Abstract

The optimisation of span length when designing optical communication systems is important from both performance and cost perspectives. In this paper, the optimisation of inter-amplifier spacing and the potential increase of span length at fixed information rates in optical communication systems with practically feasible nonlinearity compensation schemes have been investigated. It is found that in DP-16QAM, DP-64QAM and DP-256QAM systems with practical transceiver noise limitations, single-channel digital backpropagation can allow a 50% reduction in the number of amplifiers without sacrificing information rates compared to systems with optimal span lengths and linear compensation.

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  26. L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express 19(7), 5953–5959 (2011).
    [Crossref] [PubMed]
  27. A. Napoli, Z. Maalej, V. Sleiffer, M. Kuschnerov, D. Rafique, E. Timmers, B. Spinnler, T. Rahman, L. Coelho, and N. Hanik, “Reduced complexity digital back-propagation methods for optical communication systems,” J. Lightwave Technol. 32(7), 1351–1362 (2014).
    [Crossref]
  28. L. Du, D. Rafique, A. Napoli, B. Spinnler, A. D. Ellis, M. Kuschnerov, and A. Lowery, “Digital fiber nonlinearity compensation,” IEEE Signal Process. Mag. 31(2), 46–56 (2014).
    [Crossref]
  29. D. Rafique, “Fiber nonlinearity compensation: commercial applications and complexity analysis,” J. Lightwave Technol. 34(2), 544–553 (2016).
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  30. L. Galdino, D. Semrau, D. Lavery, G. Saavedra, C. B. Czegledi, E. Agrell, R. I. Killey, and P. Bayvel, “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express 25(4), 4564–4578 (2017).
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  33. R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” IEEE Photonics Technol. Lett. 28(11), 1253–1256 (2016).
    [Crossref]
  34. M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightwave Technol. 31(23), 3839–3852 (2013).
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2017 (4)

2016 (3)

D. Rafique, “Fiber nonlinearity compensation: commercial applications and complexity analysis,” J. Lightwave Technol. 34(2), 544–553 (2016).
[Crossref]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (2016).
[Crossref] [PubMed]

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” IEEE Photonics Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

2015 (2)

2014 (5)

2013 (3)

2012 (1)

2011 (3)

2010 (2)

2008 (1)

2005 (1)

2000 (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulations,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

1995 (1)

J. Delavaux and J. Nagel, “Multi-stage erbium-doped fiber amplifier designs,” J. Lightwave Technol. 13(5), 703–720 (1995).
[Crossref]

1990 (2)

H. Masuda and A. Takada, “High gain two-stage amplification with erbium-doped fibre amplifier,” Electron. Lett. 26(10), 661–662 (1990).
[Crossref]

A. Yariv, “Signal-to-noise considerations in fiber links with periodic or distributed optical amplification,” Opt. Lett. 15(19), 1064–1066 (1990).
[Crossref] [PubMed]

Agrell, E.

Alvarado, A.

Ania-Castañón, J. D.

Asif, R.

R. Asif, C. Lin, and B. Schmauss, “Impact of channel baud-rate on logarithmic digital backward propagation in DP-QPSK system with uncompensated transmission links,” Opt. Commun. 284(24), 5673–5677 (2011).
[Crossref]

Bayvel, P.

Benedetto, S.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulations,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

Beygi, L.

Bononi, A.

Bosco, G.

Brochier, N.

Carena, A.

Chien, H.-C.

Coelho, L.

Curri, V.

Czegledi, C. B.

Dar, R.

Delavaux, J.

J. Delavaux and J. Nagel, “Multi-stage erbium-doped fiber amplifier designs,” J. Lightwave Technol. 13(5), 703–720 (1995).
[Crossref]

Dong, Z.

Doran, N. J.

Downie, J.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Du, L.

L. Du, D. Rafique, A. Napoli, B. Spinnler, A. D. Ellis, M. Kuschnerov, and A. Lowery, “Digital fiber nonlinearity compensation,” IEEE Signal Process. Mag. 31(2), 46–56 (2014).
[Crossref]

Ellis, A. D.

L. Du, D. Rafique, A. Napoli, B. Spinnler, A. D. Ellis, M. Kuschnerov, and A. Lowery, “Digital fiber nonlinearity compensation,” IEEE Signal Process. Mag. 31(2), 46–56 (2014).
[Crossref]

N. J. Doran and A. D. Ellis, “Minimising total energy requirements in amplified links by optimising amplifier spacing,” Opt. Express 22(16), 19810–19817 (2014).
[Crossref] [PubMed]

Essiambre, R.-J.

Feder, M.

Fehenberger, T.

Forestieri, E.

Forghieri, F.

Foschini, G.

Friberg, A. T.

Galdino, L.

Gaudino, R.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulations,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

Goebel, B.

Gunkel, M.

