Abstract

There is a large error floor in an ultra multi-level digital coherent transmission signal of 1024 QAM or higher, and we have yet to determine its origin. In this paper, we show that this large error floor results from guided acoustic-wave Brillouin scattering (GAWBS) phase noise. We prove experimentally that such an error floor can be greatly reduced by compensating for the GAWBS noise with a phase modulation technique. We show that the BER of a 1024 QAM signal was reduced from 8.7 × 10−4 to 2.7 × 10−4 after a 160 km transmission with GAWBS noise compensation. Furthermore, we successfully extend the transmission distance from 160 to 240 km with a 7% overhead forward error correction.

© 2019 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. Nakazawa, K. Kikuchi, and T. Miyazaki, eds., High Spectral Density Optical Transmission Technologies (Springer, 2010) Chap. 3.
  2. I. P. Kaminow, Tingye Li, and A. E. Willner, eds., Optical Fiber Telecommunications VIB -Systems and Networks (Academic, 2013) Chap. 7.
  3. M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.
  4. S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
    [Crossref]
  5. S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, P. J. Winzer, and S. Makovejs, “Probabilistically shaped PDM 2018-QAM transmission over up to 200 km of fiber using standard intradyne detection,” Opt. Express 26(4), 4522–4530 (2018).
    [Crossref]
  6. M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
    [Crossref]
  7. M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.
  8. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fiber,” Phys. Rev. Lett. 54(9), 939–942 (1985).
    [Crossref]
  9. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985).
    [Crossref]
  10. M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.
  11. Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express 20(11), 12508–12514 (2012). (2012).
    [Crossref]
  12. K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
    [Crossref]
  13. B. Szanfraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref]
  14. C. Paré, A. Villeneuve, P.-A. Bélanger, and N. J. Doran, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21(7), 459–461 (1996).
    [Crossref]
  15. Y. Koizumi, K. Toyoda, T. Omiya, M. Yoshida, T. Hirooka, and M. Nakazawa, “512 QAM transmission over 240 km using frequency-domain equalization in a digital coherent receiver,” Opt. Express 20(21), 23383–23389 (2012).
    [Crossref]
  16. T. Omiya, M. Yoshida, and M. Nakazawa, “400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE,” Opt. Express 21(3), 2632–2641 (2013).
    [Crossref]

2018 (3)

2013 (1)

2012 (2)

2010 (1)

2007 (1)

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

1996 (1)

1985 (2)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fiber,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[Crossref]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985).
[Crossref]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fiber,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[Crossref]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985).
[Crossref]

Bélanger, P.-A.

Chandrasekhar, S.

Chen, X.

Cho, J.

Doran, N. J.

Hirooka, T.

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

Y. Koizumi, K. Toyoda, T. Omiya, M. Yoshida, T. Hirooka, and M. Nakazawa, “512 QAM transmission over 240 km using frequency-domain equalization in a digital coherent receiver,” Opt. Express 20(21), 23383–23389 (2012).
[Crossref]

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

Hongo, J.

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

Kasai, K.

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.

Koizumi, Y.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fiber,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[Crossref]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985).
[Crossref]

Makovejs, S.

Marshall, T.

Nakazawa, M.

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

T. Omiya, M. Yoshida, and M. Nakazawa, “400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE,” Opt. Express 21(3), 2632–2641 (2013).
[Crossref]

Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express 20(11), 12508–12514 (2012). (2012).
[Crossref]

Y. Koizumi, K. Toyoda, T. Omiya, M. Yoshida, T. Hirooka, and M. Nakazawa, “512 QAM transmission over 240 km using frequency-domain equalization in a digital coherent receiver,” Opt. Express 20(21), 23383–23389 (2012).
[Crossref]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

Nebendahl, B.

Okamoto, S.

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

Olsson, S. L. I.

Omiya, T.

Paré, C.

Shelby, R. M.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985).
[Crossref]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fiber,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[Crossref]

Szanfraniec, B.

Takefushi, N.

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

Terayama, M.

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

Toyoda, K.

Villeneuve, A.

Winzer, P. J.

Yoshida, M.

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

T. Omiya, M. Yoshida, and M. Nakazawa, “400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE,” Opt. Express 21(3), 2632–2641 (2013).
[Crossref]

Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express 20(11), 12508–12514 (2012). (2012).
[Crossref]

Y. Koizumi, K. Toyoda, T. Omiya, M. Yoshida, T. Hirooka, and M. Nakazawa, “512 QAM transmission over 240 km using frequency-domain equalization in a digital coherent receiver,” Opt. Express 20(21), 23383–23389 (2012).
[Crossref]

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.

