Abstract

In this paper, we present and verify by experiments a semi-analytical model to estimate the power spectral density of the noise-to-signal ratio in dispersion unmanaged transmissions over heterogeneous fiber types. The model combines an experimental calibration and an analytical formula. After a one-span profiling calibration, the overall system performance is assessed by joining the calibration results with a cumulative summing formula, targeting as a performance estimate the spectral density of the noise-to-signal ratio. After recalling the fundamental theoretical developments, we report experimental validations for four-span long dispersion unmanaged heterogeneous testbeds. According to the experimental results, the estimation error on the signal-to-noise ratio is always below 0.3 dB. Moreover, thanks to spectral knowledge, we show that we can account for some digital signal processing performed at the transceiver, which impacts system performance, such as the carrier-phase estimation. We demonstrate that without altering the experimental calibration, we can predict the performance adaptively to the carrier-phase estimation implemented at the receiver, capping the estimation error to < 0.5 dB.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.
  2. P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30(24), 3857–3879 (2012).
    [Crossref]
  3. A. Bononi, N. Rossi, and P. Serena, “On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems,” Opt. Express 20(26), B204 (2012).
    [Crossref]
  4. P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
    [Crossref]
  5. P. Serena and A. Bononi, “A time-domain extended gaussian noise model,” J. Lightwave Technol. 33(7), 1459–1472 (2015).
    [Crossref]
  6. E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.
  7. O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the Bit-Error-Rate Performance of Nonlinear Fiber-Optic Systems,” J. Lightwave Technol. 34(15), 3482–3489 (2016).
    [Crossref]
  8. A. Ghazisaeidi, “A Theory of Nonlinear Interactions between Signal and Amplified Spontaneous Emission Noise in Coherent Wavelength Division Multiplexed Systems,” J. Lightwave Technol. 35(23), 5150–5175 (2017).
    [Crossref]
  9. J. C. Antona, S. Bigo, and J. P. Faure, “Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems,” in Optical Fiber Communication Conference (OFC), 2002.
  10. 10. J.-C. Antona and S. Bigo, “EP1736806A1 Method for determining the performance of a heterogeneous optical transmission system,” EP1736806A1, 2005.
  11. P. Jenneve, P. Ramantanis, N. Dubreuil, F. Boitier, P. Layec, and S. Bigo, “Measurement of Optical Nonlinear Distortions and Their Uncertainties in Coherent Systems,” J. Lightwave Technol. 35(24), 5432–5439 (2017).
    [Crossref]
  12. A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
    [Crossref]
  13. R. Dar and P. J. Winzer, “Nonlinear Interference Mitigation: Methods and Potential Gain,” J. Lightwave Technol. 35(4), 903–930 (2017).
    [Crossref]
  14. M. Lonardi, P. Ramantanis, P. Jenneve, and S. Bigo, “Power Spectral Density Estimation in Dispersion Unmanaged Coherent Metro Networks,” in Optical Fiber Communication Conference (OFC), 2019.
  15. F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022 (2012).
    [Crossref]
  16. N. Rossi, P. Ramantanis, and J. C. Antona, “Nonlinear interference noise statistics in unmanaged coherent networks with channels propagating over different lightpaths,” Eur. Conf. Opt. Commun. ECOC, no. c, pp. 4–6, 2014.
  17. A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-phase modulation induced by OOK channels on higher-rate DQPSK and coherent QPSK channels,” J. Lightwave Technol. 27(18), 3974–3983 (2009).
    [Crossref]
  18. M. S. Bartlett, “Smoothing periodograms from time-series with continuous spectra,” Nature 161(4096), 686–687 (1948).
    [Crossref]
  19. G. Agrawal, Nonlinear Fiber Optics (Academic, 2006).
  20. C. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK Transmission Systems - OSA Technical Digest,” in Optical Fiber Communication Conference, OFC, 2012.
  21. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Accumulation of nonlinear interference noise in multi-span fiber-optic systems,” Opt. Express 22(12), 14199–14211 (2014).
    [Crossref]
  22. O. Golani, M. Feder, A. Mecozzi, and M. Shtaif, “Correlations and phase noise in NLIN-modelling and system implications,” 2016 Opt. Fiber Commun. Conf. Exhib., pp. 1–3, 2016.
  23. O. Golani, M. Feder, and M. Shtaif, “Kalman-MLSE Equalization for NLIN Mitigation,” J. Lightwave Technol. 36(12), 2541–2550 (2018).
    [Crossref]

2018 (1)

2017 (3)

2016 (1)

2015 (1)

2014 (1)

2013 (1)

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

2012 (3)

2009 (1)

1983 (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

1948 (1)

M. S. Bartlett, “Smoothing periodograms from time-series with continuous spectra,” Nature 161(4096), 686–687 (1948).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

Antona, J. C.

