Abstract

We study the efficiency and numerical accuracy of two digital backpropagation schemes for post-compensating SOA-induced nonlinear impairments in the context of coherent receivers for advanced modulated formats. While the classical Runge–Kutta numerical techniques provide almost ideal post-compensation when the receiver sampling time tends to zero, this accuracy diminishes quickly as we approach realistic sampling times. At rates near Nyquist, despite much reduced complexity, our proposed digital filter back propagation technique outperforms Runge–Kutta techniques in terms of root mean square (rms) residual distortion. We quantify rms residual distortion for both methods as sampling time varies. We also examine bit error performance for 16-QAM, as well as the impact of SOA saturation level. We examine robustness to imperfect channel estimation.

© 2011 IEEE

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  1. P. Cho, Y. Achiam, G. Levy-Yurista, M. Margalit, Y. Gross, J. Khurgin, "Investigation of SOA nonlinearities on the amplification of DWDM channels with spectral efficiency up to 2.5 b/s/Hz," IEEE Photon. Technol. Lett. 16, 918-920 (2004).
  2. X. Wei, Y. Su, X. Liu, J. Leuthold, S. Chandrasekhar, "10-Gb/s RZ-DPSK transmitter using a saturated SOA as a power booster and limiting amplifier," IEEE Photon. Technol. Lett. 16, 1582-1584 (2004).
  3. X. Wei, L. Zhang, "Analysis of the phase noise in saturated SOAs for DPSK applications," IEEE J. Quantum Electron. 41, 554-561 (2005).
  4. M. Sauer, J. Hurley, "Experimental 43 Gb/s NRZ and DPSK performance comparison for systems with up to 8 concatenated SOAs," Proc. CLEO/QELS 2006 (2006) Paper CThY2.
  5. J. D. Downie, J. Hurley, Y. Mauro, "10.7 Gb/s uncompensated transmission over a 470 km hybrid fiber link with in-line SOAs using MLSE and duobinary signals," Opt. Exp. 16, 15759-15764 (2008).
  6. E. Ciaramella, A. D'Errico, V. Donzella, "Using semiconductor optical amplifiers with constant envelope WDM signals," IEEE J. Quantum Electron. 44, 403-409 (2008).
  7. T. Vallaitis, R. Bonk, J. Guetlein, D. Hillerkuss, J. Li, R. Brenot, F. Lelarge, G. H. Duan, W. Freude, J. Leuthold, "Quantum dot SOA input power dynamic range improvement for differential-phase encoded signals," Opt. Exp. 18, 6270-6276 (2010).
  8. R. Bonk, G. Huber, T. Vallaitis, R. Schmogrow, D. Hillerkuss, C. Koos, W. Freude, J. Leuthold, "Impact of alpha-factor on SOA dynamic range for 20 GBd BPSK, QPSK and 16-QAM signals," Proc. OFC 2011 (2011).
  9. D. Zimmerman, L. Spiekman, "Amplifiers for the masses: EDFA, EDWA, and SOA amplets for metro and access applications," IEEE J. Lightw. Technol. 22, 63-70 (2004).
  10. B. Mikkelsen, S. Danielsen, C. Joergensen, R. Pedersen, H. Poulsen, K. Stubkjaer, "All-optical noise reduction capability of interferometric wavelength converters,," Electron. Lett. 32, 566-567 (1996).
  11. T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, K. E. Stubkjaer, "All-optical wavelength conversion by semiconductor," J. Lightw. Technol. 14, 942 (1996).
  12. O. Leclerc, B. Lavigne, E. Balmefrezol, P. Brindel, L. Pierre, D. Rouvillain, F. Seguineau, "Optical regeneration at 40 Gb/s and beyond," J. Lightw. Technol. 21, 2779-2790 (2003).
  13. D. Marcenac, D. Nesset, A. Kelly, D. Gavrilovic, "40 Gbit/s transmission over 103 km of NDSF using polarisation independent midspan spectral inversion by four-wave mixing in a semiconductor optical amplifier," Electron. Lett. 34, 100-101 (1998).
  14. A. Ghazisaeidi, F. Vacondio, A. Bononi, L. A. Rusch, "SOA intensity noise suppression: Multicanonical monte carlo simulator of extremely low BER," J. Lightw. Technol. 27, 2667-2677 (2009).
  15. Q. Xu, A. Ghazisaeidi, S. Doucet, Y. B. M'Sallem, L. A. Rusch, S. LaRochelle, "Tunable SOA wavelength converter for optical packet switching router," Proc. 23rd Ann. Meeting IEEE Photon. Soc. (2010) pp. 624-625.
  16. G. Agrawal, N. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).
  17. A. Mecozzi, J. Mork, "Saturation effects in nondegenerate fourwave mixing between short optical pulses in semiconductor laser amplifiers," IEEE J. Sel. Topics Quantum Electron. 3, 1190-1207 (1997).
  18. E. Ip, "Nonlinear compensation using backpropagation for polarization-multiplexed transmission," J. Lightw. Technol. 28, 939-951 (2010).
  19. X. Li, G. Li, "Electrical postcompensation of SOA impairments for fiber-optic transmission," IEEE Photon. Technol. Lett. 21, 581-583 (2009).
  20. X. Li, G. Li, "Joint fiber and SOA compensation using digital backward propagation," IEEE Photon. J. 2, 753-758 (2010).
  21. F. Vacondio, A. Ghazisaeidi, A. Bononi, L.-A. Rusch, "Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK," J. Lightw. Technol. 28, 277-288 (2010).
  22. D. Cassioli, S. Scotti, A. Mecozzi, "A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers," IEEE J. Quantum Electron. 36, 1072-1080 (2000).
  23. M. Shtaif, B. Tromborg, G. Eisenstein, "Noise spectra of semiconductor optical amplifiers: Relation between semiclassical and quantum descriptions," IEEE J. Quantum Electron 34, 869-878 (1998).
  24. M. C. Jeruchim, P. Balaban, K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).

