Abstract

In this paper we show that, in hybrid wavelength division multiplexed systems, the performance of high datatrate QPSK channels impaired by cross-phase modulation (XPM) induced by the lower rate OOK channels can be simply estimated by an extension of a well-known linear model for XPM, and novel analytical expressions of the sensitivity penalty are provided. From such a model we prove that the reported QPSK penalty decrease with QPSK baudrate increase should be attributed to the action of the phase estimation process rather than to the walkoff effect. The model also simply shows how coherent QPSK is more affected by XPM than incoherent DQPSK, and allows to infer that even more impact is expected when the baudrate is further reduced through polarization multiplexing.

© 2009 IEEE

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  1. A. Gnauck, G. Charlet, P. Tran, P. Winzer, C. Doerr, J. Centanni, E. Burrows, T. Kawanishi, T. Sakamoto, K. Higuma, "25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals," J. Lightw. Technol. 26, 79-84 (2008).
  2. H. Sun, K.-T. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (2008).
  3. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, S. Bigo, "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).
  4. C. Fürst, "43 Gb/s RZ-DQPSK DWDM field trial over 1047 km with mixed 43 Gb/s and 10.7 Gb/s channels at 50 and 100 GHz channel spacing," Proc. ECOC 2006 (2006) PDP Th4.1.4.
  5. H. Griesser, "43 Gb/s RZ-DQPSK transmission over a 660 km 10.7 Gb/s DWDM link," Proc. ECOC 2006 (2006) paper Th1.6.6.
  6. S. Chandrasekhar, X. Liu, "Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid," IEEE Photon. Technol. Lett. 19, 1801-1803 (2007).
  7. S. Bigo, G. Charlet, O. Bertrand Pardo, J. Renaudier, "Characterization of the impact of non-linear effects in coherent transmission experiments," Digest of the IEEE/LEOS Summer Topical Meetings 2008 (2008) pp. 125-126.
  8. O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, S. Bigo, "Nonlinearity limitations when mixing 40-Gb/s coherent PDM-QPSK channels with preexisting 10-Gb/s NRZ channels," IEEE Photon. Technol. Lett. 20, 1314-1316 (2008).
  9. H. Griesser, J. Elbers, "Influence of cross-phase modulation induced nonlinear phase noise on DQPSK signals from neighbouring OOK channels," Proc. ECOC 2005 (2005) paper Tu1. 2.2.
  10. K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).
  11. R. Luis, B. Clouet, A. Teixeira, P. Monteiro, "Analytical modeling of the cross-phase modulation-induced degradation in mixed DPSK and ASK transmission systems," Proc. ICTON 2007 (2007) paper Mo.P.17.
  12. R. Luis, B. Clouet, A. Teixeira, P. Monteiro, "Pump-probe analysis of the cross-phase modulation degradation induced by 10 Gbit/s amplitude-shift-keyed signals on 40 Gbit/s DPSK signals," Opt. Lett. 32, 2786 (2007).
  13. O. Vassilieva, T. Hoshida, J. C. Rasmussen, T. Naito, "Symbol rate dependency of XPM-induced phase noise penalty on QPSK-based modulation formats," Proc. ECOC 2008 (2008) paper We.1.E.4.
  14. N. Blachman, "The effect of phase error on DPSK error probability," IEEE Trans. Commun. 29, 364-365 (1981).
  15. K.-P. Ho, "The effect of interferometer phase error on direct-detection DPSK and DQPSK signals," IEEE Photon. Technol. Lett. 16, 308-310 (2004).
  16. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).
  17. J. Gordon, L. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett 15, 1351-1353 (1990).
  18. T.-K. Chiang, N. Kagi, M. Marhic, L. Kazovsky, "Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 14, 249-260 (1996).
  19. A. Bononi, C. Francia, G. Bellotti, "Impulse response of cross-phase modulation filters in multi-span transmission systems with dispersion compensation," Opt. Fiber Technol. 4, 371-383 (1998).
  20. M. Varani, G. Bellotti, A. Bononi, C. Francia, "Analysis of cross-phase modulation induced intensity noise in high-speed dispersion compensated transmission systems," Proc. LEOS '98 (1998) paper WBB4.
  21. A. Bononi, G. Bellotti, M. Varani, C. Francia, Optical Networking (Springer-Verlag, 1999) pp. 383-398.
  22. A. Cartaxo, "Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 17, 178-190 (1999).
  23. R. Hui, Y. Wang, K. Demarest, C. Allen, "Frequency response of cross-phase modulation in multispan WDM optical fiber systems," IEEE Photon. Technol. Lett. 10, 1271-1273 (1998).
  24. A. Cartaxo, "Impact of modulation frequency on cross-phase modulation effect in intensity modulation-direct detection WDM systems," IEEE Photon. Technol. Lett. 10, 1268-1270 (1998).
  25. G. Bellotti, M. Varani, C. Francia, A. Bononi, "Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation," IEEE Photon. Technol. Lett. 10, 1745-1747 (1998).
  26. R. Killey, H. Thiele, V. Mikhailov, P. Bayvel, "Prediction of transmission penalties due to cross-phase modulation in WDM systems using a simplified technique," IEEE Photon. Technol. Lett. 12, 804-806 (2000).
  27. A. Bononi, P. Serena, M. Bertolini, "Unified analysis of weakly-nonlinear dispersion-managed optical transmission systems from perturbative approach," C. R. Physique 9, 947-962 (2008).
  28. R. Luis, A. Cartaxo, "Analytical characterization of SPM impact on XPM-induced degradation in dispersion-compensated WDM systems," J. Lightw. Technol. 23, 1503-1513 (2005).
  29. Y. Frignac, J.-C. Antona, S. Bigo, "Enhanced analytical engineering rule for fast optimization dispersion maps in 40 Gbit/s-based transmission," Proc. OFC 2004 (2008) Paper OTuN3.
  30. A. Bononi, P. Serena, A. Orlandini, "A unified design framework for single-channel dispersion-managed terrestrial systems," J. Lightw. Technol. 26, 3617-3631 (2008).
  31. E. Bedrosian, S. Rice, "Distortion and crosstalk of linearly filtered, angle modulated signals," Proc. IEEE 56, 2-13 (1968).
  32. A. J. Viterbi, A. M. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory 29, 543-551 (1983).
  33. E. Ip, J. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightw. Technol. 25, 2675-2692 (2007).
  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. M. Bertolini, P. Serena, N. Rossi, A. Bononi, "Numerical Monte Carlo comparison between coherent PDM-QPSK/OOK and incoherent DQPSK/OOK hybrid systems," Proc. ECOC2008 (2008) paper P.4.15.
  36. P. Serena, A. Orlandini, A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).
  37. G. Nicholson, "Probability of error for optical heterodyne DPSK system with quantum phase noise," Electron. Lett. 20, 1005-1007 (1984) 22.
  38. R. Pawula, S. Rice, J. Roberts, "Distribution of the phase angle between two vectors perturbed by Gaussian noise," IEEE Trans. Commun. 30, 1828-1841 (1982).
  39. J. Wang, K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightw. Technol. 10, 96-100 (1992).

