Abstract

We investigate via experiments and simulations the statistical properties and the accumulation of nonlinear transmission impairments in coherent systems without optical dispersion compensation. We experimentally show that signal distortion due to Kerr nonlinearity can be modeled as additive Gaussian noise, and we demonstrate that its variance has a supra-linear dependence on propagation distance for 100 Gb/s transmissions over both low dispersion and standard single mode fiber. We propose a simple empirical model to account for linear and nonlinear noise accumulation, and to predict system performance for a wide range of distances, signal powers and optical noise levels.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. ECOC 2010, paper P4.07 (2010).
  2. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with gaussian-distributed nonlinear noise,” Opt. Express 19(13), 12781–12788 (2011).
    [CrossRef] [PubMed]
  3. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links”, in Proc. OFC 2011, paper OTh07 (2011).
  4. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
    [CrossRef]
  5. A. Bononi, E. Grellier, P. Serena, N. Rossi, and F. Vacondio, “Modeling nonlinearity in coherent transmissions with dominant interpulse-four-wave-mixing,” in Proc. ECOC 2011, paper We.7.b.2 (2011).
  6. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [CrossRef] [PubMed]
  7. F. Forghieri, R. W. Tkach, and D. L. Favin, “Simple model of optical amplifier chains to evaluate penalties in WDM systems,” J. Lightwave Technol. 16(9), 1570–1576 (1998).
    [CrossRef]
  8. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analyitical model for nonlinear propagation in uncompensated optical links,” in Proc. ECOC 2011, paper We.7.B.2 (2011).
  9. D. Saha and T. G. Birdsall, “Quadrature-quadrature phase-shift keying,” IEEE Trans. Commun. 37(5), 437–448 (1989).
    [CrossRef]
  10. J. J. Filliben, “The probability plot correlation coefficient test for normality,” Technometrics 17(1), 111–117 (1975).
    [CrossRef]
  11. S. W. Looney and T. R. Gulledge, “Use of the correlation coefficient with normal probability plots,” Am. Stat. 39(1), 75–79 (1985).
    [CrossRef]
  12. E. Grellier, J.-C. Antona, and S. Bigo, “Global criteria to account for tolerance to nonlinearities of highly dispersive systems,” IEEE Photon. Technol. Lett. 22(10), 685–687 (2010).
    [CrossRef]
  13. A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?” in Proc. ECOC 2010, paper Th10E1 (2010).
  14. A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Proc. OFC 2011, paper OWO7 (2011).

2011

E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with gaussian-distributed nonlinear noise,” Opt. Express 19(13), 12781–12788 (2011).
[CrossRef] [PubMed]

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

2010

E. Grellier, J.-C. Antona, and S. Bigo, “Global criteria to account for tolerance to nonlinearities of highly dispersive systems,” IEEE Photon. Technol. Lett. 22(10), 685–687 (2010).
[CrossRef]

2008

1998

1989

D. Saha and T. G. Birdsall, “Quadrature-quadrature phase-shift keying,” IEEE Trans. Commun. 37(5), 437–448 (1989).
[CrossRef]

1985

S. W. Looney and T. R. Gulledge, “Use of the correlation coefficient with normal probability plots,” Am. Stat. 39(1), 75–79 (1985).
[CrossRef]

1975

J. J. Filliben, “The probability plot correlation coefficient test for normality,” Technometrics 17(1), 111–117 (1975).
[CrossRef]

Antona, J.-C.

E. Grellier, J.-C. Antona, and S. Bigo, “Global criteria to account for tolerance to nonlinearities of highly dispersive systems,” IEEE Photon. Technol. Lett. 22(10), 685–687 (2010).
[CrossRef]

Bigo, S.

E. Grellier, J.-C. Antona, and S. Bigo, “Global criteria to account for tolerance to nonlinearities of highly dispersive systems,” IEEE Photon. Technol. Lett. 22(10), 685–687 (2010).
[CrossRef]

Birdsall, T. G.

D. Saha and T. G. Birdsall, “Quadrature-quadrature phase-shift keying,” IEEE Trans. Commun. 37(5), 437–448 (1989).
[CrossRef]

Bononi, A.

Bosco, G.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

Carena, A.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

Curri, V.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

Favin, D. L.

Filliben, J. J.

J. J. Filliben, “The probability plot correlation coefficient test for normality,” Technometrics 17(1), 111–117 (1975).
[CrossRef]

Forghieri, F.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

F. Forghieri, R. W. Tkach, and D. L. Favin, “Simple model of optical amplifier chains to evaluate penalties in WDM systems,” J. Lightwave Technol. 16(9), 1570–1576 (1998).
[CrossRef]

Grellier, E.

E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with gaussian-distributed nonlinear noise,” Opt. Express 19(13), 12781–12788 (2011).
[CrossRef] [PubMed]

E. Grellier, J.-C. Antona, and S. Bigo, “Global criteria to account for tolerance to nonlinearities of highly dispersive systems,” IEEE Photon. Technol. Lett. 22(10), 685–687 (2010).
[CrossRef]

Gulledge, T. R.

