Abstract

Although fruitful investigations of carrier phase estimation (CPE) have been conducted for a traditional coherent fiber optical transmission, there are few studies on the CPE for a nonlinear Fourier transform (NFT) based transmission. A laser linewidth induced phase noise leads to a phase rotation of the nonlinear spectra and the scattering data, which is similar to its effect on the linear spectra. Here, we first identify that both feed forward the M-th power, and the blind phase search (BPS)-based CPE can function well in the nonlinear frequency division multiplexing (NFDM) transmission with discrete spectrum modulation. Then, a performance comparison between two CPE schemes is presented for various modulation formats under the scenario of a single eigenvalue NFDM transmission. Our simulation results indicate that the laser linewidth tolerances of 2 GBaud quadrature phase shift keying (QPSK), 8-phase shift keying (8-PSK), and 16-amplitude phase shift keying (16-APSK) are 2.3 MHz, 1.05 MHz, and 250 KHz, respectively, given a 1-dB optical signal to noise ratio (OSNR) penalty at BER = 10−3. Finally, the BPS algorithm is experimentally verified under the same scenario of a 2 GBaud back-to-back transmission, due to the use of a semiconductor laser with a 100 KHz linewidth.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Opt. Photonics News 26(3), 28–35 (2015).
    [Crossref]
  2. R. J. Essiambre, R. W. Tkach, and R. Ryf, Fiber nonlinearity and capacity: single mode and multimode fibers (Academic, 2013).
  3. R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [Crossref]
  4. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the nonlinear Shannon limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
    [Crossref]
  5. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411(6841), 1027–1030 (2001).
    [Crossref]
  6. E. Ip and J. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [Crossref]
  7. I. Sackey, F. D. Ros, M. Jazayerifar, T. Richter, C. Meuer, M. Nolle, L. Molle, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation in 5×28-GBd PDM 16-QAM signal transmission over a dispersion-uncompensated link with backward-pumped distributed Raman amplification,” Opt. Express 22(22), 27381–27391 (2014).
    [Crossref]
  8. S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11(9), 570–576 (2017).
    [Crossref]
  9. J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
    [Crossref]
  10. S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4(3), 307–322 (2017).
    [Crossref]
  11. M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part II: numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
    [Crossref]
  12. T. Gui, C. Lu, A. P. L. Lau, and P. K. A. Wai, “High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform,” Opt. Express 25(17), 20286–20297 (2017).
    [Crossref]
  13. H. Bülow, V. Aref, and W. Idler, “Transmission of Waveforms Determined by 7 Eigenvalues with PSK-Modulated Spectral Amplitudes,” in European Conference on Optical Communication (ECOC) 2016, Tu3E.2.
  14. X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
    [Crossref]
  15. S. Gaiarin, A. M. Perego, E. P. da Silva, F. Da Ros, and D. Zibar, “Dual-polarization nonlinear Fourier transform-based optical communication system,” Optica 5(3), 263–270 (2018).
    [Crossref]
  16. X. Yangzhang, V. Aref, S. T. Le, H. Bulow, D. Lavery, and P. Bayvel, “Dual-polarisation nonlinear frequency division multiplexed transmission with b-modulation,” J. Lightwave Technol. 37(6), 1570–1578 (2019).
    [Crossref]
  17. W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
    [Crossref]
  18. T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.
  19. F. D. Ros, S. Gaiarin, and D. Zibar, “Impact of laser phase noise on nonlinear frequency division multiplexing systems,” in Conference on Lasers and Electro-Optics (CLEO) 2019, SW3O.6.
  20. S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
    [Crossref]
  21. M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in Optical Fiber Communication Conference (OFC) 2008, OTuM2.
  22. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
    [Crossref]
  23. Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
    [Crossref]
  24. V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” in European Conference on Optical Communication (ECOC) 2015, Tu 1.1.2.
  25. M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part III: spectrum modulation,” IEEE Trans. Inf. Theory 60(7), 4346–4369 (2014).
    [Crossref]
  26. Z. Zheng, X. Zhang, R. Yu, L. Xi, and X. Zhang, “Frequency offset estimation for nonlinear frequency division multiplexing with discrete spectrum modulation,” Opt. Express 27(20), 28223–28238 (2019).
    [Crossref]
  27. T. Gui, T. H. Chan, C. Lu, A. P. T. Lau, and P.-K. A. Wai, “Alternative decoding methods for optical communications based on nonlinear Fourier transform,” J. Lightwave Technol. 35(9), 1542–1550 (2017).
    [Crossref]