2008 (6)

A. Gnauck, G. Charlet, P. Tran, P. Winzer, C. Doerr, J. Centanni, E. Burrows, T. Kawanishi, T. Sakamoto, K. Higuma, "25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals," J. Lightw. Technol. 26, 79-84 (2008).

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

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, S. Bigo, "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).

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, S. Bigo, "Nonlinearity limitations when mixing 40-Gb/s coherent PDM-QPSK channels with preexisting 10-Gb/s NRZ channels," IEEE Photon. Technol. Lett. 20, 1314-1316 (2008).

A. Bononi, P. Serena, M. Bertolini, "Unified analysis of weakly-nonlinear dispersion-managed optical transmission systems from perturbative approach," C. R. Physique 9, 947-962 (2008).

A. Bononi, P. Serena, A. Orlandini, "A unified design framework for single-channel dispersion-managed terrestrial systems," J. Lightw. Technol. 26, 3617-3631 (2008).

2007 (3)

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

R. Luis, B. Clouet, A. Teixeira, P. Monteiro, "Pump-probe analysis of the cross-phase modulation degradation induced by 10 Gbit/s amplitude-shift-keyed signals on 40 Gbit/s DPSK signals," Opt. Lett. 32, 2786 (2007).

S. Chandrasekhar, X. Liu, "Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid," IEEE Photon. Technol. Lett. 19, 1801-1803 (2007).

2006 (2)

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).

P. Serena, A. Orlandini, A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).

2005 (1)

R. Luis, A. Cartaxo, "Analytical characterization of SPM impact on XPM-induced degradation in dispersion-compensated WDM systems," J. Lightw. Technol. 23, 1503-1513 (2005).

