. S. Haykin, Adaptive Filter Theory (Prentice-Hall, 1986).
  21. W. Shieh, K.-P. Ho, "Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).
  22. W. J. Weber, "Differential encoding for multiple amplitude and phase shift keying systems," IEEE Trans. Commun. COM-26, 385-391 (1978).
  23. P. Y. Kam, Y. K. Some, "Approximate bit error probability analysis of 2 PSK and 4 PSK with partially coherent, symbol-by-symbol detection in carrier phase noise," Proc. Inst. Elect. Eng.—Commun. 146, 120-126 (1999).
  24. Y. Atzmon, M. Nazarathy, "Laser phase noise in coherent and differential optical transmission revisited in the polar domain," J. Lightw. Technol. 27, 19-29 (2009).
  25. C. P. Kaiser, M. Shafi, P. J. Smith, "Analysis methods for optical heterodyne DPSK receivers corrupted by laser phase noise," J. Lightw. Technol. 11, 1820-1830 (1993).
  26. G. Einarsson, J. Strandberg, I. T. Monroy, "Error probability evaluation of optical systems disturbed by phase noise and additive noise," J. Lightw. Technol. 13, 1847-1852 (1995).
  27. L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).
  28. Y. Atzmon, M. Nazarathy, "A gaussian polar model for error rates of differential phase detection impaired by linear, non-linear and laser phase noises," J. Lightw. Technol. 27, 4650-4659 (2009).
  29. A. Atzmon, M. Nazarathy, "Self-coherent differential transmission with decision feedback—Phase noise impairments," Proc. Coherent Opt. Technol. Applications (COTA) (2008).
  30. Y. K. Lizé, "Tolerances and receiver sensitivity penalties of multi-bit delay differential phase shift keying demodulation," IEEE Photon. Technol. Lett. 19, 1874-1876 (2007).
  31. G. Goldfarb, G. Li, "BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing," Opt. Exp. 14, 8043-8053 (2006).
  32. P. Y. Kam, K. H. Chua, X. Yu, "Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics," IEEE Trans. Commun. 46, 1275-1279 (1998).
  33. Y. Li, P. Y. Kam, C. C. Chui, "Sequence detection for MPSK/MQAM with adaptive phase tracking," Phys. Commun. 01.003, (2009).
  34. S. Zhang, X. Li, P. Y. Kam, C. Yu, J. Chen, "Pilot-assisted, decision-aided, maximum likelihood phase estimation in coherent optical phase-modulated systems with nonlinear phase noise," IEEE Photon. Technol. Lett. 22, 380-382 (2010).
  35. M. Nazarathy, X. Liu, L. Christen, Y. Lize, A. Willner, "Self-coherent optical detection of multi-symbol differential phase-shift-keyed transmission," J. Lightw. Technol. 26, 1921-1934 (2008).
  36. X. Liu, S. Chandrasekhar, A. Leven, "Digital self-coherent detection," Opt. Exp. 16, 792-803 (2008).
  37. M. Nazarathy, X. Liu, L. Christen, Y. Lize, A. Willner, "Self-coherent decision-feedback-directed 40 Gbps DQPSK receiver," IEEE Photon. Technol. Lett. 19, 828-839 (2007).

2010 (1)

S. Zhang, X. Li, P. Y. Kam, C. Yu, J. Chen, "Pilot-assisted, decision-aided, maximum likelihood phase estimation in coherent optical phase-modulated systems with nonlinear phase noise," IEEE Photon. Technol. Lett. 22, 380-382 (2010).

2009 (6)

Y. Li, P. Y. Kam, C. C. Chui, "Sequence detection for MPSK/MQAM with adaptive phase tracking," Phys. Commun. 01.003, (2009).

Y. Atzmon, M. Nazarathy, "Laser phase noise in coherent and differential optical transmission revisited in the polar domain," J. Lightw. Technol. 27, 19-29 (2009).

Y. Atzmon, M. Nazarathy, "A gaussian polar model for error rates of differential phase detection impaired by linear, non-linear and laser phase noises," J. Lightw. Technol. 27, 4650-4659 (2009).

