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Optica Publishing Group
  • Journal of Lightwave Technology
  • Vol. 40,
  • Issue 16,
  • pp. 5567-5574
  • (2022)

An Enhanced Analytical Model of Nonlinear Fiber Effects for Four-Dimensional Symmetric Modulation Formats

Open Access Open Access

Abstract

Optical transmission systems intrinsically enjoy a four-dimensional (4D) constellation space, corresponding to two quadratures in two polarization states. In this paper, we introduce a general nonlinear model that is valid for 4D symmetric modulation formats. We take the inter-polarization dependency into account to derive this model. The model accounts for all perturbative nonlinear interference (NLI) terms, including self-channel, cross-channel and multi-channel interferences. Split-step Fourier simulations show that the proposed model has the ability to predict the NLI with high levels of accuracy for both low and high fiber dispersion regimes. The simulation results further show that previous models, including the EGN model, inaccurately predict the NLI in certain scenarios.

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References

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  1. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” IEEE J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.
  2. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” IEEE J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.
  3. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.
  4. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.
  5. A. Mecozzi and F. Matera, “Polarization scattering by intra-channel collisions,” Opt. Exp., vol. 20, no. 2, pp. 1213–1218, 2012.
  6. P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” IEEE J. Lightw. Technol., vol. 31, no. 8, pp. 1273–1282, 2013.
  7. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Exp., vol. 21, no. 22, pp. 25685–25699, 2013.
  8. V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.
  9. A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.
  10. A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 41–44.
  11. K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” IEEE J. Lightw. Technol., vol. 15, no. 12, pp. 2232–2241, 1997.
  12. L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun., vol. 60, no. 11, pp. 3440–3450, 2012.
  13. A. Mecozzi and R. J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” IEEE J. Lightw. Technol., vol. 30, no. 12, pp. 2011–2024, 2012.
  14. E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiber-optic channels: A primer,” in Proc. IEEE Inf. Theory Workshop, ITW, 2015, pp. 1–5.
  15. H. Rabbani, “A general analytical model of nonlinear fiber propagation in the presence of Kerr nonlinearity and stimulated Raman scattering,” 2020, arXiv:1909.08714v2.
  16. G. Liga, A. Barreiro, H. Rabbani, and A. Alvarado, “Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats,” Entropy, vol. 22, no. 11, 2020, Art. no. .
  17. H. Rabbani, “Analytical modeling of nonlinear fiber propagation for four dimensional symmetric constellations,” IEEE J. Lightw. Technol., vol. 39, no. 9, pp. 2704–2713, 2021.
  18. O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.
  19. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” IEEE J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053, 2015.
  20. E. Agrell, “Database of sphere packings,” 2016. [Online]. Available: http://codes.se/packings/
  21. P. Poggiolini, “Analytical and experimental results on system maximum reach increase through symbol rate optimization,” IEEE J. Lightw. Technol., vol. 34, no. 8, pp. 1872–1885, 2016.
  22. M. Sjodin, E. Agrell, and M. Karlsson, “Subset-optimized polarization-multiplexed PSK for fiber-optic communications,” IEEE Commun. Lett., vol. 17, no. 5, pp. 838–840, 2013.
  23. T. A. Eriksson, “Experimental investigation of a four-dimensional 256-ary lattice-based modulation format,” in Proc. Opt. Fiber Commun. Conf., 2015, pp. 1–3.
  24. I. Roberts, J. M. Kahn, and D. Boertjes, “Convex channel power optimization in nonlinear WDM systems using Gaussian noise model,” IEEE J. Lightw. Technol., vol. 34, no. 13, pp. 3212–3222, 2016.
  25. P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

2021 (1)

H. Rabbani, “Analytical modeling of nonlinear fiber propagation for four dimensional symmetric constellations,” IEEE J. Lightw. Technol., vol. 39, no. 9, pp. 2704–2713, 2021.

2020 (1)

G. Liga, A. Barreiro, H. Rabbani, and A. Alvarado, “Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats,” Entropy, vol. 22, no. 11, 2020, Art. no. .

