Abstract

We propose and demonstrate a single-step digital back propagation (DBP) algorithm for metro and regional transmissions with high order modulation formats. Based on subcarrier-multiplexing (SCM)-DBP, two modifications are made to improve performance and reduce complexity for the targeted link scenarios. First, an infinite impulse response (IIR) filter is adopted in self-subcarrier nonlinear compensation. Second, the second stage chromatic dispersion (CD) compensation is incorporated into an existing adaptive filter. Through experiment, we demonstrate the performance of the proposed scheme, denoted as M-SCM-DBP, for single channel 34.94-GBd SCM PDM-32QAM transmission. With 86.3% complexity reduction compared with the low-pass filter assisted DBP, the proposed M-SCM-DBP achieves 0.6-dB Q2 improvement for SCM-PDM-32QAM transmission over 960-km standard single mode fiber (SSMF). The reach extension of 36% to 1220-km is achieved with only 30.5 complex multiplications per sample, in comparison with the linear compensation scheme. Since the adaptive filter is used to simultaneously compensate 50% CD and other linear impairments, we also investigate the required number of filter taps and its polarization tracking ability.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Low complexity digital backpropagation for high baud subcarrier-multiplexing systems

Fangyuan Zhang, Qunbi Zhuge, Meng Qiu, and David V. Plant
Opt. Express 24(15) 17027-17040 (2016)

Low complexity split digital backpropagation for digital subcarrier-multiplexing optical transmissions

Zhuopeng Xiao, Qunbi Zhuge, Songnian Fu, Fangyuan Zhang, Meng Qiu, Ming Tang, Deming Liu, and David V. Plant
Opt. Express 25(22) 27824-27833 (2017)

Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission

Chien-Yu Lin, Rameez Asif, Michael Holtmannspoetter, and Bernhard Schmauss
Opt. Express 20(26) B405-B412 (2012)

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [Crossref]
  3. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intra-channel nonlinearity compensation algorithm operating at symbol rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011).
    [Crossref]
  4. S. Zhou, X. Li, L. Yi, Q. Yang, and S. Fu, “Transmission of 2×56Gb/s PAM-4 signal over 100 km SMF using 18 GHz DMLs,” Opt. Lett. 41(8), 1805–1808 (2016).
    [Crossref]
  5. X. Qi, X. Zhang, H. Wei, and D. V. Plant, “Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations,” J. Opt. Soc. Am. B 23(10), 2032–2039 (2006).
    [Crossref]
  6. R. Dar and P. J. Winzer, “Nonlinear interference mitigation: methods and potential Gain,” J. Lightwave Technol. 35(4), 903–930 (2017).
    [Crossref]
  7. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [Crossref]
  8. L. Liu, L. Li, Y. Huang, K. Cui, Q. Xiong, F. N. Hauske, C. Xie, and Y. Cai, “Intra-channel nonlinearity compensation by inverse Volterra series transfer function,” J. Lightwave Technol. 30(3), 310–316 (2012).
    [Crossref]
  9. W. Shieh and Y. Tang, “Ultrahigh-speed signal transmission over nonlinear and dispersive fiber optic channel: the multicarrier advantage,” IEEE Photonics J. 2(3), 276–283 (2010).
    [Crossref]
  10. P. Poggiolini, A. Nespola, Y. Jiang, G. Bosco, A. Carena, L. Bertignono, S. M. Bilal, S. Abrate, and F. Forghieri, “Analytical and experimental results on system maximum reach increase through symbol rate optimization,” J. Lightwave Technol. 34(8), 1872–1885 (2016).
    [Crossref]
  11. M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. M. Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).
    [Crossref]
  12. 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]
  13. F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightwave Technol. 33(24), 5140–5150 (2015).
    [Crossref]
  14. L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010).
    [Crossref]
  15. F. Zhang, Q. Zhuge, M. Qiu, and D. V. Plant, “Low complexity digital backpropagation for high baud subcarrier-multiplexing systems,” Opt. Express 24(15), 17027–17040 (2016).
    [Crossref]
  16. Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity split digital backpropagation for digital subcarrier-multiplexing optical transmissions,” Opt. Express 25(22), 27824–27833 (2017).
    [Crossref]
  17. J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.
  18. Q. Zhuge, B. Chatelain, and D. V. Plant, “Comparison of intra-channel nonlinearity tolerance between reduced guard-interval CO-OFDM systems and Nyquist single carrier systems,” in proceedings of Optical Fiber Communication Conference (OFC, 2012), paper OTh1B.3.
  19. M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. M. Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).
    [Crossref]
  20. Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity single-step digital backpropagation for high order QAM subcarrier-multiplexing transmission,” in proceedings of Asia Communications and Photonics Conference (ACP, 2017), paper Su4B.2.
  21. S. J. Savory, “Digital filters for coherent optical receivers,” Opt.Express 16(2), 804–817(2008).
    [Crossref]
  22. Z. Xiao, S. Fu, S. Yao, M. Tang, P. Shum, and D. Liu, “ICI mitigation for dual-carrier super-channel transmission based on m-PSK and m-QAM formats,” J. Lightwave Technol. 34(23), 5526–5533 (2016).
    [Crossref]

2017 (2)

2016 (4)

2015 (1)

2014 (2)

2012 (1)

2011 (2)

2010 (3)

2008 (3)

2006 (1)

Abrate, S.

