Abstract

An empirical phase noise channel model suitable for performance evaluation of high spectrally efficient modulations in 100G long-haul coherent optical transmission systems using polarization-division multiplexed and wavelength-division multiplexing channels is presented. The derivation of the model is worked out by exploiting the similarity between the power spectral density of the carrier extracted from the analysis of propagation measurements and the Lorentzian spectrum that is usually adopted to describe instabilities of semiconductor lasers. The proposed channel model is characterized by only two parameters: the linewidth of the carrier and the signal-to-noise ratio. We show that in the case of quadrature phase-shift keying transmission a good agreement exists between quantitative measures of performance extracted by processing experimental data and those obtained from simulations based on the use of the empirical model.

© 2011 OSA

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References

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  1. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2120 .
    [CrossRef] [PubMed]
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    [CrossRef]
  3. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
    [CrossRef]
  4. C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
    [CrossRef]
  5. A. Barbieri, G. Colavolpe, and G. Caire, “Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset,” IEEE Trans. Commun. 55(1), 171–179 (2007).
    [CrossRef]
  6. R. W. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
    [CrossRef]
  7. G. J. Foschini and G. Vannucci, “Characterizing filtered light waves corrupted by phase noise,” IEEE Trans. Inf. Theory 34(6), 1437–1448 (1988).
    [CrossRef]
  8. K. P. Ho, Phase-Modulated Optical Communication Systems, (Springer-Verlag, New York, NY, 2005).
  9. A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of non-linear phase noise,” J. Lightwave Technol. 25(10), 3008–3016 (2007).
    [CrossRef]
  10. A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Optical Fiber Communication Conference and Exposition, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO7.
  11. Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
    [CrossRef]
  12. M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. 4(11), 1269–1272 (1992).
    [CrossRef]
  13. Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
    [CrossRef]
  14. A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst., I Fundam. Theory Appl. 47, 655–674 (2000).
  15. J.-C. Antona, M. Lefrançois, S. Bigo, and G. Le Meur, “Investigation of advanced dispersion management techniques for ultra-long haul transmissions,” in Proceedings of European Conference on Optical Communications, Glasgow, Scotland, 2005, Mo.3.2.6.
  16. M. Salsi, C. Koebele, P. Tran, H. Mardoyan, E. Dutisseuil, J. Renaudier, M. Bigot-Astruc, L. Provost, S. Richard, P. Sillard, S. Bigo, and G. Charlet, “Transmission of 96×100Gb/s with 23% Super-FEC Overhead over 11,680km, using Optical Spectral Engineering,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMR2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OMR2
  17. T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWC2. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2011-NWC2
  18. U. Mengali and A. N. D'Andrea, Synchronization Techniques for Digital Receivers, (Plenum Press, New York, NY, 1997).
  19. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
    [CrossRef]

2011

2010

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

2009

2007

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2120 .
[CrossRef] [PubMed]

A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of non-linear phase noise,” J. Lightwave Technol. 25(10), 3008–3016 (2007).
[CrossRef]

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

A. Barbieri, G. Colavolpe, and G. Caire, “Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset,” IEEE Trans. Commun. 55(1), 171–179 (2007).
[CrossRef]

2000

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst., I Fundam. Theory Appl. 47, 655–674 (2000).

1992

M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. 4(11), 1269–1272 (1992).
[CrossRef]

1988

G. J. Foschini and G. Vannucci, “Characterizing filtered light waves corrupted by phase noise,” IEEE Trans. Inf. Theory 34(6), 1437–1448 (1988).
[CrossRef]

1986

R. W. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[CrossRef]

Arabaci, M.

Barbieri, A.

A. Barbieri, G. Colavolpe, and G. Caire, “Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset,” IEEE Trans. Commun. 55(1), 171–179 (2007).
[CrossRef]

Bayvel, P.

Caire, G.

A. Barbieri, G. Colavolpe, and G. Caire, “Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset,” IEEE Trans. Commun. 55(1), 171–179 (2007).
[CrossRef]

Chang, F.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[CrossRef]

Colavolpe, G.

A. Barbieri, G. Colavolpe, and G. Caire, “Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset,” IEEE Trans. Commun. 55(1), 171–179 (2007).
[CrossRef]

Demir, A.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst., I Fundam. Theory Appl. 47, 655–674 (2000).

Djordjevic, I. B.

Foschini, G. J.

G. J. Foschini and G. Vannucci, “Characterizing filtered light waves corrupted by phase noise,” IEEE Trans. Inf. Theory 34(6), 1437–1448 (1988).
[CrossRef]

Gavioli, G.