S. Zhang, P. Y. Kam, C. Yu, J. Chen, "Laser linewidth tolerance of decision-aided maximum likelihood phase estimation in coherent optical $M$-ary PSK and QAM systems," IEEE Photon. Technol. Lett. 21, 1075-1077 (2009).

S. Zhang, P. Y. Kam, J. Chen, C. Yu, "Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system," Opt. Exp. 17, 703-715 (2009).

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, K. Kikuchi, "Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver," Opt. Exp. 17, 1435-1441 (2009).

2008 (3)

W. Shieh, K.-P. Ho, "Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).

M. Nazarathy, X. Liu, L. Christen, Y. Lize, A. Willner, "Self-coherent optical detection of multi-symbol differential phase-shift-keyed transmission," J. Lightw. Technol. 26, 1921-1934 (2008).

X. Liu, S. Chandrasekhar, A. Leven, "Digital self-coherent detection," Opt. Exp. 16, 792-803 (2008).

2007 (5)

M. Nazarathy, X. Liu, L. Christen, Y. Lize, A. Willner, "Self-coherent decision-feedback-directed 40 Gbps DQPSK receiver," IEEE Photon. Technol. Lett. 19, 828-839 (2007).

Y. K. Lizé, "Tolerances and receiver sensitivity penalties of multi-bit delay differential phase shift keying demodulation," IEEE Photon. Technol. Lett. 19, 1874-1876 (2007).

E. Ip, J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightw. Technol. 25, 2675-2692 (2007).

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

S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Transmission of 42.8 Gbit/s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation," Proc. OFC Paper OTuA1 (2007).

2006 (3)

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S. K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (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).

G. Goldfarb, G. Li, "BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing," Opt. Exp. 14, 8043-8053 (2006).

2005 (2)

R. No'e, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).

A. H. Gnauck, P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightw. Technol. 23, 115-130 (2005).

2004 (1)

C. Xu, X. Liu, X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).

2002 (1)

F. Rice, M. Rice, B. Cowley, "A new algorithm for 16 QAM carrier phase estimation using QPSK partitioning," Digital Signal Process. 12, 77-86 (2002).

1999 (1)

P. Y. Kam, Y. K. Some, "Approximate bit error probability analysis of 2 PSK and 4 PSK with partially coherent, symbol-by-symbol detection in carrier phase noise," Proc. Inst. Elect. Eng.—Commun. 146, 120-126 (1999).

1998 (1)

P. Y. Kam, K. H. Chua, X. Yu, "Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics," IEEE Trans. Commun. 46, 1275-1279 (1998).

1995 (1)

G. Einarsson, J. Strandberg, I. T. Monroy, "Error probability evaluation of optical systems disturbed by phase noise and additive noise," J. Lightw. Technol. 13, 1847-1852 (1995).

1993 (1)

C. P. Kaiser, M. Shafi, P. J. Smith, "Analysis methods for optical heterodyne DPSK receivers corrupted by laser phase noise," J. Lightw. Technol. 11, 1820-1830 (1993).

1986 (1)

P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).

1983 (1)

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

1978 (1)

W. J. Weber, "Differential encoding for multiple amplitude and phase shift keying systems," IEEE Trans. Commun. COM-26, 385-391 (1978).

Digital Signal Process. (1)

F. Rice, M. Rice, B. Cowley, "A new algorithm for 16 QAM carrier phase estimation using QPSK partitioning," Digital Signal Process. 12, 77-86 (2002).

IEEE J. Sel. Top. Quantum Electron. (1)

C. Xu, X. Liu, X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).

IEEE Photon. Technol. Lett. (6)

R. No'e, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S. K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).

S. Zhang, P. Y. Kam, C. Yu, J. Chen, "Laser linewidth tolerance of decision-aided maximum likelihood phase estimation in coherent optical $M$-ary PSK and QAM systems," IEEE Photon. Technol. Lett. 21, 1075-1077 (2009).

Y. K. Lizé, "Tolerances and receiver sensitivity penalties of multi-bit delay differential phase shift keying demodulation," IEEE Photon. Technol. Lett. 19, 1874-1876 (2007).