Bertignono, L.

Bilal, S. M.

Bolshtyansky, M.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Bosco, G.

Cai, J. X.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Cai, Y.

Carena, A.

Chagnon, M.

Chatelain, B.

Q. Zhuge, B. Chatelain, and D. V. Plant, “Comparison of intra-channel nonlinearity tolerance between reduced guard-interval CO-OFDM systems and Nyquist single carrier systems,” in proceedings of Optical Fiber Communication Conference (OFC, 2012), paper OTh1B.3.

Cui, K.

Dar, R.

Dou, L.

Du, L. B.

Essiambre, R. J.

Forghieri, F.

Foschini, G. J.

Foursa, D. G.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Fu, S.

Gao, Y.

Goebel, B.

Hauske, F. N.

Hoshida, T.

Huang, Y.

Ip, E.

Jiang, Y.

Kahn, J. M.

Kramer, G.

Li, L.

Li, X.

Liu, D.

Liu, L.

Lowery, A. J.

Mazurczyk, M.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Nespola, A.

Oda, S.

Osman, M. M.

Pilipetskii, A.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Plant, D. V.

Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity split digital backpropagation for digital subcarrier-multiplexing optical transmissions,” Opt. Express 25(22), 27824–27833 (2017).
[Crossref]

F. Zhang, Q. Zhuge, M. Qiu, and D. V. Plant, “Low complexity digital backpropagation for high baud subcarrier-multiplexing systems,” Opt. Express 24(15), 17027–17040 (2016).
[Crossref]

F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightwave Technol. 33(24), 5140–5150 (2015).
[Crossref]

M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. M. Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).
[Crossref]

M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. M. Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).
[Crossref]

X. Qi, X. Zhang, H. Wei, and D. V. Plant, “Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations,” J. Opt. Soc. Am. B 23(10), 2032–2039 (2006).
[Crossref]

Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity single-step digital backpropagation for high order QAM subcarrier-multiplexing transmission,” in proceedings of Asia Communications and Photonics Conference (ACP, 2017), paper Su4B.2.

Q. Zhuge, B. Chatelain, and D. V. Plant, “Comparison of intra-channel nonlinearity tolerance between reduced guard-interval CO-OFDM systems and Nyquist single carrier systems,” in proceedings of Optical Fiber Communication Conference (OFC, 2012), paper OTh1B.3.

Poggiolini, P.

Qi, X.

Qiu, M.

Rasmussen, J. C.

Savory, S. J.

S. J. Savory, “Digital filters for coherent optical receivers,” Opt.Express 16(2), 804–817(2008).
[Crossref]

Shieh, W.

W. Shieh and Y. Tang, “Ultrahigh-speed signal transmission over nonlinear and dispersive fiber optic channel: the multicarrier advantage,” IEEE Photonics J. 2(3), 276–283 (2010).
[Crossref]

Shum, P.

Sinkin, O. V.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Tang, M.

Tang, Y.

W. Shieh and Y. Tang, “Ultrahigh-speed signal transmission over nonlinear and dispersive fiber optic channel: the multicarrier advantage,” IEEE Photonics J. 2(3), 276–283 (2010).
[Crossref]

Tao, Z.

Wang, W.

Wei, H.

Winzer, P. J.

Xiao, Z.

Xie, C.

Xiong, Q.

Xu, X.

Yan, W.

Yang, Q.

Yao, S.

Yi, L.

Zhang, F.

Zhang, X.

Zhou, S.

Zhuge, Q.

Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity split digital backpropagation for digital subcarrier-multiplexing optical transmissions,” Opt. Express 25(22), 27824–27833 (2017).
[Crossref]

F. Zhang, Q. Zhuge, M. Qiu, and D. V. Plant, “Low complexity digital backpropagation for high baud subcarrier-multiplexing systems,” Opt. Express 24(15), 17027–17040 (2016).
[Crossref]

F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightwave Technol. 33(24), 5140–5150 (2015).
[Crossref]

M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. M. Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).
[Crossref]

M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. M. Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).
[Crossref]

Q. Zhuge, B. Chatelain, and D. V. Plant, “Comparison of intra-channel nonlinearity tolerance between reduced guard-interval CO-OFDM systems and Nyquist single carrier systems,” in proceedings of Optical Fiber Communication Conference (OFC, 2012), paper OTh1B.3.

Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity single-step digital backpropagation for high order QAM subcarrier-multiplexing transmission,” in proceedings of Asia Communications and Photonics Conference (ACP, 2017), paper Su4B.2.