2016 (3)

I. Roberts, J. M. Kahn, and D. Boertjes, “Convex channel power optimization in nonlinear WDM systems using Gaussian noise model,” IEEE J. Lightw. Technol., vol. 34, no. 13, pp. 3212–3222, 2016.

P. Poggiolini, “Analytical and experimental results on system maximum reach increase through symbol rate optimization,” IEEE J. Lightw. Technol., vol. 34, no. 8, pp. 1872–1885, 2016.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.

2015 (1)

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” IEEE J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053, 2015.

2014 (1)

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

2013 (4)

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” IEEE J. Lightw. Technol., vol. 31, no. 8, pp. 1273–1282, 2013.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Exp., vol. 21, no. 22, pp. 25685–25699, 2013.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.

M. Sjodin, E. Agrell, and M. Karlsson, “Subset-optimized polarization-multiplexed PSK for fiber-optic communications,” IEEE Commun. Lett., vol. 17, no. 5, pp. 838–840, 2013.

2012 (4)

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun., vol. 60, no. 11, pp. 3440–3450, 2012.

A. Mecozzi and R. J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” IEEE J. Lightw. Technol., vol. 30, no. 12, pp. 2011–2024, 2012.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.

A. Mecozzi and F. Matera, “Polarization scattering by intra-channel collisions,” Opt. Exp., vol. 20, no. 2, pp. 1213–1218, 2012.

2010 (1)

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” IEEE J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

2009 (2)

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” IEEE J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.

1997 (1)

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” IEEE J. Lightw. Technol., vol. 15, no. 12, pp. 2232–2241, 1997.

Agrell, E.

M. Sjodin, E. Agrell, and M. Karlsson, “Subset-optimized polarization-multiplexed PSK for fiber-optic communications,” IEEE Commun. Lett., vol. 17, no. 5, pp. 838–840, 2013.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun., vol. 60, no. 11, pp. 3440–3450, 2012.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” IEEE J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiber-optic channels: A primer,” in Proc. IEEE Inf. Theory Workshop, ITW, 2015, pp. 1–5.

E. Agrell, “Database of sphere packings,” 2016. [Online]. Available: http://codes.se/packings/

Alvarado, A.

G. Liga, A. Barreiro, H. Rabbani, and A. Alvarado, “Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats,” Entropy, vol. 22, no. 11, 2020, Art. no. .

Barreiro, A.

G. Liga, A. Barreiro, H. Rabbani, and A. Alvarado, “Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats,” Entropy, vol. 22, no. 11, 2020, Art. no. .

Beygi, L.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun., vol. 60, no. 11, pp. 3440–3450, 2012.

Boertjes, D.

I. Roberts, J. M. Kahn, and D. Boertjes, “Convex channel power optimization in nonlinear WDM systems using Gaussian noise model,” IEEE J. Lightw. Technol., vol. 34, no. 13, pp. 3212–3222, 2016.

Bosco, G.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

Brandt-Pearce, M.

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” IEEE J. Lightw. Technol., vol. 15, no. 12, pp. 2232–2241, 1997.

Carena, A.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

Curri, V.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

Dar, R.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” IEEE J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053, 2015.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Exp., vol. 21, no. 22, pp. 25685–25699, 2013.

Durisi, G.

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiber-optic channels: A primer,” in Proc. IEEE Inf. Theory Workshop, ITW, 2015, pp. 1–5.

Eriksson, T. A.

T. A. Eriksson, “Experimental investigation of a four-dimensional 256-ary lattice-based modulation format,” in Proc. Opt. Fiber Commun. Conf., 2015, pp. 1–3.

Essiambre, R. J.

A. Mecozzi and R. J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” IEEE J. Lightw. Technol., vol. 30, no. 12, pp. 2011–2024, 2012.

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” IEEE J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Feder, M.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” IEEE J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053, 2015.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Exp., vol. 21, no. 22, pp. 25685–25699, 2013.

Forghieri, F.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

Foschini, G. J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” IEEE J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Goebel, B.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” IEEE J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Golani, O.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.

Jiang, Y.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

Johannisson, P.