N. Rossi, P. Ramantanis, and J. C. Antona, “Nonlinear interference noise statistics in unmanaged coherent networks with channels propagating over different lightpaths,” Eur. Conf. Opt. Commun. ECOC, no. c, pp. 4–6, 2014.

J. C. Antona, S. Bigo, and J. P. Faure, “Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems,” in Optical Fiber Communication Conference (OFC), 2002.

Antona, J.-C.

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022 (2012).
[Crossref]

10. J.-C. Antona and S. Bigo, “EP1736806A1 Method for determining the performance of a heterogeneous optical transmission system,” EP1736806A1, 2005.

Antonia, J.-C.

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Bartlett, M. S.

M. S. Bartlett, “Smoothing periodograms from time-series with continuous spectra,” Nature 161(4096), 686–687 (1948).
[Crossref]

Bellotti, G.

Bertolini, M.

Bigo, S.

P. Jenneve, P. Ramantanis, N. Dubreuil, F. Boitier, P. Layec, and S. Bigo, “Measurement of Optical Nonlinear Distortions and Their Uncertainties in Coherent Systems,” J. Lightwave Technol. 35(24), 5432–5439 (2017).
[Crossref]

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022 (2012).
[Crossref]

10. J.-C. Antona and S. Bigo, “EP1736806A1 Method for determining the performance of a heterogeneous optical transmission system,” EP1736806A1, 2005.

M. Lonardi, P. Ramantanis, P. Jenneve, and S. Bigo, “Power Spectral Density Estimation in Dispersion Unmanaged Coherent Metro Networks,” in Optical Fiber Communication Conference (OFC), 2019.

J. C. Antona, S. Bigo, and J. P. Faure, “Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems,” in Optical Fiber Communication Conference (OFC), 2002.

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Blendin, J.

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

Boitier, F.

Bononi, A.

Dar, R.

Dubreuil, N.

Faure, J. P.

J. C. Antona, S. Bigo, and J. P. Faure, “Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems,” in Optical Fiber Communication Conference (OFC), 2002.

Feder, M.

Fludger, C.

C. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK Transmission Systems - OSA Technical Digest,” in Optical Fiber Communication Conference, OFC, 2012.

Ghazisaeidi, A.

Golani, O.

Grellier, E.

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022 (2012).
[Crossref]

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Gunkel, M.

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

Hausheer, D.

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

Herrmann, D.

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

Jenneve, P.

P. Jenneve, P. Ramantanis, N. Dubreuil, F. Boitier, P. Layec, and S. Bigo, “Measurement of Optical Nonlinear Distortions and Their Uncertainties in Coherent Systems,” J. Lightwave Technol. 35(24), 5432–5439 (2017).
[Crossref]

M. Lonardi, P. Ramantanis, P. Jenneve, and S. Bigo, “Power Spectral Density Estimation in Dispersion Unmanaged Coherent Metro Networks,” in Optical Fiber Communication Conference (OFC), 2019.

Johannisson, P.

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

Karlsson, M.

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

Kupfer, T.

C. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK Transmission Systems - OSA Technical Digest,” in Optical Fiber Communication Conference, OFC, 2012.

Layec, P.

Lonardi, M.

M. Lonardi, P. Ramantanis, P. Jenneve, and S. Bigo, “Power Spectral Density Estimation in Dispersion Unmanaged Coherent Metro Networks,” in Optical Fiber Communication Conference (OFC), 2019.

Lorcy, L.

Mecozzi, A.

Nuss, D.

C. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK Transmission Systems - OSA Technical Digest,” in Optical Fiber Communication Conference, OFC, 2012.

Poggiolini, P.

Ramantanis, P.