S. W. Looney and T. R. Gulledge, “Use of the correlation coefficient with normal probability plots,” Am. Stat. 39(1), 75–79 (1985).
[CrossRef]

Looney, S. W.

S. W. Looney and T. R. Gulledge, “Use of the correlation coefficient with normal probability plots,” Am. Stat. 39(1), 75–79 (1985).
[CrossRef]

Poggiolini, P.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

Saha, D.

D. Saha and T. G. Birdsall, “Quadrature-quadrature phase-shift keying,” IEEE Trans. Commun. 37(5), 437–448 (1989).
[CrossRef]

Savory, S. J.

Tkach, R. W.

Am. Stat.

S. W. Looney and T. R. Gulledge, “Use of the correlation coefficient with normal probability plots,” Am. Stat. 39(1), 75–79 (1985).
[CrossRef]

IEEE Photon. Technol. Lett.

E. Grellier, J.-C. Antona, and S. Bigo, “Global criteria to account for tolerance to nonlinearities of highly dispersive systems,” IEEE Photon. Technol. Lett. 22(10), 685–687 (2010).
[CrossRef]

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011).
[CrossRef]

IEEE Trans. Commun.

D. Saha and T. G. Birdsall, “Quadrature-quadrature phase-shift keying,” IEEE Trans. Commun. 37(5), 437–448 (1989).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Technometrics

J. J. Filliben, “The probability plot correlation coefficient test for normality,” Technometrics 17(1), 111–117 (1975).
[CrossRef]

Other

A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?” in Proc. ECOC 2010, paper Th10E1 (2010).

A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Proc. OFC 2011, paper OWO7 (2011).

G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links”, in Proc. OFC 2011, paper OTh07 (2011).

A. Bononi, E. Grellier, P. Serena, N. Rossi, and F. Vacondio, “Modeling nonlinearity in coherent transmissions with dominant interpulse-four-wave-mixing,” in Proc. ECOC 2011, paper We.7.b.2 (2011).

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. ECOC 2010, paper P4.07 (2010).

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analyitical model for nonlinear propagation in uncompensated optical links,” in Proc. ECOC 2011, paper We.7.B.2 (2011).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Experimental setup of (a) transmitter and (b) recirculating loop.

Fig. 2
Fig. 2

(a) Back to back electrical SNR at the decision gate as function of the optical signal to noise ratio (b) Back to back BER-equivalent Q2 factor as function of the electrical SNR at the decision gate.

Fig. 3
Fig. 3

(a) Typical measured QPSK constellation from which SNR and BER are measured (b) Measured OSNRASE in 0.1nm after 15 spans of SSMF, as a function of channel power (without noise loading).

Fig. 4
Fig. 4

Probability plot correlation coefficient for normality testing calculated over 1000 samples. The test is repeated more than 2500 times, and for real and imaginary parts. (a) PL = −3 dBm (b) PH = + 4 dBm.

Fig. 5
Fig. 5

PDF of real and imaginary components of total noise (markers: measured signals, line: theoretical Gaussian). Insets show an example of measured constellations. (a) PL = −3 dBm (b) PH = + 4 dBm.

Fig. 6
Fig. 6

(a) Measured and modeled total SNR after 15x100km SSMF transmission with and without noise loading versus channel power (b) 1/SNRlin and 1/SNRNL are shown as percentage of the total 1/SNR.

Fig. 7
Fig. 7

(a) Q2 factor versus power per channel for 15x100km SSMF transmission, with and without noise loading (Solid lines: model, markers: experiment). (b) Model error vs. power per channel.

Fig. 8
Fig. 8

(a) Q2 factor versus power per channel for 15x100km NZDSF transmission, with and without noise loading (Solid lines: model, markers: experiment). (b) Model error vs. power per channel.

Fig. 9
Fig. 9

1/SNRNL calculated from measurements for different channel powers as function of number of spans in dB scale. Solid lines are linear fit. Transmission over (a) SSMF, (b) NZDSF

Fig. 10
Fig. 10

Measured BER-equivalent Q2 factor is shown as function of the number of spans in linear scale. Solid lines are the results of the model. Transmission over (a) SSMF, (b) NZDSF

Fig. 11
Fig. 11

Numerically calculated variance of nonlinear noise normalized to signal power (a) As function of the number of spans for NZDSF and SSMF, and (b) For a single span as function of chromatic dispersion at the input of the span.

Equations (6)

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

1/SNR = 1/ OSNR ASE + K TRX
BER = 0.5erfc( ηSNR )
1/ SNR tot = 1/ SNR lin + 1/ SNR NL
a NL = α NL N 1+ε
var( f k )=A P 3 C k ξ
var( f tot )=var( f 1 )+ k=2 N A P 3 C k ξ = A 1 P 3 +A P 3 D ξ L span ξ k=2 N (k1) ξ A 1 P 3 + A P 3 D ξ L span ξ 1+ξ (N1) 1+ξ

Metrics