IEICE Electron. Express (1)

K. Kasai, J. Hongo, M. Yoshida, and M. Nakazawa, “Optical phase-locked loop for coherent transmission over 500 km using heterodyne detection with fiber lasers,” IEICE Electron. Express 4(3), 77–81 (2007).
[Crossref]

Opt. Express (7)

B. Szanfraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
[Crossref]

Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km,” Opt. Express 20(11), 12508–12514 (2012). (2012).
[Crossref]

Y. Koizumi, K. Toyoda, T. Omiya, M. Yoshida, T. Hirooka, and M. Nakazawa, “512 QAM transmission over 240 km using frequency-domain equalization in a digital coherent receiver,” Opt. Express 20(21), 23383–23389 (2012).
[Crossref]

T. Omiya, M. Yoshida, and M. Nakazawa, “400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE,” Opt. Express 21(3), 2632–2641 (2013).
[Crossref]

S. Okamoto, M. Terayama, M. Yoshida, K. Kasai, T. Hirooka, and M. Nakazawa, “Experimental and numerical comparison between probabilistically-shaped 4096 QAM and uniformly-shaped 1024 QAM in all-Raman amplified 160 km transmission,” Opt. Express 26(3), 3535–3543 (2018).
[Crossref]

S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, P. J. Winzer, and S. Makovejs, “Probabilistically shaped PDM 2018-QAM transmission over up to 200 km of fiber using standard intradyne detection,” Opt. Express 26(4), 4522–4530 (2018).
[Crossref]

M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018).
[Crossref]

Opt. Lett. (1)

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985).
[Crossref]

Phys. Rev. Lett. (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fiber,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[Crossref]

Other (5)

M. Yoshida, N. Takefushi, M. Terayama, K. Kasai, T. Hirooka, and M. Nakazawa, “Reverse phase modulation technique for GAWBS noise error floor elimination in 1024 QAM-160 km digital coherent transmission,” in OptoElectronics and Communications Conference2018, paper, 4B1-3.

M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds., High Spectral Density Optical Transmission Technologies (Springer, 2010) Chap. 3.

I. P. Kaminow, Tingye Li, and A. E. Willner, eds., Optical Fiber Telecommunications VIB -Systems and Networks (Academic, 2013) Chap. 7.

M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and M. Nakazawa, “QAM (72 Gbit/s) single-carrier coherent optical transmission with a potential SE of 15.8 bit/s/Hz in all-Raman amplified 160 km fiber link,” in Optical Fiber Communication Conference2018. paper Th1F.2.

M. Nakazawa, M. Terayama, S. Okamoto, M. Yoshida, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering and its digital compensation in coherent QAM transmission,” in Optical Fiber Communication Conference2018, paper M4B.2.

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Figures (9)

Fig. 1.
Fig. 1. Experimental setup for GAWBS noise compensation with a phase modulation method.
Fig. 2.
Fig. 2. Constellations of a carrier signal after a 160 km transmission. (a) Without GAWBS noise compensation and (b) with GAWBS noise compensation.
Fig. 3.
Fig. 3. Experimental setup for polarization-multiplexed, 3 Gbaud, 1024 QAM transmission over a 160 km transmission with a GAWBS noise compensator.
Fig. 4.
Fig. 4. Constellations of X- and Y-polarization data after a 160 km transmission. (a) Without GAWBS noise compensation and (b) with GAWBS noise compensation.
Fig. 5.
Fig. 5. BER performance of X- and Y-polarization data after 160 km transmission as a function of fiber launched power.
Fig. 6.
Fig. 6. RF spectrum of demodulated QAM signal after 160 km transmission with a launched power of 3 dBm.
Fig. 7.
Fig. 7. BER performance of a 1024 QAM signal after a 160 km transmission as a function of SNR. The solid and broken lines are theoretical curves calculated by using Eq. (3) with different X values.
Fig. 8.
Fig. 8. BER performance of a 1024 QAM signal as a function of transmission distance.
Fig. 9.
Fig. 9. Spectral layout of a WDM transmission system with GAWBS noise compensation.

Equations (3)

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

S N R = P S / P A S E ,
S N R = P S P A S E + P a d d = 1 1 / S N R + X .
B E R = 31 160 e r f c S N R 682