Hanik, N.

Huo, D.

Ip, E.

Irukulapati, N. V.

Jacobsen, G.

Jia, Z.

Jiang, Y.

Johannisson, P.

Kahn, J.

Kaliteevskiy, N.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Karlsson, M.

Killey, R. I.

Kramer, G.

Kuschnerov, M.

Lavery, D.

Li, G.

Li, J.

Li, X.

Liga, G.

Lin, C.

R. Asif, C. Lin, and B. Schmauss, “Impact of channel baud-rate on logarithmic digital backward propagation in DP-QPSK system with uncompensated transmission links,” Opt. Commun. 284(24), 5673–5677 (2011).
[Crossref]

Lowery, A.

L. Du, D. Rafique, A. Napoli, B. Spinnler, A. D. Ellis, M. Kuschnerov, and A. Lowery, “Digital fiber nonlinearity compensation,” IEEE Signal Process. Mag. 31(2), 46–56 (2014).
[Crossref]

Maalej, Z.

Maher, R.

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (2016).
[Crossref] [PubMed]

Masuda, H.

H. Masuda and A. Takada, “High gain two-stage amplification with erbium-doped fibre amplifier,” Electron. Lett. 26(10), 661–662 (1990).
[Crossref]

Mayer, H.

Mecozzi, A.

Nagel, J.

J. Delavaux and J. Nagel, “Multi-stage erbium-doped fiber amplifier designs,” J. Lightwave Technol. 13(5), 703–720 (1995).
[Crossref]

Napoli, A.

Nasieva, I. O.

Paskov, M.

Pincemin, E.

Poggiolini, P.

Popov, S.

Prati, G.

Rafique, D.

Rahman, T.

Roudas, I.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Rukosueva, M.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Saavedra, G.

Schippel, A.

Schmauss, B.

R. Asif, C. Lin, and B. Schmauss, “Impact of channel baud-rate on logarithmic digital backward propagation in DP-QPSK system with uncompensated transmission links,” Opt. Commun. 284(24), 5673–5677 (2011).
[Crossref]

Secondini, M.

Semrau, D.

Serena, P.

Shevchenko, N. A.

Shtaif, M.

Sleiffer, V.

Spinnler, B.

Sterlingov, P.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Takada, A.

H. Masuda and A. Takada, “High gain two-stage amplification with erbium-doped fibre amplifier,” Electron. Lett. 26(10), 661–662 (1990).
[Crossref]

Ten, S.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Timmers, E.

Turitsyn, S. K.

Vanin, E.

Wagner, P.

Wang, K.

Winzer, P. J.

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” IEEE Photonics Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

Wood, W. A.

W. A. Wood, S. Ten, I. Roudas, P. Sterlingov, N. Kaliteevskiy, J. Downie, and M. Rukosueva, “Relative importance of optical fiber effective area and attenuation in span length optimization of ultra-long 100 Gbps PM-QPSK systems,” in Proceedings of SubOptic conference (2013), paper TU1C–3.

Wymeersch, H.

Xu, T.

Yariv, A.

Yu, J.

Zhang, Y.

Zhu, L.

Electron. Lett. (1)

H. Masuda and A. Takada, “High gain two-stage amplification with erbium-doped fibre amplifier,” Electron. Lett. 26(10), 661–662 (1990).
[Crossref]

IEEE Photonics Technol. Lett. (2)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Suppression of spurious tones induced by the split-step method in fiber systems simulations,” IEEE Photonics Technol. Lett. 12(5), 489–491 (2000).
[Crossref]

R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” IEEE Photonics Technol. Lett. 28(11), 1253–1256 (2016).
[Crossref]

IEEE Signal Process. Mag. (1)

L. Du, D. Rafique, A. Napoli, B. Spinnler, A. D. Ellis, M. Kuschnerov, and A. Lowery, “Digital fiber nonlinearity compensation,” IEEE Signal Process. Mag. 31(2), 46–56 (2014).
[Crossref]

J. Lightwave Technol. (11)

E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
[Crossref]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

G. Bosco, V. Curri, A. Carena, P. Poggiolini, and F. Forghieri, “On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers,” J. Lightwave Technol. 29(1), 53–61 (2011).
[Crossref]

A. Mecozzi and R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightwave Technol. 30(12), 2011–2024 (2012).
[Crossref]

J. Yu, Z. Dong, H.-C. Chien, Z. Jia, X. Li, D. Huo, M. Gunkel, P. Wagner, H. Mayer, and A. Schippel, “Transmission of 200 G PDM-CSRZ-QPSK and PDM-16 QAM With a SE of 4 b/s/Hz,” J. Lightwave Technol. 31(4), 515–522 (2013).
[Crossref]

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightwave Technol. 31(23), 3839–3852 (2013).
[Crossref]

