Abstract

In this paper, we propose two modifications to reduce the complexity of the subcarrier-multiplexing (SCM) based digital backpropagation (DBP) for high symbol rate SCM systems. The first one is to reduce the number of interfering subcarriers (RS-SCM-DBP) when evaluating the cross-subcarrier nonlinearity (CSN). The second one is to replace the original frequency domain CSN filters with the infinite impulse response (IIR) filters (IIR-RS-SCM-DBP) in the CSN compensation. The performance of the proposed schemes are numerically evaluated in three-channel dual-polarization (DP) 16QAM wavelength-division multiplexing (WDM) transmissions. The aggregate symbol rate for each channel is 120 GBaud and the transmission distance is 1600 km. For the SCM system with 16 subcarriers, the IIR-RS-SCM-DBP with only 4 interfering subcarriers and 2 steps can achieve a 0.3 dB Q-factor improvement in the WDM transmission. Compared to the original SCM-DBP, the proposed IIR-RS-SCM-DBP reduces the complexity by 48% at a performance loss of only 0.07 dB.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  21. Y. Gao, J. H. Ke, K. P. Zhong, J. C. Cartledge, and S. S. H. Yam, “Assessment of intrachannel nonlinear compensation for 112 Gb/s dual-polarization 16-QAM systems,” J. Lightwave Technol. 30(24), 3902–3910 (2012).
    [Crossref]
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2015 (2)

2014 (4)

2013 (1)

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

2012 (1)

2011 (2)

2010 (3)

2008 (2)

1994 (1)

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightwave Technol. 12(5), 885–890 (1994).
[Crossref]

1991 (1)

S. R. Powell and P. M. Chau, “A technique for realizing linear-phase IIR filters,” IEEE T. Signal Process. 39(11), 2425–2435 (1991).

Adamiecki, A.

Akiyama, Y.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

Buhl, L. L.

Cartledge, J. C.

Chagnon, M.

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission [An overview of recent advances in DSP-enabled superchannels],” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

Chandrashekhar, S.

Chau, P. M.

S. R. Powell and P. M. Chau, “A technique for realizing linear-phase IIR filters,” IEEE T. Signal Process. 39(11), 2425–2435 (1991).

Chien, H.-C.

Chraplyvy, A. R.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightwave Technol. 12(5), 885–890 (1994).
[Crossref]

Dou, L.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

Draving, S.

Du, L. B.

Dupuy, J. Y.

Fan, Y.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

Gao, Y.

Grove, M.

Hoshida, T.

Ip, E.

Jia, Z.

Jorge, F.

Kahn, J. M.

Ke, J. H.

Konczykowska, A.

Li, G.

Li, L.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

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

Liu, L.

Liu, X.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission [An overview of recent advances in DSP-enabled superchannels],” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

Lowery, A. J.

Marcuse, D.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightwave Technol. 12(5), 885–890 (1994).
[Crossref]

Mateo, E.

Morsy-Osman, M.

Nakashima, H.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

Oda, S.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

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

Plant, D.

Plant, D. V.

Powell, S. R.

S. R. Powell and P. M. Chau, “A technique for realizing linear-phase IIR filters,” IEEE T. Signal Process. 39(11), 2425–2435 (1991).

Qiu, M.

Randel, S.

Rasmussen, J. C.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

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

Raybon, G.

Rezania, A.

Rush, K.

Salamanca, L.

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]

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.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

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

Tkach, R. W.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightwave Technol. 12(5), 885–890 (1994).
[Crossref]

Urbanke, R.

Wang, W.

Winzer, P. J.

G. Raybon, A. Adamiecki, P. J. Winzer, S. Randel, L. Salamanca, A. Konczykowska, F. Jorge, J. Y. Dupuy, L. L. Buhl, S. Chandrashekhar, C. Xie, S. Draving, M. Grove, K. Rush, and R. Urbanke, “High symbol rate coherent optical transmission systems: 80 and 107 GBaud,” J. Lightwave Technol. 32(4), 824–831 (2014).
[Crossref]

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission [An overview of recent advances in DSP-enabled superchannels],” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

Xie, C.

Xu, X.

Yam, S. S. H.

Yan, W.

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

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

Yu, J.

Zhang, F.

Zhang, J.

Zhong, K. P.

Zhu, L.

Zhuge, Q.