2004 (2)

K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).

K.-P. Ho, "The effect of interferometer phase error on direct-detection DPSK and DQPSK signals," IEEE Photon. Technol. Lett. 16, 308-310 (2004).

2000 (1)

R. Killey, H. Thiele, V. Mikhailov, P. Bayvel, "Prediction of transmission penalties due to cross-phase modulation in WDM systems using a simplified technique," IEEE Photon. Technol. Lett. 12, 804-806 (2000).

1999 (1)

A. Cartaxo, "Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 17, 178-190 (1999).

1998 (4)

R. Hui, Y. Wang, K. Demarest, C. Allen, "Frequency response of cross-phase modulation in multispan WDM optical fiber systems," IEEE Photon. Technol. Lett. 10, 1271-1273 (1998).

A. Cartaxo, "Impact of modulation frequency on cross-phase modulation effect in intensity modulation-direct detection WDM systems," IEEE Photon. Technol. Lett. 10, 1268-1270 (1998).

G. Bellotti, M. Varani, C. Francia, A. Bononi, "Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation," IEEE Photon. Technol. Lett. 10, 1745-1747 (1998).

A. Bononi, C. Francia, G. Bellotti, "Impulse response of cross-phase modulation filters in multi-span transmission systems with dispersion compensation," Opt. Fiber Technol. 4, 371-383 (1998).

1996 (1)

T.-K. Chiang, N. Kagi, M. Marhic, L. Kazovsky, "Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 14, 249-260 (1996).

1992 (1)

J. Wang, K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightw. Technol. 10, 96-100 (1992).

1990 (1)

J. Gordon, L. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett 15, 1351-1353 (1990).

1984 (1)

G. Nicholson, "Probability of error for optical heterodyne DPSK system with quantum phase noise," Electron. Lett. 20, 1005-1007 (1984) 22.

1983 (1)

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

1982 (1)

R. Pawula, S. Rice, J. Roberts, "Distribution of the phase angle between two vectors perturbed by Gaussian noise," IEEE Trans. Commun. 30, 1828-1841 (1982).

1981 (1)

N. Blachman, "The effect of phase error on DPSK error probability," IEEE Trans. Commun. 29, 364-365 (1981).

1968 (1)

E. Bedrosian, S. Rice, "Distortion and crosstalk of linearly filtered, angle modulated signals," Proc. IEEE 56, 2-13 (1968).

C. R. Physique (1)

A. Bononi, P. Serena, M. Bertolini, "Unified analysis of weakly-nonlinear dispersion-managed optical transmission systems from perturbative approach," C. R. Physique 9, 947-962 (2008).

Electron. Lett. (1)

G. Nicholson, "Probability of error for optical heterodyne DPSK system with quantum phase noise," Electron. Lett. 20, 1005-1007 (1984) 22.

IEEE Photon. Technol. Lett. (1)

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, S. Bigo, "Nonlinearity limitations when mixing 40-Gb/s coherent PDM-QPSK channels with preexisting 10-Gb/s NRZ channels," IEEE Photon. Technol. Lett. 20, 1314-1316 (2008).

IEEE Trans. Commun. (1)

R. Pawula, S. Rice, J. Roberts, "Distribution of the phase angle between two vectors perturbed by Gaussian noise," IEEE Trans. Commun. 30, 1828-1841 (1982).

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

K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).

IEEE Photon. Technol. Lett. (1)

G. Bellotti, M. Varani, C. Francia, A. Bononi, "Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation," IEEE Photon. Technol. Lett. 10, 1745-1747 (1998).

IEEE Photon. Technol. Lett. (1)

R. Hui, Y. Wang, K. Demarest, C. Allen, "Frequency response of cross-phase modulation in multispan WDM optical fiber systems," IEEE Photon. Technol. Lett. 10, 1271-1273 (1998).

IEEE Photon. Technol. Lett. (4)

A. Cartaxo, "Impact of modulation frequency on cross-phase modulation effect in intensity modulation-direct detection WDM systems," IEEE Photon. Technol. Lett. 10, 1268-1270 (1998).

R. Killey, H. Thiele, V. Mikhailov, P. Bayvel, "Prediction of transmission penalties due to cross-phase modulation in WDM systems using a simplified technique," IEEE Photon. Technol. Lett. 12, 804-806 (2000).

K.-P. Ho, "The effect of interferometer phase error on direct-detection DPSK and DQPSK signals," IEEE Photon. Technol. Lett. 16, 308-310 (2004).

