Abstract

This paper presents an alternative derivation of the Gaussian noise (GN) model of the nonlinear interference (NLI) in strongly dispersive optical systems. The basic idea is to exploit an enhanced regular perturbation expansion of the NLI, which highlights several interesting features of the GN model. Using the framework, we derive a fast algorithm to evaluate the received NLI power spectral density (PSD) for any input PSD. In the paper we also provide an asymptotic expression of the NLI PSD which further speeds up the computation without losing significant accuracy. Moreover, we show how the asymptotic expression can be used to optimize system performance. For instance, we are able to prove why a flat spectrum is best to minimize the NLI variance when the input is constrained to a fixed bandwidth and power. Finally, we also provide a generalization of the NLI GN model to arbitrarily correlated X and Y polarizations.

© 2013 IEEE

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  1. A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, F. Forghieri, "Statistical Characterization of PM-QPSK Signals after Propagation in Uncompensated Fiber Links," presented at the Eur. Conf. Opt. Commun. 2010 TurinItaly, Paper P4.07.
  2. F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, S. Bigo, " On nonlinear distortions of highly dispersive optical coherent systems," Opt. Exp. 2, 1022-1032 (2012).
  3. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, F. Forghieri, "Performance prediction for WDM PM-QPSK transmission over uncompensated links," presented at the Opt. Fiber Conf., 2011 Los AngelesCAUSA Paper OThO7 .
  4. E. Grellier, A. Bononi, "Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise ," Opt. Exp. 19, 12781-12788 (2011).
  5. X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039 -19054 (2010).
  6. 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).
  7. A. Mecozzi, R. J. Essiambre, "Nonlinear Shannon limit in pseudolinear coherent systems," J. Lightw. Technol. 30, 2011 -2024 (2012).
  8. 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).
  9. L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Andrekson, "discrete-time model for uncompensated single-channel fiber-optical links," IEEE Trans. Commun. 60, 3440 -3450 (2012).
  10. P. Poggiolini, "The GN model of non-linear propagation in uncompensated coherent optical systems," J. Lightw. Technol. 30 , 3857-3879 (2012 ).
  11. P. Serena, A. Bononi, "On the accuracy of the Gaussian nonlinear model for dispersion-unmanaged coherent links ," presented at the Eur. Conf. Opt. Commun., 2013 London U.K. Paper Th.1.D.3.
  12. P. Johannisson, M. Karlsson, "Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system," J. Lightw. Technol. 31, 1273-1282 (2013).
  13. P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, (2012, Jul. 2), “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,”[Online]. Available: arXiv:1209.0394v2 [Phys. Opt.]. .
  14. A. Bononi and P. Serena, (2012, Jul. 19), “An alternative derivation of Johannisson’s regular perturbation model,”[Online]. Available: arXiv:1207.4729v1 [Phys. Opt.].
  15. M. J. Ablowitz, T. Hirooka, T. Inoue, "Higher-order asymptotic analysis of dispersion-managed transmission systems: Solutions and their characteristics," J. Opt. Soc. Amer. B 19, 2876 -2885 (2002).
  16. 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).
  17. P. M. Lushnikov, "Fully parallel algorithm for simulating dispersion-managed wavelength-division-multiplexed optical fiber systems," Opt. Lett. 27, 939-41 (2002).
  18. A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schroedinger equation," J. Lightw. Technol. 20, 1102-1112 (2002).
  19. M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, Pak 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).
  20. K. V. Peddanarappagari, M. Brandt-Pearce, "Volterra series transfer function of single-mode fibers ," J. Lightw. Technol. 15, 2232-2241 (1997).
  21. 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).
  22. C. Bender, S. Orszag, Advanced Mathematical Methods for Engineers (McGraw-Hill, 1978).
  23. X. Wei, "Power-weighted dispersion distribution function for characterizing nonlinear properties of long-haul optical transmission links," Opt. Lett. 31, 2544-2546 (2006).
  24. G. P. Agrawal, Nonlinear Fiber Optics (Academic , 2001).
  25. E. Grellier, Etude des effets non-linéaires à l’oeuvre dans les systèmes de transmissions optiques fortement dispersifs Ph.D. dissertation Dept. d'Optique, Université de Franche-comté BesançonFrance (2011, p. 89).
  26. E. Ciaramella, E. Forestieri, "Analytical approximation of nonlinear distortions," IEEE Photon. Technol. Lett. 17, 91-93 (2005).
  27. B. Xu, M. Brandt-Pearce, "Modified Volterra series transfer function method," IEEE Photon. Technol. Lett. 14, 47-49 (2002).
  28. H. Louchet, A. Hodzic, K. Petermann, A. Robinson, R. Epworth, "Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems," IEEE Photon. Technol. Lett. 17, 2089-2091 (2005).
  29. A. O. Korotkevich, P. M. Lushnikov, "Proof-of-concept implementation of the massively parallel algorithm for simulation of dispersion-managed WDM optical fiber systems," Opt. Lett. 36 , 1851-1853 (2011).
  30. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).
  31. I. S. Reed, "On a Moment Theorem for Complex Gaussian Processes ," IRE Trans. Inform. Theory 8, 194-195 (1962).
  32. A. Bononi, N. Rossi, P. Serena, "On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems," Opt. Exp. 20, B204-B216 (2012).
  33. S. J. Savory, "Digital filters for coherent optical receivers ," Opt. Exp. 16, 804-817 (2008).
  34. R. Weinstock, Calculus of Variations With Applications to Physics and Engineering (Dover, 1974).