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” IEEE J. Lightw. Technol., vol. 31, no. 8, pp. 1273–1282, 2013.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun., vol. 60, no. 11, pp. 3440–3450, 2012.

E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiber-optic channels: A primer,” in Proc. IEEE Inf. Theory Workshop, ITW, 2015, pp. 1–5.

Kahn, J. M.

I. Roberts, J. M. Kahn, and D. Boertjes, “Convex channel power optimization in nonlinear WDM systems using Gaussian noise model,” IEEE J. Lightw. Technol., vol. 34, no. 13, pp. 3212–3222, 2016.

Karlsson, M.

M. Sjodin, E. Agrell, and M. Karlsson, “Subset-optimized polarization-multiplexed PSK for fiber-optic communications,” IEEE Commun. Lett., vol. 17, no. 5, pp. 838–840, 2013.

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” IEEE J. Lightw. Technol., vol. 31, no. 8, pp. 1273–1282, 2013.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun., vol. 60, no. 11, pp. 3440–3450, 2012.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” IEEE J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.

Kramer, G.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” IEEE J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Kurtzke, C.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 41–44.

Liga, G.

G. Liga, A. Barreiro, H. Rabbani, and A. Alvarado, “Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats,” Entropy, vol. 22, no. 11, 2020, Art. no. .

Matera, F.

A. Mecozzi and F. Matera, “Polarization scattering by intra-channel collisions,” Opt. Exp., vol. 20, no. 2, pp. 1213–1218, 2012.

Mecozzi, A.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” IEEE J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053, 2015.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Exp., vol. 21, no. 22, pp. 25685–25699, 2013.

A. Mecozzi and F. Matera, “Polarization scattering by intra-channel collisions,” Opt. Exp., vol. 20, no. 2, pp. 1213–1218, 2012.

A. Mecozzi and R. J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” IEEE J. Lightw. Technol., vol. 30, no. 12, pp. 2011–2024, 2012.

Peddanarappagari, K.

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” IEEE J. Lightw. Technol., vol. 15, no. 12, pp. 2232–2241, 1997.

Petermann, K.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 41–44.

Poggiolini, P.

P. Poggiolini, “Analytical and experimental results on system maximum reach increase through symbol rate optimization,” IEEE J. Lightw. Technol., vol. 34, no. 8, pp. 1872–1885, 2016.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Exp., vol. 22, no. 13, pp. 16335–16362, 2014.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Exp., vol. 21, no. 3, pp. 3308–3317, 2013.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” IEEE J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539, 2012.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

Rabbani, H.

H. Rabbani, “Analytical modeling of nonlinear fiber propagation for four dimensional symmetric constellations,” IEEE J. Lightw. Technol., vol. 39, no. 9, pp. 2704–2713, 2021.

G. Liga, A. Barreiro, H. Rabbani, and A. Alvarado, “Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats,” Entropy, vol. 22, no. 11, 2020, Art. no. .

H. Rabbani, “A general analytical model of nonlinear fiber propagation in the presence of Kerr nonlinearity and stimulated Raman scattering,” 2020, arXiv:1909.08714v2.

Roberts, I.

I. Roberts, J. M. Kahn, and D. Boertjes, “Convex channel power optimization in nonlinear WDM systems using Gaussian noise model,” IEEE J. Lightw. Technol., vol. 34, no. 13, pp. 3212–3222, 2016.

Shtaif, M.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” IEEE J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489, 2016.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” IEEE J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053, 2015.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Exp., vol. 21, no. 22, pp. 25685–25699, 2013.

Sjodin, M.

M. Sjodin, E. Agrell, and M. Karlsson, “Subset-optimized polarization-multiplexed PSK for fiber-optic communications,” IEEE Commun. Lett., vol. 17, no. 5, pp. 838–840, 2013.

Splett, A.

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E. Agrell, G. Durisi, and P. Johannisson, “Information-theory-friendly models for fiber-optic channels: A primer,” in Proc. IEEE Inf. Theory Workshop, ITW, 2015, pp. 1–5.

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P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” 2014, arXiv:1209.0394.

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