2010 (4)

T. Vallaitis, R. Bonk, J. Guetlein, D. Hillerkuss, J. Li, R. Brenot, F. Lelarge, G. H. Duan, W. Freude, J. Leuthold, "Quantum dot SOA input power dynamic range improvement for differential-phase encoded signals," Opt. Exp. 18, 6270-6276 (2010).

E. Ip, "Nonlinear compensation using backpropagation for polarization-multiplexed transmission," J. Lightw. Technol. 28, 939-951 (2010).

X. Li, G. Li, "Joint fiber and SOA compensation using digital backward propagation," IEEE Photon. J. 2, 753-758 (2010).

F. Vacondio, A. Ghazisaeidi, A. Bononi, L.-A. Rusch, "Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK," J. Lightw. Technol. 28, 277-288 (2010).

2009 (2)

X. Li, G. Li, "Electrical postcompensation of SOA impairments for fiber-optic transmission," IEEE Photon. Technol. Lett. 21, 581-583 (2009).

A. Ghazisaeidi, F. Vacondio, A. Bononi, L. A. Rusch, "SOA intensity noise suppression: Multicanonical monte carlo simulator of extremely low BER," J. Lightw. Technol. 27, 2667-2677 (2009).

2008 (2)

J. D. Downie, J. Hurley, Y. Mauro, "10.7 Gb/s uncompensated transmission over a 470 km hybrid fiber link with in-line SOAs using MLSE and duobinary signals," Opt. Exp. 16, 15759-15764 (2008).

E. Ciaramella, A. D'Errico, V. Donzella, "Using semiconductor optical amplifiers with constant envelope WDM signals," IEEE J. Quantum Electron. 44, 403-409 (2008).

2006 (1)

M. Sauer, J. Hurley, "Experimental 43 Gb/s NRZ and DPSK performance comparison for systems with up to 8 concatenated SOAs," Proc. CLEO/QELS 2006 (2006) Paper CThY2.

2005 (1)

X. Wei, L. Zhang, "Analysis of the phase noise in saturated SOAs for DPSK applications," IEEE J. Quantum Electron. 41, 554-561 (2005).