2019 (3)

2018 (2)

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

S. Gaiarin, A. M. Perego, E. P. da Silva, F. Da Ros, and D. Zibar, “Dual-polarization nonlinear Fourier transform-based optical communication system,” Optica 5(3), 263–270 (2018).
[Crossref]

2017 (4)

2015 (2)

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Opt. Photonics News 26(3), 28–35 (2015).
[Crossref]

2014 (4)

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

I. Sackey, F. D. Ros, M. Jazayerifar, T. Richter, C. Meuer, M. Nolle, L. Molle, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation in 5×28-GBd PDM 16-QAM signal transmission over a dispersion-uncompensated link with backward-pumped distributed Raman amplification,” Opt. Express 22(22), 27381–27391 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part II: numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part III: spectrum modulation,” IEEE Trans. Inf. Theory 60(7), 4346–4369 (2014).
[Crossref]

2010 (2)

2009 (2)

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
[Crossref]

2008 (1)

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref]

Aref, V.

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

X. Yangzhang, V. Aref, S. T. Le, H. Bulow, D. Lavery, and P. Bayvel, “Dual-polarisation nonlinear frequency division multiplexed transmission with b-modulation,” J. Lightwave Technol. 37(6), 1570–1578 (2019).
[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11(9), 570–576 (2017).
[Crossref]

H. Bülow, V. Aref, and W. Idler, “Transmission of Waveforms Determined by 7 Eigenvalues with PSK-Modulated Spectral Amplitudes,” in European Conference on Optical Communication (ECOC) 2016, Tu3E.2.

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” in European Conference on Optical Communication (ECOC) 2015, Tu 1.1.2.

Bayvel, P.

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

X. Yangzhang, V. Aref, S. T. Le, H. Bulow, D. Lavery, and P. Bayvel, “Dual-polarisation nonlinear frequency division multiplexed transmission with b-modulation,” J. Lightwave Technol. 37(6), 1570–1578 (2019).
[Crossref]

Blow, K. J.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

Buelow, H.

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11(9), 570–576 (2017).
[Crossref]

Bulow, H.

Bülow, H.

H. Bülow, V. Aref, and W. Idler, “Transmission of Waveforms Determined by 7 Eigenvalues with PSK-Modulated Spectral Amplitudes,” in European Conference on Optical Communication (ECOC) 2016, Tu3E.2.

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” in European Conference on Optical Communication (ECOC) 2015, Tu 1.1.2.

Chan, T. H.

Chen, J.

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Cotter, D.

Da Ros, F.

da Silva, E. P.

Derevyanko, S. A.

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4(3), 307–322 (2017).
[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

Dong, Z.

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.

Ellis, A. D.

Essiambre, R. J.

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

R. J. Essiambre, R. W. Tkach, and R. Ryf, Fiber nonlinearity and capacity: single mode and multimode fibers (Academic, 2013).

Foschini, G. J.

Frumin, L. L.

Gabitov, I.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

Gaiarin, S.

S. Gaiarin, A. M. Perego, E. P. da Silva, F. Da Ros, and D. Zibar, “Dual-polarization nonlinear Fourier transform-based optical communication system,” Optica 5(3), 263–270 (2018).
[Crossref]

F. D. Ros, S. Gaiarin, and D. Zibar, “Impact of laser phase noise on nonlinear frequency division multiplexing systems,” in Conference on Lasers and Electro-Optics (CLEO) 2019, SW3O.6.

