Abstract

This paper is devoted to an in-depth discussion of the Gaussian Noise (GN) model which describes non-linear propagation in uncompensated coherent transmission systems. Similar models and validation efforts are reviewed. Then, the main equations of the GN model are introduced. An intuitive physical interpretation of the equations and their features is proposed. The main characteristics of the non-linear interference (NLI) noise spectra that the GN model produces are discussed. To ease model exploitation, a new formulation in hyperbolic coordinates is proposed, which makes numerical integration faster. New approximate closed-form solutions are also provided. An extension of the GN model to distributed-amplification scenarios is introduced. NLI noise accumulation versus distance and bandwidth are studied in depth. Finally, the GN model implications as to system and networks design and optimization are discussed.

© 2012 IEEE

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  1. A. Carena, V. Curri, G. Bosco, P. Poggiolini, F. Forghieri, "Modeling of the impact of non-linear propagation effects in uncompensated optical coherent transmission links," J. Lightw. Technol. 30, 1524-1539 (2012).
  2. K. V. Peddanarappagari, M. Brandt-Pearce, "Volterra series transfer function of single-mode fibers," J. Lightw. Technol. 15, 2232-2241 (1997).
  3. 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).
  4. J. Tang, "A comparison study of the Shannon channel capacity of various nonlinear optical fibers," J. Lightw. Technol. 24, 2070-2075 (2006).
  5. 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.
  6. H. Louchet, "Analytical model for the performance evaluation of DWDM transmission systems," IEEE Photon. Technol. Lett. 15, 1219-1221 (2003).
  7. 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).
  8. A. Mecozzi, C. B. Clausen, M. Shtaif, "System impact of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 1633-1635 (2000).
  9. 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).
  10. X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).
  11. 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).
  12. 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).
  13. A. Mecozzi, R. Essiambre, "Nonlinear shannon limit in pseudolinear coherent systems," J. Lightw. Technol. 30, 2011-2024 (2012).
  14. A. Bononi, P. Serena, N. Rossi, E. Grellier, F. Vacondio, "Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing," Opt. Exp. 20, 7777-7791 (2012).
  15. F. Vacondio, "On nonlinear distortions of highly dispersive optical coherent systems," Opt. Exp. 20, 1022-1032 (2012).
  16. A. Carena, "Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links," Proc. ECOC 2010 (2010).
  17. E. Torrengo, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," Opt. Exp. 19, 790-798 (2011).
  18. O. V. Sinkin, "Scaling of nonlinear impairments in dispersion-uncompensated long-haul transmission," Proc. OFC 2012 (2012).
  19. G. Bosco, "Experimental investigation of nonlinear interference accumulation in uncompensated links," IEEE Photon. Technol. Lett. 24, 1230-1232 (2012).
  20. J. F. Pina, C. Xia, A. G. Striegler, D. van den Borne, "Nonlinear tolerance of polarization-multiplexed QPSK transmission over mixed fiber," Proc. ECOC 2011 (2011).
  21. K. Inoue, H. Toba, "Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion," J. Lightw. Technol. 13, 88-93 (1995).
  22. 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).
  23. G. Bosco, P. Poggiolini, A. Carena, V. Curri, F. Forghieri, "Analytical results on channel capacity in uncompensated optical links with coherent detection," Opt. Exp. 19, B438-B449 (2011).
  24. 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).
  25. S. R. Chinn, "Analysis of counter-pumped small-signal fibre Raman amplifiers," Electr. Lett. 33, 607-608 (1997).
  26. P. Poggiolini, G. Bosco, A. Carena, V. Curri, F. Forghieri, A Detailed Analytical Derivation of the GN Model of Non-Linear Interference in Coherent Optical Transmission Systems www.arxiv.org arXiv, paper identifier 1209.0394 (2012).
  27. A. Carena, P. Poggiolini, V. Curri, G. Bosco, F. Forghieri, "Evaluation of the dependence on system parameters of non-linear interference accumulation in multi-span links," Proc. ECOC 2012 (2012).
  28. R. Pastorelli, "Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks," Proc. ECOC 2012 (2012).

2012 (5)

A. Carena, V. Curri, G. Bosco, P. Poggiolini, F. Forghieri, "Modeling of the impact of non-linear propagation effects in uncompensated optical coherent transmission links," J. Lightw. Technol. 30, 1524-1539 (2012).