2013 (1)

P. Johannisson, M. Karlsson, "Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system," J. Lightw. Technol. 31, 1273-1282 (2013).

2012 (6)

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, S. Bigo, " On nonlinear distortions of highly dispersive optical coherent systems," Opt. Exp. 2, 1022-1032 (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).

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

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).

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Andrekson, "discrete-time model for uncompensated single-channel fiber-optical links," IEEE Trans. Commun. 60, 3440 -3450 (2012).

A. Bononi, N. Rossi, P. Serena, "On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems," Opt. Exp. 20, B204-B216 (2012).

2011 (2)

A. O. Korotkevich, P. M. Lushnikov, "Proof-of-concept implementation of the massively parallel algorithm for simulation of dispersion-managed WDM optical fiber systems," Opt. Lett. 36 , 1851-1853 (2011).

E. Grellier, A. Bononi, "Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise ," Opt. Exp. 19, 12781-12788 (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 (2)

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, Pak 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).

S. J. Savory, "Digital filters for coherent optical receivers ," Opt. Exp. 16, 804-817 (2008).

2006 (1)

X. Wei, "Power-weighted dispersion distribution function for characterizing nonlinear properties of long-haul optical transmission links," Opt. Lett. 31, 2544-2546 (2006).

2005 (2)

E. Ciaramella, E. Forestieri, "Analytical approximation of nonlinear distortions," IEEE Photon. Technol. Lett. 17, 91-93 (2005).

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, R. Epworth, "Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems," IEEE Photon. Technol. Lett. 17, 2089-2091 (2005).

2002 (5)

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).

B. Xu, M. Brandt-Pearce, "Modified Volterra series transfer function method," IEEE Photon. Technol. Lett. 14, 47-49 (2002).

P. M. Lushnikov, "Fully parallel algorithm for simulating dispersion-managed wavelength-division-multiplexed optical fiber systems," Opt. Lett. 27, 939-41 (2002).

A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schroedinger equation," J. Lightw. Technol. 20, 1102-1112 (2002).

M. J. Ablowitz, T. Hirooka, T. Inoue, "Higher-order asymptotic analysis of dispersion-managed transmission systems: Solutions and their characteristics," J. Opt. Soc. Amer. B 19, 2876 -2885 (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 (1)

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

1962 (1)

I. S. Reed, "On a Moment Theorem for Complex Gaussian Processes ," IRE Trans. Inform. Theory 8, 194-195 (1962).

IEEE Photon. Technol. Lett. (2)

E. Ciaramella, E. Forestieri, "Analytical approximation of nonlinear distortions," IEEE Photon. Technol. Lett. 17, 91-93 (2005).