A. Napoli, Z. Maalej, V. Sleiffer, M. Kuschnerov, D. Rafique, E. Timmers, B. Spinnler, T. Rahman, L. Coelho, and N. Hanik, “Reduced complexity digital back-propagation methods for optical communication systems,” J. Lightwave Technol. 32(7), 1351–1362 (2014).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightwave Technol. 33(2), 459–473 (2015).
[Crossref]

D. Rafique, “Fiber nonlinearity compensation: commercial applications and complexity analysis,” J. Lightwave Technol. 34(2), 544–553 (2016).
[Crossref]

J. Delavaux and J. Nagel, “Multi-stage erbium-doped fiber amplifier designs,” J. Lightwave Technol. 13(5), 703–720 (1995).
[Crossref]

G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” J. Lightwave Technol. 35(1), 113–123 (2017).
[Crossref]

Opt. Commun. (1)

R. Asif, C. Lin, and B. Schmauss, “Impact of channel baud-rate on logarithmic digital backward propagation in DP-QPSK system with uncompensated transmission links,” Opt. Commun. 284(24), 5673–5677 (2011).
[Crossref]

Opt. Express (8)

L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express 19(7), 5953–5959 (2011).
[Crossref] [PubMed]

T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010).
[Crossref] [PubMed]

L. Galdino, D. Semrau, D. Lavery, G. Saavedra, C. B. Czegledi, E. Agrell, R. I. Killey, and P. Bayvel, “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express 25(4), 4564–4578 (2017).
[Crossref] [PubMed]

T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, “Modulation format dependence of digital nonlinearity compensation performance in optical fibre communication systems,” Opt. Express 25(4), 3311–3326 (2017).
[Crossref] [PubMed]

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Opt. Express 23(7), 9183–9191 (2015).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Accumulation of nonlinear interference noise in fiber-optic systems,” Opt. Express 22(12), 14199–14211 (2014).
[Crossref] [PubMed]

N. J. Doran and A. D. Ellis, “Minimising total energy requirements in amplified links by optimising amplifier spacing,” Opt. Express 22(16), 19810–19817 (2014).
[Crossref] [PubMed]

L. Beygi, N. V. Irukulapati, E. Agrell, P. Johannisson, M. Karlsson, H. Wymeersch, P. Serena, and A. Bononi, “On nonlinearly-induced noise in single-channel optical links with digital backpropagation,” Opt. Express 21(22), 26376–26386 (2013).
[Crossref] [PubMed]

Opt. Lett. (4)

Philos Trans A Math Phys Eng Sci (1)

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, “Maximizing the optical network capacity,” Philos Trans A Math Phys Eng Sci 374(2062), 20140440 (2016).
[Crossref] [PubMed]

Other (6)

T. Fehenberger and N. Hanik, “Digital back-propagation of a superchannel: achievable rates and adaptation of the GN model,” in Proceedings of European Conference on Optical Communication (ECOC), (Institute of Electrical and Electronics Engineers, 2014), paper We.3.3.6.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematics of the Nyquist-spaced optical fibre communication system using EDC and single-channel DBP. PBS: polarisation beam splitter, PBC: polarisation beam combiner, LO: local oscillator, ADC: analogue-to-digital converter, MI: mutual information, Nch: number of WDM channels, N: number of spans.

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Fig. 2
Fig. 2 MI as a function of SNR for DP-QPSK, DP-16QAM, DP-64QAM and DP-256QAM based on the assumption of an AWGN channel model.

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Fig. 3
Fig. 3 MI versus span length for different modulation formats at 2400 km total reach in EDC and single-channel DBP schemes. Span lengths that achieve maximum MI are encircled with black dashed line.

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Fig. 4
Fig. 4 MI versus span length for DP-64QAM at varied total transmission distance with EDC and single-channel DBP.

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Fig. 5
Fig. 5 Span length as a function of target mutual information at different total system reach for DP-16QAM (a), DP-64QAM (b), and DP-256QAM (c) with single-channel DBP and EDC. The maximum MI values in linear compensation schemes and the span length at which single-channel DBP achieves them are indicated.

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Tables (2)

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Table 1 Transmission system parameters

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Table 2 DP-16QAM optimum launch powers for different span lengths at total distances of 2400, 4800 and 7200 km with both EDC and single-channel DBP

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Equations (5)

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Y=X+Z
σ z 2 =Var[ |  Z  | ]=Ε  [  |  Y−X  |   2 ]
SNR= σ x 2 σ z 2 .
MI= 2 M   ∑ x ∈ X   ∫ C   P Y|X ( y|x )   log 2 p Y|X ( y|x ) 1 M ∑ x ′  ∈ X p Y|X ( y| x ′ )  dy,
p Y|X ( y|x )= 1 π σ z 2 exp( − |  y−x  |   2 σ z 2 ).

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