Abstract

We address perturbative models for the impact of nonlinear propagation in uncompensated links. We concentrate on a recently-proposed model which splits up the signal into spectral components and then resorts to a four-wave-mixing-like approach to assess the generation of nonlinear interference due to the beating of the signal spectral components. We put its founding assumptions on firmer ground and we provide a detailed derivation for its main analytical results. We then carry out an extensive simulative validation by addressing an ample and significant set of formats encompassing PM-BPSK, PM-QPSK, PM-8QAM, and PM-16QAM, all operating at 32 GBaud. We compare the model prediction of maximum system reach and optimum launch power versus simulation results, for all four formats, three different kinds of fibers (PSCF, SMF, and NZDSF) and for several values of WDM channel spacing, ranging from 50 GHz down to the symbol-rate. We found that, throughout all tests, the model delivers accurate predictions, potentially making it an effective general-purpose system design tool for coherent uncompensated transmission systems.

© 2012 IEEE

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  1. J.-X. Cai, "112$\,\times\,$112 Gb/s transmission over 9 360 km with channel spacing set to the baud rate (360% spectral efficiency)," Proc. ECOC 2010 (2010).
  2. M. Salsi, "Transmission of 96$\,\times\,$100 Gb/s with 23 super-FEC overhead over 11 680 km, using optical spectral engineering," Proc. OFC 2011 (2011).
  3. S. Yamanaka, "11$\,\times\,$171 Gb/s PDM 16-QAM transmission over 1440 km with a spectral efficiency of 6.4 b/s/Hz using high-speed DAC," Proc. ECOC 2010 (2010).
  4. A. Sano, "100$\,\times\,$120 Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent receiver," Proc. ECOC 2010 (2010).
  5. D. Qian, "101.7 Tb/s (370$\,\times\,$294-Gb/s) PDM-128QAM-OFDM transmission over 3$\,\times\,$55-km SSMF using pilot-based phase noise mitigation," Proc. OFC 2011 (2011).
  6. V. Curri, P. Poggiolini, A. Carena, F. Forghieri, "Dispersion compensation and mitigation of non-linear effects in 111 Gb/s WDM coherent PM-QPSK systems," IEEE Photon. Technol. Lett. 20, 1473-1475 (2008).
  7. D. van den Borne, V. Sleiffer, M. Alfiad, S. Jansen, T. Wuth, "POLMUX-QPSK modulation and coherent detection: The challenge of long-haul 100G transmission," Proc. of ECOC 2009 (2009).
  8. G. Gavioli, "NRZ-PM-QPSK 16$\,\times\,$100 Gb/s transmission over installed fiber with different dispersion maps," IEEE Photon. Technol. Lett. 22, 371-373 (2010).
  9. A. Carena, "Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links," Proc. of ECOC 2010 (2010).
  10. F. Vacondio, C. Simonneau, L. Lorcy, J. C. Antona, A. Bononi, S. Bigo, "Experimental characterization of Gaussian-distributed nonlinear distortions," Proc. of ECOC 2011 (2011).
  11. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, F. Forghieri, "Performance prediction for WDM PM-QPSK transmission over uncompensated links," Proc. OFC 2011 (2011).
  12. E. Grellier, A. Bononi, "Quality parameter for coherent transmissions with Gaussian-distributed non-linear noise," Opt. Exp. 19, 12781-12788 (2011).
  13. K. V. Peddanarappagari, M. Brandt-Pearce, "Volterra series transfer function of single-mode fibers," J. Lightw. Technol. 15, 2232-2241 (1997).
  14. J. Tang, "The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver," J. Lightw. Technol. 20, 1095-1101 (2002).
  15. A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
  16. M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, "Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links," Opt. Exp. 16, 15778-15810 (2008).
  17. X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).
  18. W. Shieh, X. Chen, "Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems," IEEE Photon. J. 3, 158-173 (2011).
  19. A. Splett, C. Kurzke, K. Petermann, "Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities," Proc. ECOC 1993 (1993) pp. 41-44.
  20. H. Louchet, "Analytical model for the performance evaluation of DWDM transmission systems," IEEE Photon. Technol. Lett. 15, 1219-1221 (2003).
  21. P. Poggiolini, A. Carena, V. Curri, G. Bosco, F. Forghieri, "Analytical modeling of non-linear propagation in uncompensated optical transmission links," IEEE Photon. Technol. Lett. 23, 742-744 (2011).
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  23. Y. Han, G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Exp. 13, 7527-7534 (2005).
  24. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, F. Forghieri, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," Opt. Exp. 19, B790-B798 (2011).
  25. K. Inoue, H. Toba, "Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion," J. Lightw. Technol. 13, 88-93 (1995).
  26. D. Marcuse, C. R. Menyuk, P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightw. Technol. 15, 1735-1746 (1997).
  27. W. Zeiler, F. Di Pasquale, P. Bayvel, J. E. Midwinter, "Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks," J. Lightw. Technol. 14, 1933-1942 (1996).

2011 (4)

E. Grellier, A. Bononi, "Quality parameter for coherent transmissions with Gaussian-distributed non-linear noise," Opt. Exp. 19, 12781-12788 (2011).

W. Shieh, X. Chen, "Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems," IEEE Photon. J. 3, 158-173 (2011).

P. Poggiolini, A. Carena, V. Curri, G. Bosco, F. Forghieri, "Analytical modeling of non-linear propagation in uncompensated optical transmission links," IEEE Photon. Technol. Lett. 23, 742-744 (2011).

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, F. Forghieri, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," Opt. Exp. 19, B790-B798 (2011).