B. Xu, M. Brandt-Pearce, "Modified Volterra series transfer function method," IEEE Photon. Technol. Lett. 14, 47-49 (2002).

IEEE Trans. Commun. (1)

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Andrekson, "discrete-time model for uncompensated single-channel fiber-optical links," IEEE Trans. Commun. 60, 3440 -3450 (2012).

IEEE Photon. Technol. Lett. (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).

IEEE Photon. Technol. Lett. (1)

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, R. Epworth, "Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems," IEEE Photon. Technol. Lett. 17, 2089-2091 (2005).

IRE Trans. Inform. Theory (1)

I. S. Reed, "On a Moment Theorem for Complex Gaussian Processes ," IRE Trans. Inform. Theory 8, 194-195 (1962).

J. Lightw. Technol. (2)

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. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schroedinger equation," J. Lightw. Technol. 20, 1102-1112 (2002).

J. Lightw. Technol. (5)

P. Johannisson, M. Karlsson, "Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system," J. Lightw. Technol. 31, 1273-1282 (2013).

P. Poggiolini, "The GN model of non-linear propagation in uncompensated coherent optical systems," J. Lightw. Technol. 30 , 3857-3879 (2012 ).

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

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).

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

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

M. J. Ablowitz, T. Hirooka, T. Inoue, "Higher-order asymptotic analysis of dispersion-managed transmission systems: Solutions and their characteristics," J. Opt. Soc. Amer. B 19, 2876 -2885 (2002).

Opt. Exp. (2)

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, S. Bigo, " On nonlinear distortions of highly dispersive optical coherent systems," Opt. Exp. 2, 1022-1032 (2012).

A. Bononi, N. Rossi, P. Serena, "On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems," Opt. Exp. 20, B204-B216 (2012).

Opt. Exp. (5)

S. J. Savory, "Digital filters for coherent optical receivers ," Opt. Exp. 16, 804-817 (2008).

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

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

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).

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, Pak 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).

Opt. Lett. (2)

P. M. Lushnikov, "Fully parallel algorithm for simulating dispersion-managed wavelength-division-multiplexed optical fiber systems," Opt. Lett. 27, 939-41 (2002).

X. Wei, "Power-weighted dispersion distribution function for characterizing nonlinear properties of long-haul optical transmission links," Opt. Lett. 31, 2544-2546 (2006).

Opt. Lett. (1)

A. O. Korotkevich, P. M. Lushnikov, "Proof-of-concept implementation of the massively parallel algorithm for simulation of dispersion-managed WDM optical fiber systems," Opt. Lett. 36 , 1851-1853 (2011).

Other (10)

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

G. P. Agrawal, Nonlinear Fiber Optics (Academic , 2001).

E. Grellier, Etude des effets non-linéaires à l’oeuvre dans les systèmes de transmissions optiques fortement dispersifs Ph.D. dissertation Dept. d'Optique, Université de Franche-comté BesançonFrance (2011, p. 89).

C. Bender, S. Orszag, Advanced Mathematical Methods for Engineers (McGraw-Hill, 1978).

R. Weinstock, Calculus of Variations With Applications to Physics and Engineering (Dover, 1974).

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, F. Forghieri, "Statistical Characterization of PM-QPSK Signals after Propagation in Uncompensated Fiber Links," presented at the Eur. Conf. Opt. Commun. 2010 TurinItaly, Paper P4.07.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, (2012, Jul. 2), “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,”[Online]. Available: arXiv:1209.0394v2 [Phys. Opt.]. .

A. Bononi and P. Serena, (2012, Jul. 19), “An alternative derivation of Johannisson’s regular perturbation model,”[Online]. Available: arXiv:1207.4729v1 [Phys. Opt.].

G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, F. Forghieri, "Performance prediction for WDM PM-QPSK transmission over uncompensated links," presented at the Opt. Fiber Conf., 2011 Los AngelesCAUSA Paper OThO7 .

P. Serena, A. Bononi, "On the accuracy of the Gaussian nonlinear model for dispersion-unmanaged coherent links ," presented at the Eur. Conf. Opt. Commun., 2013 London U.K. Paper Th.1.D.3.

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