Gemechu, W. A.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

Goebel, B.

Goossens, J. W.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

Gui, T.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

T. Gui, C. Lu, A. P. L. Lau, and P. K. A. Wai, “High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform,” Opt. Express 25(17), 20286–20297 (2017).
[Crossref]

T. Gui, T. H. Chan, C. Lu, A. P. T. Lau, and P.-K. A. Wai, “Alternative decoding methods for optical communications based on nonlinear Fourier transform,” J. Lightwave Technol. 35(9), 1542–1550 (2017).
[Crossref]

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.

Hafermann, H.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

Hari, S.

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

Hoffmann, S.

Idler, W.

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” in European Conference on Optical Communication (ECOC) 2015, Tu 1.1.2.

H. Bülow, V. Aref, and W. Idler, “Transmission of Waveforms Determined by 7 Eigenvalues with PSK-Modulated Spectral Amplitudes,” in European Conference on Optical Communication (ECOC) 2016, Tu3E.2.

Ip, E.

Jaouen, Y.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

Jazayerifar, M.

Kahn, J.

Kam, P. Y.

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Kamalian, M.

Kramer, G.

Kschischang, F. R.

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part III: spectrum modulation,” IEEE Trans. Inf. Theory 60(7), 4346–4369 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part II: numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
[Crossref]

Lau, A. P. L.

T. Gui, C. Lu, A. P. L. Lau, and P. K. A. Wai, “High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform,” Opt. Express 25(17), 20286–20297 (2017).
[Crossref]

T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.

Lau, A. P. T.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

T. Gui, T. H. Chan, C. Lu, A. P. T. Lau, and P.-K. A. Wai, “Alternative decoding methods for optical communications based on nonlinear Fourier transform,” J. Lightwave Technol. 35(9), 1542–1550 (2017).
[Crossref]

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

Lavery, D.

X. Yangzhang, V. Aref, S. T. Le, H. Bulow, D. Lavery, and P. Bayvel, “Dual-polarisation nonlinear frequency division multiplexed transmission with b-modulation,” J. Lightwave Technol. 37(6), 1570–1578 (2019).
[Crossref]

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

Le, S. T.

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

X. Yangzhang, V. Aref, S. T. Le, H. Bulow, D. Lavery, and P. Bayvel, “Dual-polarisation nonlinear frequency division multiplexed transmission with b-modulation,” J. Lightwave Technol. 37(6), 1570–1578 (2019).
[Crossref]

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4(3), 307–322 (2017).
[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11(9), 570–576 (2017).
[Crossref]

Lu, C.

T. Gui, C. Lu, A. P. L. Lau, and P. K. A. Wai, “High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform,” Opt. Express 25(17), 20286–20297 (2017).
[Crossref]

T. Gui, T. H. Chan, C. Lu, A. P. T. Lau, and P.-K. A. Wai, “Alternative decoding methods for optical communications based on nonlinear Fourier transform,” J. Lightwave Technol. 35(9), 1542–1550 (2017).
[Crossref]

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.

Meuer, C.

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref]

Molle, L.

Noe, R.

Nolle, M.

Perego, A. M.

Petermann, K.

Peucheret, C.

Pfau, T.

Prilepsky, J. E.

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4(3), 307–322 (2017).
[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

Richter, T.

Ros, F. D.

Ryf, R.

R. J. Essiambre, R. W. Tkach, and R. Ryf, Fiber nonlinearity and capacity: single mode and multimode fibers (Academic, 2013).

Sackey, I.

Schubert, C.

Schuh, K.

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” in European Conference on Optical Communication (ECOC) 2015, Tu 1.1.2.

Seimetz, M.

M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in Optical Fiber Communication Conference (OFC) 2008, OTuM2.

Song, M.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref]

Tkach, R. W.

R. J. Essiambre, R. W. Tkach, and R. Ryf, Fiber nonlinearity and capacity: single mode and multimode fibers (Academic, 2013).

Turitsyn, S. K.

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4(3), 307–322 (2017).
[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

Wabnitz, S.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

Wahls, S.

