Abstract

We investigate the effect of nonlinear self-phase modulation (SPM) on clock recovery in long-haul coherent optical communication systems with low to moderate baud rates. We consider dual-polarization, multilevel quadrature amplitude modulation, and evaluate conventional timing estimators as well as a modified Cramér–Rao bound. As the latter is hard to compute in the presence of nonlinear channel impairments, we derive an approximate closed-form expression. Contrary to linear channel impairments, the nonlinear impairments can degrade the performance for higher input powers. In addition, the bounds exhibit oscillatory behavior due to the oscillations in the signal spectrum in the presence of SPM.

© 2012 IEEE

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  1. A. S. Tan, H. Wymeersch, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, "The impact of self-phase modulation on digital clock recovery in coherent optical communication," Proc. 36th Eur. Conf. Exhib. Opt. Commun. (2010).
  2. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo, "Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation," Proc. Eur. Conf. Exhib. Opt. Commun. (2006) pp. 43-44.
  3. R. Stolen, C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).
  4. J. Gordon, L. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
  5. A. P. Lau, J. M. Kahn, "Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems," J. Lightw. Technol. 24, 1334-1341 (2006).
  6. K.-P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Commun. 245, 391-398 (2005).
  7. K.-P. Ho, J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightw. Technol. 22, 779-783 (2004).
  8. E. Ip, J. M. Kahn, "Compensation of dispersion and nonlinear impairments using digital backpropagation," J. Lightw. Technol. 26, 3416-3425 (2008).
  9. G. Li, "Recent advances in coherent optical communication," Adv. Opt. Photon. 1, 279-307 (2009).
  10. H. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, 1968).
  11. K. P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Amer. B 20, 1875-1879 (2003).
  12. A. P. Lau, J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightw. Technol. 25, 3008-3016 (2007).
  13. L. Beygi, E. Agrell, M. Karlsson, P. Johannisson, "Signal statistics in fiber-optical channels with polarization multiplexing and self-phase modulation," J. Lightw. Technol. 29, 2379-2386 (2011).
  14. M. Shtaif, "Analytical description of cross-phase modulation in dispersive optical fibers," Opt. Lett. 23, 1191-1193 (1998).
  15. M. E. Marhic, N. Kagi, T.-K. Chiang, L. G. Kazovsky, "Broadband fiber optical parametric amplifiers," Opt. Lett. 21, 573-575 (1996).
  16. H. Zhao, E. Agrell, M. Karlsson, "Unequal bit error probability in coherent QPSK fiber-optic systems using phase modulator based transmitters," Eur. Trans. Telecommun. 19, 895-906 (2008).
  17. E. Ip, J. M. Kahn, "Power spectra of return-to-zero optical signals," J. Lightw. Technol. 24, 1610-1618 (2006).
  18. T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. Rasmussen, "Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset," Proc. 34th Eur. Conf. Opt. Commun. (2008).
  19. A. S. Tan, H. Wymeersch, P. Johannisson, E. Agrell, P. A. Andrekson, M. Karlsson, "An ML-based detector for optical communication in the presence of nonlinear phase noise," Proc. IEEE Int. Conf. Commun. (2011) pp. 1-5.
  20. U. Mengali, A. N. D'Andrea, Synchronization Techniques for Digital Receivers (Plenum, 1997).

2011 (1)

L. Beygi, E. Agrell, M. Karlsson, P. Johannisson, "Signal statistics in fiber-optical channels with polarization multiplexing and self-phase modulation," J. Lightw. Technol. 29, 2379-2386 (2011).

2009 (1)

2008 (2)

H. Zhao, E. Agrell, M. Karlsson, "Unequal bit error probability in coherent QPSK fiber-optic systems using phase modulator based transmitters," Eur. Trans. Telecommun. 19, 895-906 (2008).

E. Ip, J. M. Kahn, "Compensation of dispersion and nonlinear impairments using digital backpropagation," J. Lightw. Technol. 26, 3416-3425 (2008).

2007 (1)

A. P. Lau, J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightw. Technol. 25, 3008-3016 (2007).

2006 (2)

A. P. Lau, J. M. Kahn, "Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems," J. Lightw. Technol. 24, 1334-1341 (2006).

E. Ip, J. M. Kahn, "Power spectra of return-to-zero optical signals," J. Lightw. Technol. 24, 1610-1618 (2006).

2005 (1)

K.-P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Commun. 245, 391-398 (2005).

2004 (1)

K.-P. Ho, J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightw. Technol. 22, 779-783 (2004).

2003 (1)

K. P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Amer. B 20, 1875-1879 (2003).

1998 (1)

M. Shtaif, "Analytical description of cross-phase modulation in dispersive optical fibers," Opt. Lett. 23, 1191-1193 (1998).

1996 (1)

1990 (1)

1978 (1)

R. Stolen, C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).

Adv. Opt. Photon. (1)

Eur. Trans. Telecommun. (1)

H. Zhao, E. Agrell, M. Karlsson, "Unequal bit error probability in coherent QPSK fiber-optic systems using phase modulator based transmitters," Eur. Trans. Telecommun. 19, 895-906 (2008).

J. Lightw. Technol. (2)

A. P. Lau, J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightw. Technol. 25, 3008-3016 (2007).

K.-P. Ho, J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightw. Technol. 22, 779-783 (2004).

J. Lightw. Technol. (4)

E. Ip, J. M. Kahn, "Compensation of dispersion and nonlinear impairments using digital backpropagation," J. Lightw. Technol. 26, 3416-3425 (2008).

A. P. Lau, J. M. Kahn, "Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems," J. Lightw. Technol. 24, 1334-1341 (2006).

L. Beygi, E. Agrell, M. Karlsson, P. Johannisson, "Signal statistics in fiber-optical channels with polarization multiplexing and self-phase modulation," J. Lightw. Technol. 29, 2379-2386 (2011).

E. Ip, J. M. Kahn, "Power spectra of return-to-zero optical signals," J. Lightw. Technol. 24, 1610-1618 (2006).

J. Opt. Soc. Amer. B (1)

K. P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Amer. B 20, 1875-1879 (2003).

Opt. Lett. (1)

M. Shtaif, "Analytical description of cross-phase modulation in dispersive optical fibers," Opt. Lett. 23, 1191-1193 (1998).

Opt. Commun. (1)

K.-P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Commun. 245, 391-398 (2005).

Opt. Lett. (2)

Phys. Rev. A (1)

R. Stolen, C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).

Other (6)

H. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, 1968).

A. S. Tan, H. Wymeersch, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, "The impact of self-phase modulation on digital clock recovery in coherent optical communication," Proc. 36th Eur. Conf. Exhib. Opt. Commun. (2010).

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo, "Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation," Proc. Eur. Conf. Exhib. Opt. Commun. (2006) pp. 43-44.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. Rasmussen, "Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset," Proc. 34th Eur. Conf. Opt. Commun. (2008).

A. S. Tan, H. Wymeersch, P. Johannisson, E. Agrell, P. A. Andrekson, M. Karlsson, "An ML-based detector for optical communication in the presence of nonlinear phase noise," Proc. IEEE Int. Conf. Commun. (2011) pp. 1-5.

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

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