S. Zhang, X. Li, P. Y. Kam, C. Yu, J. Chen, "Pilot-assisted, decision-aided, maximum likelihood phase estimation in coherent optical phase-modulated systems with nonlinear phase noise," IEEE Photon. Technol. Lett. 22, 380-382 (2010).

M. Nazarathy, X. Liu, L. Christen, Y. Lize, A. Willner, "Self-coherent decision-feedback-directed 40 Gbps DQPSK receiver," IEEE Photon. Technol. Lett. 19, 828-839 (2007).

IEEE Trans. Commun. (3)

P. Y. Kam, K. H. Chua, X. Yu, "Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics," IEEE Trans. Commun. 46, 1275-1279 (1998).

W. J. Weber, "Differential encoding for multiple amplitude and phase shift keying systems," IEEE Trans. Commun. COM-26, 385-391 (1978).

P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).

IEEE Trans. Inf. Theory (1)

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

J. Lightw. Technol. (9)

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).

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

A. H. Gnauck, P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightw. Technol. 23, 115-130 (2005).

E. Ip, J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightw. Technol. 25, 2675-2692 (2007).

Y. Atzmon, M. Nazarathy, "Laser phase noise in coherent and differential optical transmission revisited in the polar domain," J. Lightw. Technol. 27, 19-29 (2009).

C. P. Kaiser, M. Shafi, P. J. Smith, "Analysis methods for optical heterodyne DPSK receivers corrupted by laser phase noise," J. Lightw. Technol. 11, 1820-1830 (1993).

G. Einarsson, J. Strandberg, I. T. Monroy, "Error probability evaluation of optical systems disturbed by phase noise and additive noise," J. Lightw. Technol. 13, 1847-1852 (1995).

M. Nazarathy, X. Liu, L. Christen, Y. Lize, A. Willner, "Self-coherent optical detection of multi-symbol differential phase-shift-keyed transmission," J. Lightw. Technol. 26, 1921-1934 (2008).

Y. Atzmon, M. Nazarathy, "A gaussian polar model for error rates of differential phase detection impaired by linear, non-linear and laser phase noises," J. Lightw. Technol. 27, 4650-4659 (2009).

Opt. Exp. (5)

G. Goldfarb, G. Li, "BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing," Opt. Exp. 14, 8043-8053 (2006).

X. Liu, S. Chandrasekhar, A. Leven, "Digital self-coherent detection," Opt. Exp. 16, 792-803 (2008).

S. Zhang, P. Y. Kam, J. Chen, C. Yu, "Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system," Opt. Exp. 17, 703-715 (2009).

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, K. Kikuchi, "Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver," Opt. Exp. 17, 1435-1441 (2009).

W. Shieh, K.-P. Ho, "Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).

Phys. Commun. (1)

Y. Li, P. Y. Kam, C. C. Chui, "Sequence detection for MPSK/MQAM with adaptive phase tracking," Phys. Commun. 01.003, (2009).

Proc. Inst. Elect. Eng.—Commun. (1)

P. Y. Kam, Y. K. Some, "Approximate bit error probability analysis of 2 PSK and 4 PSK with partially coherent, symbol-by-symbol detection in carrier phase noise," Proc. Inst. Elect. Eng.—Commun. 146, 120-126 (1999).

Proc. OFC Paper OTuA1 (1)

S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Transmission of 42.8 Gbit/s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation," Proc. OFC Paper OTuA1 (2007).

Other (8)

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).

M. Seimetz, "Laser linewidth limitations for optical systems with high-order modulation employing feed-forward digital carrier phase estimation," Proc. OFC/NFOEC 2008, Paper OTuM2 .

S. Haykin, Adaptive Filter Theory (Prentice-Hall, 1986).

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

M. G. Taylor, "Accurate digital phase estimation for coherent detection using a parallel digital processor," Proc. ECOC (2005) pp. 263-264.

L. M. Pessoa, H. M. Salgado, I. Darwazeh, "Joint mitigation of optical impairments and phase estimation in coherent optical systems," Proc. IEEE LEOS Summer Topical Meetings (2008) pp. 169-170.

L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).

A. Atzmon, M. Nazarathy, "Self-coherent differential transmission with decision feedback—Phase noise impairments," Proc. Coherent Opt. Technol. Applications (COTA) (2008).

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