IEEE Photonics J. (1)

W. Shieh and Y. Tang, “Ultrahigh-speed signal transmission over nonlinear and dispersive fiber optic channel: the multicarrier advantage,” IEEE Photonics J. 2(3), 276–283 (2010).
[Crossref]

J. Lightwave Technol. (10)

P. Poggiolini, A. Nespola, Y. Jiang, G. Bosco, A. Carena, L. Bertignono, S. M. Bilal, S. Abrate, and F. Forghieri, “Analytical and experimental results on system maximum reach increase through symbol rate optimization,” J. Lightwave Technol. 34(8), 1872–1885 (2016).
[Crossref]

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: methods and potential Gain,” J. Lightwave Technol. 35(4), 903–930 (2017).
[Crossref]

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
[Crossref]

L. Liu, L. Li, Y. Huang, K. Cui, Q. Xiong, F. N. Hauske, C. Xie, and Y. Cai, “Intra-channel nonlinearity compensation by inverse Volterra series transfer function,” J. Lightwave Technol. 30(3), 310–316 (2012).
[Crossref]

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]

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
[Crossref]

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intra-channel nonlinearity compensation algorithm operating at symbol rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011).
[Crossref]

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]

F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightwave Technol. 33(24), 5140–5150 (2015).
[Crossref]

Z. Xiao, S. Fu, S. Yao, M. Tang, P. Shum, and D. Liu, “ICI mitigation for dual-carrier super-channel transmission based on m-PSK and m-QAM formats,” J. Lightwave Technol. 34(23), 5526–5533 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (5)

Opt. Lett. (1)

Opt.Express (1)

S. J. Savory, “Digital filters for coherent optical receivers,” Opt.Express 16(2), 804–817(2008).
[Crossref]

Other (3)

Z. Xiao, Q. Zhuge, S. Fu, F. Zhang, M. Qiu, M. Tang, D. Liu, and D. V. Plant, “Low complexity single-step digital backpropagation for high order QAM subcarrier-multiplexing transmission,” in proceedings of Asia Communications and Photonics Conference (ACP, 2017), paper Su4B.2.

J. X. Cai, M. Mazurczyk, O. V. Sinkin, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “Experimental study of subcarrier multiplexing benefit in 74 nm bandwidth transmission up to 20,450 km,” in proceedings of European Conferance Optical Communication (ECOC, 2016), 677–679.

Q. Zhuge, B. Chatelain, and D. V. Plant, “Comparison of intra-channel nonlinearity tolerance between reduced guard-interval CO-OFDM systems and Nyquist single carrier systems,” in proceedings of Optical Fiber Communication Conference (OFC, 2012), paper OTh1B.3.

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 (10)

Fig. 1.
Fig. 1. Block diagram of NLC of the single-step M-SCM-DBP.
Fig. 2.
Fig. 2. (a) Simulation setup. (b) Receiver DSP.
Fig. 3.
Fig. 3. Required number of filter taps for (a) PDM-32QAM and (b) PDM-64QAM.
Fig. 4.
Fig. 4. Transmission results of (a) PDM-32QAM and (b) PDM-64QAM.
Fig. 5.
Fig. 5. (a) Experimental setup and spectrum of the generated signal. VOA: variable optical attenuator. SW: switch. (b) Receiver-side DSP flow.
Fig. 6.
Fig. 6. BTB performance of PDM-32QAM signals.
Fig. 7.
Fig. 7. Transmission performance over 960-km SSMF.
Fig. 8.
Fig. 8. Required number of taps for the adaptive filter.
Fig. 9.
Fig. 9. Polarization tracking ability of DD-LMS.
Fig. 10.
Fig. 10. Transmission distance for various DBP schemes.

Tables (1)

Tables Icon

Table 1. Number of complex multiplications per sample of the DBP schemes

Equations (8)

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

v p / i , x / y ( t ) = E p / i , x / y ( t ) e x p [ j ε γ L e f f ( | E p / i , x ( t ) | 2 + | E p / i , y ( t ) | 2 ) ]
M ( t ) = [ e j ϕ x ( t ) w y x ( t ) e j [ ϕ x ( t ) + ϕ y ( t ) ] 2 w x y ( t ) e j [ ϕ x ( t ) + ϕ y ( t ) ] 2 e j ϕ y ( t ) ]
w x y / y x ( t ) = v i , y / x ( t ) v i , x / y ( t ) I F F T [ j k = N 2 + 1 N 2 e x p ( j Δ β ω k L s p a n ) × H ( ω ) ]
ϕ x / y ( t ) = ( 2 | v i , x / y ( t ) | 2 + | v i , y / x ( t ) | 2 ) I F F T [ j k = N 2 + 1 N 2 e x p ( j Δ β ω k L s p a n ) × H ( ω ) ]
H ( ω ) = 8 9 γ × 1 e x p ( α L s p a n + j Δ β ω L s p a n ) α j Δ β ω
N = 50 % × 2 ( 1 + h ) | β 2 | π ( 2 R S ) 2 L
M K C D ( log 2 K C D + 1 ) K C D P C D + M [ 5.5 + 3 N s ]
5.5 + 3 N s + 1