2004 (3)

P. Cho, Y. Achiam, G. Levy-Yurista, M. Margalit, Y. Gross, J. Khurgin, "Investigation of SOA nonlinearities on the amplification of DWDM channels with spectral efficiency up to 2.5 b/s/Hz," IEEE Photon. Technol. Lett. 16, 918-920 (2004).

X. Wei, Y. Su, X. Liu, J. Leuthold, S. Chandrasekhar, "10-Gb/s RZ-DPSK transmitter using a saturated SOA as a power booster and limiting amplifier," IEEE Photon. Technol. Lett. 16, 1582-1584 (2004).

D. Zimmerman, L. Spiekman, "Amplifiers for the masses: EDFA, EDWA, and SOA amplets for metro and access applications," IEEE J. Lightw. Technol. 22, 63-70 (2004).

2003 (1)

O. Leclerc, B. Lavigne, E. Balmefrezol, P. Brindel, L. Pierre, D. Rouvillain, F. Seguineau, "Optical regeneration at 40 Gb/s and beyond," J. Lightw. Technol. 21, 2779-2790 (2003).

2000 (1)

D. Cassioli, S. Scotti, A. Mecozzi, "A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers," IEEE J. Quantum Electron. 36, 1072-1080 (2000).

1998 (2)

M. Shtaif, B. Tromborg, G. Eisenstein, "Noise spectra of semiconductor optical amplifiers: Relation between semiclassical and quantum descriptions," IEEE J. Quantum Electron 34, 869-878 (1998).

D. Marcenac, D. Nesset, A. Kelly, D. Gavrilovic, "40 Gbit/s transmission over 103 km of NDSF using polarisation independent midspan spectral inversion by four-wave mixing in a semiconductor optical amplifier," Electron. Lett. 34, 100-101 (1998).

1997 (1)

A. Mecozzi, J. Mork, "Saturation effects in nondegenerate fourwave mixing between short optical pulses in semiconductor laser amplifiers," IEEE J. Sel. Topics Quantum Electron. 3, 1190-1207 (1997).

1996 (2)

B. Mikkelsen, S. Danielsen, C. Joergensen, R. Pedersen, H. Poulsen, K. Stubkjaer, "All-optical noise reduction capability of interferometric wavelength converters,," Electron. Lett. 32, 566-567 (1996).

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, K. E. Stubkjaer, "All-optical wavelength conversion by semiconductor," J. Lightw. Technol. 14, 942 (1996).

1989 (1)

G. Agrawal, N. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).

Electron. Lett. (2)

B. Mikkelsen, S. Danielsen, C. Joergensen, R. Pedersen, H. Poulsen, K. Stubkjaer, "All-optical noise reduction capability of interferometric wavelength converters,," Electron. Lett. 32, 566-567 (1996).

D. Marcenac, D. Nesset, A. Kelly, D. Gavrilovic, "40 Gbit/s transmission over 103 km of NDSF using polarisation independent midspan spectral inversion by four-wave mixing in a semiconductor optical amplifier," Electron. Lett. 34, 100-101 (1998).

IEEE J. Quantum Electron. (1)

E. Ciaramella, A. D'Errico, V. Donzella, "Using semiconductor optical amplifiers with constant envelope WDM signals," IEEE J. Quantum Electron. 44, 403-409 (2008).

IEEE J. Lightw. Technol. (1)

D. Zimmerman, L. Spiekman, "Amplifiers for the masses: EDFA, EDWA, and SOA amplets for metro and access applications," IEEE J. Lightw. Technol. 22, 63-70 (2004).

IEEE J. Quantum Electron. (1)

X. Wei, L. Zhang, "Analysis of the phase noise in saturated SOAs for DPSK applications," IEEE J. Quantum Electron. 41, 554-561 (2005).

IEEE J. Quantum Electron (1)

M. Shtaif, B. Tromborg, G. Eisenstein, "Noise spectra of semiconductor optical amplifiers: Relation between semiclassical and quantum descriptions," IEEE J. Quantum Electron 34, 869-878 (1998).