Wai, P. A.

T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.

Wai, P. K. A.

T. Gui, C. Lu, A. P. L. Lau, and P. K. A. Wai, “High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform,” Opt. Express 25(17), 20286–20297 (2017).
[Crossref]

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

Wai, P.-K. A.

Winzer, P. J.

Xi, L.

Yangzhang, X.

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

X. Yangzhang, V. Aref, S. T. Le, H. Bulow, D. Lavery, and P. Bayvel, “Dual-polarisation nonlinear frequency division multiplexed transmission with b-modulation,” J. Lightwave Technol. 37(6), 1570–1578 (2019).
[Crossref]

Yousefi, M.

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

Yousefi, M. I.

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part II: numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part III: spectrum modulation,” IEEE Trans. Inf. Theory 60(7), 4346–4369 (2014).
[Crossref]

Yu, C.

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Yu, R.

Zhang, S.

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Zhang, X.

Zhao, J.

Zheng, Z.

Zhong, K.

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

Zibar, D.

S. Gaiarin, A. M. Perego, E. P. da Silva, F. Da Ros, and D. Zibar, “Dual-polarization nonlinear Fourier transform-based optical communication system,” Optica 5(3), 263–270 (2018).
[Crossref]

F. D. Ros, S. Gaiarin, and D. Zibar, “Impact of laser phase noise on nonlinear frequency division multiplexing systems,” in Conference on Lasers and Electro-Optics (CLEO) 2019, SW3O.6.

IEEE Photonics Technol. Lett. (4)

X. Yangzhang, S. T. Le, V. Aref, H. Buelow, D. Lavery, and P. Bayvel, “Experimental Demonstration of Dual-polarisation NFDM Transmission with b-Modulation,” IEEE Photonics Technol. Lett. 31(11), 885–888 (2019).
[Crossref]

W. A. Gemechu, T. Gui, J. W. Goossens, M. Song, S. Wabnitz, H. Hafermann, A. P. T. Lau, M. I. Yousefi, and Y. Jaouen, “Dual polarization nonlinear frequency division multiplexing transmission,” IEEE Photonics Technol. Lett. 30(18), 1589–1592 (2018).
[Crossref]

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of Decision-Aided Maximum Likelihood phase estimation in coherent optical M-ary PSK and QAM Systems,” IEEE Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Z. Dong, S. Hari, T. Gui, K. Zhong, M. Yousefi, C. Lu, P. K. A. Wai, F. R. Kschischang, and A. P. T. Lau, “Nonlinear Frequency Division Multiplexed Transmissions based on NFT,” IEEE Photonics Technol. Lett. 27(15), 1621–1623 (2015).
[Crossref]

IEEE Trans. Inf. Theory (2)

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part III: spectrum modulation,” IEEE Trans. Inf. Theory 60(7), 4346–4369 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Part II: numerical methods,” IEEE Trans. Inf. Theory 60(7), 4329–4345 (2014).
[Crossref]

J. Lightwave Technol. (6)

Nat. Photonics (1)

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11(9), 570–576 (2017).
[Crossref]

Nature (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref]

Opt. Express (3)

Opt. Photonics News (1)

P. J. Winzer, “Scaling optical fiber networks: challenges and solutions,” Opt. Photonics News 26(3), 28–35 (2015).
[Crossref]

Optica (2)

Phys. Rev. Lett. (1)

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels,” Phys. Rev. Lett. 113(1), 013901 (2014).
[Crossref]

Other (6)

R. J. Essiambre, R. W. Tkach, and R. Ryf, Fiber nonlinearity and capacity: single mode and multimode fibers (Academic, 2013).

T. Gui, Z. Dong, C. Lu, P. A. Wai, and A. P. L. Lau, “Phase Modulation on Nonlinear Discrete Spectrum for Nonlinear Frequency Division Multiplexed Transmissions,” in Optical Fiber Communication Conference (OFC) 2016, W3A.2.