P. Jenneve, P. Ramantanis, N. Dubreuil, F. Boitier, P. Layec, and S. Bigo, “Measurement of Optical Nonlinear Distortions and Their Uncertainties in Coherent Systems,” J. Lightwave Technol. 35(24), 5432–5439 (2017).
[Crossref]

N. Rossi, P. Ramantanis, and J. C. Antona, “Nonlinear interference noise statistics in unmanaged coherent networks with channels propagating over different lightpaths,” Eur. Conf. Opt. Commun. ECOC, no. c, pp. 4–6, 2014.

M. Lonardi, P. Ramantanis, P. Jenneve, and S. Bigo, “Power Spectral Density Estimation in Dispersion Unmanaged Coherent Metro Networks,” in Optical Fiber Communication Conference (OFC), 2019.

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Rival, O.

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022 (2012).
[Crossref]

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Rossi, N.

A. Bononi, N. Rossi, and P. Serena, “On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems,” Opt. Express 20(26), B204 (2012).
[Crossref]

N. Rossi, P. Ramantanis, and J. C. Antona, “Nonlinear interference noise statistics in unmanaged coherent networks with channels propagating over different lightpaths,” Eur. Conf. Opt. Commun. ECOC, no. c, pp. 4–6, 2014.

Serena, P.

Seve, E.

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Shtaif, M.

Simonneau, C.

Vacondio, F.

F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022 (2012).
[Crossref]

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

Viterbi, A. J.

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

Viterbi, A. M.

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

Wichtlhuber, M.

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

Winzer, P. J.

Wissel, F.

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

IEEE Trans. Inf. Theory (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

J. Lightwave Technol. (9)

A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-phase modulation induced by OOK channels on higher-rate DQPSK and coherent QPSK channels,” J. Lightwave Technol. 27(18), 3974–3983 (2009).
[Crossref]

P. Serena and A. Bononi, “A time-domain extended gaussian noise model,” J. Lightwave Technol. 33(7), 1459–1472 (2015).
[Crossref]

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the Bit-Error-Rate Performance of Nonlinear Fiber-Optic Systems,” J. Lightwave Technol. 34(15), 3482–3489 (2016).
[Crossref]

R. Dar and P. J. Winzer, “Nonlinear Interference Mitigation: Methods and Potential Gain,” J. Lightwave Technol. 35(4), 903–930 (2017).
[Crossref]

A. Ghazisaeidi, “A Theory of Nonlinear Interactions between Signal and Amplified Spontaneous Emission Noise in Coherent Wavelength Division Multiplexed Systems,” J. Lightwave Technol. 35(23), 5150–5175 (2017).
[Crossref]

P. Jenneve, P. Ramantanis, N. Dubreuil, F. Boitier, P. Layec, and S. Bigo, “Measurement of Optical Nonlinear Distortions and Their Uncertainties in Coherent Systems,” J. Lightwave Technol. 35(24), 5432–5439 (2017).
[Crossref]

O. Golani, M. Feder, and M. Shtaif, “Kalman-MLSE Equalization for NLIN Mitigation,” J. Lightwave Technol. 36(12), 2541–2550 (2018).
[Crossref]

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightwave Technol. 31(8), 1273–1282 (2013).
[Crossref]

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30(24), 3857–3879 (2012).
[Crossref]

Nature (1)

M. S. Bartlett, “Smoothing periodograms from time-series with continuous spectra,” Nature 161(4096), 686–687 (1948).
[Crossref]

Opt. Express (3)

Other (9)

M. Gunkel, F. Wissel, J. Blendin, D. Herrmann, M. Wichtlhuber, and D. Hausheer, “Efficient Partial Recovery of Flexible-Rate Transceivers with SDN- based Asymmetric Multipath Routing of IP Traffic Recovery and Elastic Transmis- sion Technology,” in Photonic Networks; 17. ITG-Symposium, 2016, pp. 70–75.

M. Lonardi, P. Ramantanis, P. Jenneve, and S. Bigo, “Power Spectral Density Estimation in Dispersion Unmanaged Coherent Metro Networks,” in Optical Fiber Communication Conference (OFC), 2019.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

C. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK Transmission Systems - OSA Technical Digest,” in Optical Fiber Communication Conference, OFC, 2012.

N. Rossi, P. Ramantanis, and J. C. Antona, “Nonlinear interference noise statistics in unmanaged coherent networks with channels propagating over different lightpaths,” Eur. Conf. Opt. Commun. ECOC, no. c, pp. 4–6, 2014.