Herzet, C.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Hoffmann, S.

Hoshida, T.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Kahn, J. M.

Killey, R. I.

Lau, A. P. T.

Li, L.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Liu, L.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Lottici, V.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Luise, M.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Mehrotra, A.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst., I Fundam. Theory Appl. 47, 655–674 (2000).

Minkov, L. L.

Mizuochi, T.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

Moeneclaey, M.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Murakami, M.

M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. 4(11), 1269–1272 (1992).
[CrossRef]

Nakashima, H.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Noe, R.

Noels, N.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Oda, S.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Onohara, K.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

Pfau, T.

Rasmussen, J. C.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Roychowdhury, J.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst., I Fundam. Theory Appl. 47, 655–674 (2000).

Saito, S.

M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. 4(11), 1269–1272 (1992).
[CrossRef]

Savory, S. J.

Tanimura, T.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Tao, Z.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[CrossRef]

Vandendorpe, L.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Vannucci, G.

G. J. Foschini and G. Vannucci, “Characterizing filtered light waves corrupted by phase noise,” IEEE Trans. Inf. Theory 34(6), 1437–1448 (1988).
[CrossRef]

Wymeersch, H.

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Yan, W.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
[CrossRef]

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

IEEE Commun. Mag.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

IEEE J. Select. Top. Quantum Electron.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Select. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. 4(11), 1269–1272 (1992).
[CrossRef]

IEEE Trans. Circuits Syst., I Fundam. Theory Appl.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst., I Fundam. Theory Appl. 47, 655–674 (2000).

IEEE Trans. Commun.

A. Barbieri, G. Colavolpe, and G. Caire, “Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset,” IEEE Trans. Commun. 55(1), 171–179 (2007).
[CrossRef]

IEEE Trans. Inf. Theory

G. J. Foschini and G. Vannucci, “Characterizing filtered light waves corrupted by phase noise,” IEEE Trans. Inf. Theory 34(6), 1437–1448 (1988).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Proc. IEEE

C. Herzet, N. Noels, V. Lottici, H. Wymeersch, M. Luise, M. Moeneclaey, and L. Vandendorpe, “Code-aided turbo synchronization,” Proc. IEEE 95(6), 1255–1271 (2007).
[CrossRef]

Other

K. P. Ho, Phase-Modulated Optical Communication Systems, (Springer-Verlag, New York, NY, 2005).

A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Optical Fiber Communication Conference and Exposition, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO7.

J.-C. Antona, M. Lefrançois, S. Bigo, and G. Le Meur, “Investigation of advanced dispersion management techniques for ultra-long haul transmissions,” in Proceedings of European Conference on Optical Communications, Glasgow, Scotland, 2005, Mo.3.2.6.

M. Salsi, C. Koebele, P. Tran, H. Mardoyan, E. Dutisseuil, J. Renaudier, M. Bigot-Astruc, L. Provost, S. Richard, P. Sillard, S. Bigo, and G. Charlet, “Transmission of 96×100Gb/s with 23% Super-FEC Overhead over 11,680km, using Optical Spectral Engineering,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMR2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OMR2

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWC2. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2011-NWC2

U. Mengali and A. N. D'Andrea, Synchronization Techniques for Digital Receivers, (Plenum Press, New York, NY, 1997).

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Figures (3)

Fig. 1
Fig. 1

Experimental set-up for (a) generation, and (b) transmission and coherent detection of 100G homogeneous and hybrid WDM transmission.

Fig. 2
Fig. 2

Spectrum of the carrier plus AWGN for the empirical model and for the experimental data. (a) homogeneous case; (b) hybrid case.

Fig. 3
Fig. 3

Distribution of inter-arrival time between two consecutive errors after differential QPSK decoding. (a) homogeneous transmission; (b) hybrid transmission case.

Tables (1)

Tables Icon

Table 1 BER and MSEθ measures extracted from the experimental data and those obtained by simulation using the empirical model

Equations (7)

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

x k = s k e j θ k + n k ,
θ k+1 = θ k +δ w k ,
L θ ( f )= 4 δ 2 T δ 4 +16 π 2 f 2 T 2 ,
f HWHM = δ 2 4πT .
c k = x k s k = e j θ k + n k ,
S c ( f ) 1 T L θ ( f )+ 1 SNR , 1 2 fT < 1 2
MSE ϑ =E{ [ ( θ ^ k θ k ) modπ/2 ] 2 },

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