F. D. Ros, S. Gaiarin, and D. Zibar, “Impact of laser phase noise on nonlinear frequency division multiplexing systems,” in Conference on Lasers and Electro-Optics (CLEO) 2019, SW3O.6.

H. Bülow, V. Aref, and W. Idler, “Transmission of Waveforms Determined by 7 Eigenvalues with PSK-Modulated Spectral Amplitudes,” in European Conference on Optical Communication (ECOC) 2016, Tu3E.2.

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” in European Conference on Optical Communication (ECOC) 2015, Tu 1.1.2.

M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in Optical Fiber Communication Conference (OFC) 2008, OTuM2.

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Figures (8)

Fig. 1.
Fig. 1. Phase noise on the scattering dada $b(\lambda )$ under the back-to-back configuration, (a) without considering the laser linewidth and (b) with a linewidth of 100 KHz.
Fig. 2.
Fig. 2. (a) Flow of feed forward M-th power-based CPE; (b) class partitioning for 16-APSK format.
Fig. 3.
Fig. 3. Flow of feed forward BPS based CPE.
Fig. 4.
Fig. 4. Numerical simulation setup and corresponding DSP follows.
Fig. 5.
Fig. 5. BPS performance with respect to the number of test angles.
Fig. 6.
Fig. 6. OSNR penalty at BER = 10−3 with respect to the laser linewidth and block length for each modulation format under the condition of individual CPE algorithm, (a) feed forward M-th power and (b) feed forward BPS.
Fig. 7.
Fig. 7. OSNR penalty at BER = 10−3 vs the laser linewidth and symbol duration product under the condition of optimal block length (dashed lines denote BPS and solid lines denotes M-th power, respectively).
Fig. 8.
Fig. 8. BER performance for three modulation formats under the B2B transmission after the use of BPS (dashed lines are experiment results and solid lines represent the simulation results).

Tables (3)

Tables Icon

Table 1. Parameters of different modulation schemes.

Tables Icon

Table 2. Optimal block length for different modulation formats using tow CPE algorithms.

Tables Icon

Table 3. Laser linewidth tolerance under the condition of 1 dB OSNR penalty.

Equations (13)

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

j q z + 1 2 q t t + q | q | 2 = 0.
d v d t = ( j λ q ( t ) q ( t ) j λ ) v , lim t v ( t , λ ) = ( 1 0 ) e j λ t .
a ( λ ) = v 1 ( T 2 , λ ) e j λ T 2 , b ( λ ) = v 2 ( T 2 , λ ) e j λ T 2 .
q ~ c ( λ )  =  b ( λ ) / a ( λ ) , λ R , q ~ d ( λ n )  =  b ( λ n ) / a ( λ n ) , λ n C + .
a ( λ , z ) = a ( λ , 0 ) , b ( λ , z ) = b ( λ , 0 ) e 4 j λ 2 z , q ~ ( λ , z ) = q ~ ( λ , 0 ) e 4 j λ 2 z .
e j φ q ( t ) e j φ q ~ ( λ ) , q ( t ) e 2 j ω t q ~ ( λ ω ) .
S ( t ) = [ k = 0 M 1 Q k ( t k T 0 ) + Υ ] e j Ω t e j φ .
S ( t ) = k = 0 M 1 [ Q k ( t k T 0 ) e j Ω ( t k T 0 ) e j Ω k T 0 e j φ k + Υ ] { q ~ ( λ n ω ) e 4 j λ n 2 z e j k θ } k = 0 M 1 e j φ k + ξ .
b ( λ n , z ) = [ b ( λ n ω , 0 ) e 4 j λ n 2 z e j k θ ] e j φ k + ξ .
X k = A e j θ m e j ( φ k + φ n ) .
φ e s t = 1 M arg { k = 1 N b l o c k X k M } .
| d k , b | 2 = | X k , b d e c i s i o n ( X k , b ) | 2 .
b k d = { b | min ( e k , b ) , b = 1 , 2 , , B } , φ e s t = ( 2 b k d B 1 ) π M .

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