A. Mecozzi, R. Essiambre, "Nonlinear shannon limit in pseudolinear coherent systems," J. Lightw. Technol. 30, 2011-2024 (2012).

A. Bononi, P. Serena, N. Rossi, E. Grellier, F. Vacondio, "Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing," Opt. Exp. 20, 7777-7791 (2012).

F. Vacondio, "On nonlinear distortions of highly dispersive optical coherent systems," Opt. Exp. 20, 1022-1032 (2012).

G. Bosco, "Experimental investigation of nonlinear interference accumulation in uncompensated links," IEEE Photon. Technol. Lett. 24, 1230-1232 (2012).

2011 (4)

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, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," Opt. Exp. 19, 790-798 (2011).

G. Bosco, P. Poggiolini, A. Carena, V. Curri, F. Forghieri, "Analytical results on channel capacity in uncompensated optical links with coherent detection," Opt. Exp. 19, B438-B449 (2011).

2010 (1)

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 (1)

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).

2006 (1)

J. Tang, "A comparison study of the Shannon channel capacity of various nonlinear optical fibers," J. Lightw. Technol. 24, 2070-2075 (2006).

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 (2)

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).

A. Mecozzi, C. B. Clausen, M. Shtaif, "System impact of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 1633-1635 (2000).

1997 (2)

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

S. R. Chinn, "Analysis of counter-pumped small-signal fibre Raman amplifiers," Electr. Lett. 33, 607-608 (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).

Electr. Lett. (1)

S. R. Chinn, "Analysis of counter-pumped small-signal fibre Raman amplifiers," Electr. Lett. 33, 607-608 (1997).

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)

G. Bosco, "Experimental investigation of nonlinear interference accumulation in uncompensated links," IEEE Photon. Technol. Lett. 24, 1230-1232 (2012).

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).

A. Mecozzi, C. B. Clausen, M. Shtaif, "System impact of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 1633-1635 (2000).

J. Lightw. Technol. (3)

A. Carena, V. Curri, G. Bosco, P. Poggiolini, F. Forghieri, "Modeling of the impact of non-linear propagation effects in uncompensated optical coherent transmission links," J. Lightw. Technol. 30, 1524-1539 (2012).

J. Tang, "A comparison study of the Shannon channel capacity of various nonlinear optical fibers," J. Lightw. Technol. 24, 2070-2075 (2006).

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)

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).

A. Mecozzi, R. Essiambre, "Nonlinear shannon limit in pseudolinear coherent systems," J. Lightw. Technol. 30, 2011-2024 (2012).

Opt. Exp. (3)

A. Bononi, P. Serena, N. Rossi, E. Grellier, F. Vacondio, "Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing," Opt. Exp. 20, 7777-7791 (2012).

F. Vacondio, "On nonlinear distortions of highly dispersive optical coherent systems," Opt. Exp. 20, 1022-1032 (2012).

G. Bosco, P. Poggiolini, A. Carena, V. Curri, F. Forghieri, "Analytical results on channel capacity in uncompensated optical links with coherent detection," Opt. Exp. 19, B438-B449 (2011).

Opt. Exp. (3)

E. Torrengo, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," Opt. Exp. 19, 790-798 (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 (8)

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.

O. V. Sinkin, "Scaling of nonlinear impairments in dispersion-uncompensated long-haul transmission," Proc. OFC 2012 (2012).

J. F. Pina, C. Xia, A. G. Striegler, D. van den Borne, "Nonlinear tolerance of polarization-multiplexed QPSK transmission over mixed fiber," Proc. ECOC 2011 (2011).

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

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).

P. Poggiolini, G. Bosco, A. Carena, V. Curri, F. Forghieri, A Detailed Analytical Derivation of the GN Model of Non-Linear Interference in Coherent Optical Transmission Systems www.arxiv.org arXiv, paper identifier 1209.0394 (2012).

A. Carena, P. Poggiolini, V. Curri, G. Bosco, F. Forghieri, "Evaluation of the dependence on system parameters of non-linear interference accumulation in multi-span links," Proc. ECOC 2012 (2012).

R. Pastorelli, "Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks," Proc. ECOC 2012 (2012).

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