O. Golani, M. Feder, A. Mecozzi, and M. Shtaif, “Correlations and phase noise in NLIN-modelling and system implications,” 2016 Opt. Fiber Commun. Conf. Exhib., pp. 1–3, 2016.

E. Seve, P. Ramantanis, J.-C. Antonia, E. Grellier, O. Rival, F. Vacondio, and S. Bigo, “Semi-analytical model for the performance estimation of 100Gb/s PDM-QPSK optical transmission systems without inline dispersion compensation and mixed fiber types,” in European Conference on Optical Communication (ECOC), 2013.

J. C. Antona, S. Bigo, and J. P. Faure, “Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems,” in Optical Fiber Communication Conference (OFC), 2002.

10. J.-C. Antona and S. Bigo, “EP1736806A1 Method for determining the performance of a heterogeneous optical transmission system,” EP1736806A1, 2005.

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Figures (8)

Fig. 1.
Fig. 1. Mapper-to-demapper performance estimation concept. Looking at the source-to-destination communication line, the model not only estimates optical channel performance, i.e., from transducer-to-transducer, but also accounts for the digital signal processing unit, i.e., from mapper-to-demapper.
Fig. 2.
Fig. 2. One-span profiling calibration setup. ECL: external-cavity laser; DAC: digital-to-analog converter: ADC: analog-to-digital converter; PDM: polarization division multiplexer; I/Q: in-phase/quadrature; LEAF: large effective-area fiber; SSMF: standard single-mode fiber; LO: local oscillator; DSP: digital signal processing; EDFA erbium-doped fiber amplifier; WSS: wavelength selective switch; WDM: wavelength-division multiplex.
Fig. 3.
Fig. 3. Single-span calibrations spectral-densities for large effective area fiber (LEAF) (a) and standard single-mode fiber (SSMF) (b) at various input dispersion pre-distortion (D^in). As the pre-dispersion increases, the nonlinear effects become whiter, i.e. the central lobe narrows down, and stronger, i.e., the height of the curve rises.
Fig. 4.
Fig. 4. Heterogeneous four-span transmission setups. The experiment replicates the target system of [6] and uses the same transceiver of the setup of Fig. 2. A span is a concatenation of an erbium-doped fiber amplifier (EDFA), assuring a constant power at the input of the span, and a transmission fiber – either a large effective-area fiber (LEAF) or a standard single-mode fiber (SSMF).
Fig. 5.
Fig. 5. Power spectral densities of the investigated heterogeneous transmission links. On the left-hand side we have the total spectral density, while on the right-hand side we have the in-phase and quadrature components separated. PSD: power spectral density; S: standard single-mode fiber; L: large effective-area fiber;
Fig. 6.
Fig. 6. Experimental and estimated performance in terms of SNR versus wavelength-division multiplex (WDM) launch power for SSLL and LLSS (a) and SLLL and LLLS links (b). SNR: signal-to-noise ratio; NL: nonlinear.
Fig. 7.
Fig. 7. On the left-hand side, the magnitude-squared frequency response for different phase-estimation averaging taps (a). On the right-hand side, the actual (red) and the estimated by filtering of the quadrature component (blue) spectral densities for the LEAF-LEAF-SSMF-SSMF case using carrier-phase estimation with K=10 (b). K: half-window number of taps; Q: quadrature; PSD: power spectral density. Normalized Frequency = (Relative Frequency*2) / Symbol Rate.
Fig. 8.
Fig. 8. On the left-hand side, the experimental and estimated performance curves for the LLSS link for different number of phase-estimation half-window averaging taps, K (a). On the right-hand side, the estimation error at 20 dBm in terms of the SNR difference between estimated and real ΔSNR for the LLSS link with filtering and without filtering the quadrature component (b). At the bottom, the model estimation error for each investigated number of taps in terms of ΔSNR versus power (c). WDM: wavelength division multiplex; SNR: signal-to-noise ratio.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

STOTNSR(f)=NspSASENSR(f)+STRXNSR(f)+k=1Nsp[SaNLI(f,Dkin,Fk)+SaNLQ(f,Dkin,Fk)]P2
SNR=(R2R2SNLINSR(f)df)1
SaNLI/Q(f,Dkin,Fk)=(SI/Q(f,Dkin,Fk)12SASENSR(f)12STRXNSR(f))/P2
SNSR(f)=k=1NspSkQ(f)HKVV(f)+SkI(f)