2010 (2)

G. Gavioli, "NRZ-PM-QPSK 16$\,\times\,$100 Gb/s transmission over installed fiber with different dispersion maps," IEEE Photon. Technol. Lett. 22, 371-373 (2010).

X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).

2008 (2)

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, "Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links," Opt. Exp. 16, 15778-15810 (2008).

V. Curri, P. Poggiolini, A. Carena, F. Forghieri, "Dispersion compensation and mitigation of non-linear effects in 111 Gb/s WDM coherent PM-QPSK systems," IEEE Photon. Technol. Lett. 20, 1473-1475 (2008).

2005 (1)

Y. Han, G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Exp. 13, 7527-7534 (2005).

2003 (1)

H. Louchet, "Analytical model for the performance evaluation of DWDM transmission systems," IEEE Photon. Technol. Lett. 15, 1219-1221 (2003).

2002 (1)

J. Tang, "The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver," J. Lightw. Technol. 20, 1095-1101 (2002).

2000 (1)

A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).

1997 (2)

K. V. Peddanarappagari, M. Brandt-Pearce, "Volterra series transfer function of single-mode fibers," J. Lightw. Technol. 15, 2232-2241 (1997).

D. Marcuse, C. R. Menyuk, P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightw. Technol. 15, 1735-1746 (1997).

1996 (1)

W. Zeiler, F. Di Pasquale, P. Bayvel, J. E. Midwinter, "Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks," J. Lightw. Technol. 14, 1933-1942 (1996).

1995 (1)

K. Inoue, H. Toba, "Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion," J. Lightw. Technol. 13, 88-93 (1995).

IEEE Photon. J. (1)

W. Shieh, X. Chen, "Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems," IEEE Photon. J. 3, 158-173 (2011).

IEEE Photon. Technol. Lett. (1)

P. Poggiolini, A. Carena, V. Curri, G. Bosco, F. Forghieri, "Analytical modeling of non-linear propagation in uncompensated optical transmission links," IEEE Photon. Technol. Lett. 23, 742-744 (2011).

IEEE Photon. Technol. Lett. (4)

H. Louchet, "Analytical model for the performance evaluation of DWDM transmission systems," IEEE Photon. Technol. Lett. 15, 1219-1221 (2003).

A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).

V. Curri, P. Poggiolini, A. Carena, F. Forghieri, "Dispersion compensation and mitigation of non-linear effects in 111 Gb/s WDM coherent PM-QPSK systems," IEEE Photon. Technol. Lett. 20, 1473-1475 (2008).

G. Gavioli, "NRZ-PM-QPSK 16$\,\times\,$100 Gb/s transmission over installed fiber with different dispersion maps," IEEE Photon. Technol. Lett. 22, 371-373 (2010).

J. Lightw. Technol. (1)

K. Inoue, H. Toba, "Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion," J. Lightw. Technol. 13, 88-93 (1995).

J. Lightw. Technol. (4)

D. Marcuse, C. R. Menyuk, P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightw. Technol. 15, 1735-1746 (1997).

W. Zeiler, F. Di Pasquale, P. Bayvel, J. E. Midwinter, "Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks," J. Lightw. Technol. 14, 1933-1942 (1996).

K. V. Peddanarappagari, M. Brandt-Pearce, "Volterra series transfer function of single-mode fibers," J. Lightw. Technol. 15, 2232-2241 (1997).

J. Tang, "The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver," J. Lightw. Technol. 20, 1095-1101 (2002).

Opt. Exp. (1)

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, F. Forghieri, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," Opt. Exp. 19, B790-B798 (2011).

Opt. Exp. (4)

Y. Han, G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Exp. 13, 7527-7534 (2005).

E. Grellier, A. Bononi, "Quality parameter for coherent transmissions with Gaussian-distributed non-linear noise," Opt. Exp. 19, 12781-12788 (2011).

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, "Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links," Opt. Exp. 16, 15778-15810 (2008).

X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).

Other (11)

A. Splett, C. Kurzke, K. Petermann, "Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities," Proc. ECOC 1993 (1993) pp. 41-44.

D. van den Borne, V. Sleiffer, M. Alfiad, S. Jansen, T. Wuth, "POLMUX-QPSK modulation and coherent detection: The challenge of long-haul 100G transmission," Proc. of ECOC 2009 (2009).

A. Carena, "Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links," Proc. of ECOC 2010 (2010).

F. Vacondio, C. Simonneau, L. Lorcy, J. C. Antona, A. Bononi, S. Bigo, "Experimental characterization of Gaussian-distributed nonlinear distortions," Proc. of ECOC 2011 (2011).

G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, F. Forghieri, "Performance prediction for WDM PM-QPSK transmission over uncompensated links," Proc. OFC 2011 (2011).

J.-X. Cai, "112$\,\times\,$112 Gb/s transmission over 9 360 km with channel spacing set to the baud rate (360% spectral efficiency)," Proc. ECOC 2010 (2010).

M. Salsi, "Transmission of 96$\,\times\,$100 Gb/s with 23 super-FEC overhead over 11 680 km, using optical spectral engineering," Proc. OFC 2011 (2011).

S. Yamanaka, "11$\,\times\,$171 Gb/s PDM 16-QAM transmission over 1440 km with a spectral efficiency of 6.4 b/s/Hz using high-speed DAC," Proc. ECOC 2010 (2010).

A. Sano, "100$\,\times\,$120 Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent receiver," Proc. ECOC 2010 (2010).

D. Qian, "101.7 Tb/s (370$\,\times\,$294-Gb/s) PDM-128QAM-OFDM transmission over 3$\,\times\,$55-km SSMF using pilot-based phase noise mitigation," Proc. OFC 2011 (2011).

J. G. Proakis, Digital Communication (McGraw-Hill, 1989).

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