IEEE J. Quantum Electron. (2)

D. Cassioli, S. Scotti, A. Mecozzi, "A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers," IEEE J. Quantum Electron. 36, 1072-1080 (2000).

G. Agrawal, N. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).

IEEE J. Sel. Topics Quantum Electron. (1)

A. Mecozzi, J. Mork, "Saturation effects in nondegenerate fourwave mixing between short optical pulses in semiconductor laser amplifiers," IEEE J. Sel. Topics Quantum Electron. 3, 1190-1207 (1997).

IEEE Photon. Technol. Lett. (2)

X. Li, G. Li, "Electrical postcompensation of SOA impairments for fiber-optic transmission," IEEE Photon. Technol. Lett. 21, 581-583 (2009).

X. Wei, Y. Su, X. Liu, J. Leuthold, S. Chandrasekhar, "10-Gb/s RZ-DPSK transmitter using a saturated SOA as a power booster and limiting amplifier," IEEE Photon. Technol. Lett. 16, 1582-1584 (2004).

IEEE Photon. J. (1)

X. Li, G. Li, "Joint fiber and SOA compensation using digital backward propagation," IEEE Photon. J. 2, 753-758 (2010).

IEEE Photon. Technol. Lett. (1)

P. Cho, Y. Achiam, G. Levy-Yurista, M. Margalit, Y. Gross, J. Khurgin, "Investigation of SOA nonlinearities on the amplification of DWDM channels with spectral efficiency up to 2.5 b/s/Hz," IEEE Photon. Technol. Lett. 16, 918-920 (2004).

J. Lightw. Technol. (1)

F. Vacondio, A. Ghazisaeidi, A. Bononi, L.-A. Rusch, "Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK," J. Lightw. Technol. 28, 277-288 (2010).

J. Lightw. Technol. (4)

E. Ip, "Nonlinear compensation using backpropagation for polarization-multiplexed transmission," J. Lightw. Technol. 28, 939-951 (2010).

A. Ghazisaeidi, F. Vacondio, A. Bononi, L. A. Rusch, "SOA intensity noise suppression: Multicanonical monte carlo simulator of extremely low BER," J. Lightw. Technol. 27, 2667-2677 (2009).

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, K. E. Stubkjaer, "All-optical wavelength conversion by semiconductor," J. Lightw. Technol. 14, 942 (1996).

O. Leclerc, B. Lavigne, E. Balmefrezol, P. Brindel, L. Pierre, D. Rouvillain, F. Seguineau, "Optical regeneration at 40 Gb/s and beyond," J. Lightw. Technol. 21, 2779-2790 (2003).

Opt. Exp. (2)

J. D. Downie, J. Hurley, Y. Mauro, "10.7 Gb/s uncompensated transmission over a 470 km hybrid fiber link with in-line SOAs using MLSE and duobinary signals," Opt. Exp. 16, 15759-15764 (2008).

T. Vallaitis, R. Bonk, J. Guetlein, D. Hillerkuss, J. Li, R. Brenot, F. Lelarge, G. H. Duan, W. Freude, J. Leuthold, "Quantum dot SOA input power dynamic range improvement for differential-phase encoded signals," Opt. Exp. 18, 6270-6276 (2010).

Proc. CLEO/QELS 2006 (1)

M. Sauer, J. Hurley, "Experimental 43 Gb/s NRZ and DPSK performance comparison for systems with up to 8 concatenated SOAs," Proc. CLEO/QELS 2006 (2006) Paper CThY2.

Other (3)

R. Bonk, G. Huber, T. Vallaitis, R. Schmogrow, D. Hillerkuss, C. Koos, W. Freude, J. Leuthold, "Impact of alpha-factor on SOA dynamic range for 20 GBd BPSK, QPSK and 16-QAM signals," Proc. OFC 2011 (2011).

Q. Xu, A. Ghazisaeidi, S. Doucet, Y. B. M'Sallem, L. A. Rusch, S. LaRochelle, "Tunable SOA wavelength converter for optical packet switching router," Proc. 23rd Ann. Meeting IEEE Photon. Soc. (2010) pp. 624-625.

M. C. Jeruchim, P. Balaban, K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).

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