S. Chandrasekhar, X. Liu, "Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid," IEEE Photon. Technol. Lett. 19, 1801-1803 (2007).

IEEE Trans. Commun. (1)

N. Blachman, "The effect of phase error on DPSK error probability," IEEE Trans. Commun. 29, 364-365 (1981).

IEEE Trans. Inf. Theory (1)

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

J. Lightw. Technol. (1)

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, S. Bigo, "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).

J. Lightw. Technol. (1)

J. Wang, K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightw. Technol. 10, 96-100 (1992).

J. Lightw. Technol. (8)

A. Cartaxo, "Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 17, 178-190 (1999).

P. Serena, A. Orlandini, A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).

A. Gnauck, G. Charlet, P. Tran, P. Winzer, C. Doerr, J. Centanni, E. Burrows, T. Kawanishi, T. Sakamoto, K. Higuma, "25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals," J. Lightw. Technol. 26, 79-84 (2008).

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

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).

R. Luis, A. Cartaxo, "Analytical characterization of SPM impact on XPM-induced degradation in dispersion-compensated WDM systems," J. Lightw. Technol. 23, 1503-1513 (2005).

A. Bononi, P. Serena, A. Orlandini, "A unified design framework for single-channel dispersion-managed terrestrial systems," J. Lightw. Technol. 26, 3617-3631 (2008).

T.-K. Chiang, N. Kagi, M. Marhic, L. Kazovsky, "Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 14, 249-260 (1996).

Opt. Exp. (1)

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

Opt. Fiber Technol. (1)

A. Bononi, C. Francia, G. Bellotti, "Impulse response of cross-phase modulation filters in multi-span transmission systems with dispersion compensation," Opt. Fiber Technol. 4, 371-383 (1998).

Opt. Lett (1)

J. Gordon, L. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett 15, 1351-1353 (1990).

Opt. Lett. (1)

Proc. IEEE (1)

E. Bedrosian, S. Rice, "Distortion and crosstalk of linearly filtered, angle modulated signals," Proc. IEEE 56, 2-13 (1968).

Other (11)

Y. Frignac, J.-C. Antona, S. Bigo, "Enhanced analytical engineering rule for fast optimization dispersion maps in 40 Gbit/s-based transmission," Proc. OFC 2004 (2008) Paper OTuN3.

M. Bertolini, P. Serena, N. Rossi, A. Bononi, "Numerical Monte Carlo comparison between coherent PDM-QPSK/OOK and incoherent DQPSK/OOK hybrid systems," Proc. ECOC2008 (2008) paper P.4.15.

M. Varani, G. Bellotti, A. Bononi, C. Francia, "Analysis of cross-phase modulation induced intensity noise in high-speed dispersion compensated transmission systems," Proc. LEOS '98 (1998) paper WBB4.

A. Bononi, G. Bellotti, M. Varani, C. Francia, Optical Networking (Springer-Verlag, 1999) pp. 383-398.

O. Vassilieva, T. Hoshida, J. C. Rasmussen, T. Naito, "Symbol rate dependency of XPM-induced phase noise penalty on QPSK-based modulation formats," Proc. ECOC 2008 (2008) paper We.1.E.4.

R. Luis, B. Clouet, A. Teixeira, P. Monteiro, "Analytical modeling of the cross-phase modulation-induced degradation in mixed DPSK and ASK transmission systems," Proc. ICTON 2007 (2007) paper Mo.P.17.

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

C. Fürst, "43 Gb/s RZ-DQPSK DWDM field trial over 1047 km with mixed 43 Gb/s and 10.7 Gb/s channels at 50 and 100 GHz channel spacing," Proc. ECOC 2006 (2006) PDP Th4.1.4.

H. Griesser, "43 Gb/s RZ-DQPSK transmission over a 660 km 10.7 Gb/s DWDM link," Proc. ECOC 2006 (2006) paper Th1.6.6.

S. Bigo, G. Charlet, O. Bertrand Pardo, J. Renaudier, "Characterization of the impact of non-linear effects in coherent transmission experiments," Digest of the IEEE/LEOS Summer Topical Meetings 2008 (2008) pp. 125-126.

H. Griesser, J. Elbers, "Influence of cross-phase modulation induced nonlinear phase noise on DQPSK signals from neighbouring OOK channels," Proc. ECOC 2005 (2005) paper Tu1. 2.2.

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