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]

IEEE Signal Process. Mag. (1)

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission [An overview of recent advances in DSP-enabled superchannels],” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

IEEE T. Signal Process. (1)

S. R. Powell and P. M. Chau, “A technique for realizing linear-phase IIR filters,” IEEE T. Signal Process. 39(11), 2425–2435 (1991).

J. Lightwave Technol. (9)

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightwave Technol. 12(5), 885–890 (1994).
[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]

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010).
[Crossref]

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

Y. Gao, J. H. Ke, K. P. Zhong, J. C. Cartledge, and S. S. H. Yam, “Assessment of intrachannel nonlinear compensation for 112 Gb/s dual-polarization 16-QAM systems,” J. Lightwave Technol. 30(24), 3902–3910 (2012).
[Crossref]

G. Raybon, A. Adamiecki, P. J. Winzer, S. Randel, L. Salamanca, A. Konczykowska, F. Jorge, J. Y. Dupuy, L. L. Buhl, S. Chandrashekhar, C. Xie, S. Draving, M. Grove, K. Rush, and R. Urbanke, “High symbol rate coherent optical transmission systems: 80 and 107 GBaud,” J. Lightwave Technol. 32(4), 824–831 (2014).
[Crossref]

J. Zhang, J. Yu, Z. Jia, and H.-C. Chien, “400 G transmission of super-Nyquist-filtered signal based on single-carrier 110-GBaud PDM QPSK with 100-GHz grid,” J. Lightwave Technol. 32(19), 3239–3246 (2014).
[Crossref]

A. Rezania and J. C. Cartledge, “Transmission performance of 448 Gb/s single-carrier and 1.2 Tb/s three-carrier superchannel using dual-polarization 16-QAM with fixed LUT based MAP detection,” J. Lightwave Technol. 33(23), 4738–4745 (2015).
[Crossref]

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

Opt. Express (4)

Proc. SPIE (1)

Z. Tao, L. Dou, W. Yan, Y. Fan, L. Li, S. Oda, Y. Akiyama, H. Nakashima, T. Hoshida, and J. C. Rasmussen, “Complexity-reduced digital nonlinear compensation for coherent optical systems,” Proc. SPIE 8647, 86470K (2013).
[Crossref]

Other (5)

S. Ramachandran, Fiber Based Dispersion Compensation (Springer, 2007).

J. G. Proakis, D. G. Manolakis. Digital Signal Processing (Pearson Prentice Hall, 2007)

S. Randel, D. Pilori, S. Corteselli, G. Raybon, A. Adamiecki, and A. Gnauck, “All-electronic flexibly programmable 864-Gb/s single-carrier PDM-64-QAM,” in Proc. Opt. Fiber Commun. Conf. (2014), paper Th5C.8.
[Crossref]

P. Poggiolini, Y. Jiang, A. Carena, G. Bosco, and F. Forghieri, “Analytical results on system maximum reach increase through symbol rate optimization,” in Proc. Opt. Fiber Commun. Conf. (2015), paper Th3D. 6.
[Crossref]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. European Conference and Exposition on Optical Communications (2011), paper Tu.3.A.2.
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Spectrum of an eight-subcarrier SCM signal with the leftmost subcarrier as the probe subcarrier. IS: interfering subcarrier.
Fig. 2
Fig. 2 Spectrum of various CSN LPFs for different interfering subcarriers relative to the probe subcarrier.
Fig. 3
Fig. 3 The locations of the interfering subcarriers in the RS-SCM-DBP scheme with (a) the fourth subcarrier and (b) the first subcarrier as the probe subcarrier. PS: probe subcarrier.
Fig. 4
Fig. 4 (a) Comparison of IIR LPF and CSN LPF. (b) Implementation of zero-phase IIR filtering.
Fig. 5
Fig. 5 Simulation setup. OBPF: optical band-pass filter. EDFA: Erbium doped fiber amplifier.
Fig. 6
Fig. 6 The Q-factor versus the number of interfering subcarriers for SCM systems with (a) 16 subcarriers and (b) 32 subcarriers.
Fig. 7
Fig. 7 The Q-factor versus the step length for 16-subcarrier SCM systems and SC systems with various compensation schemes at the optimal launch power.
Fig. 8
Fig. 8 (a) The Q-factor versus the number of interfering subcarriers using IIR-RS-SCM-DBP. (b) Difference of Q-factor between IIR-RS-SCM-DBP and RS-SCM-DBP versus the number of interfering subcarriers
Fig. 9
Fig. 9 Various compensation schemes for 16-subcarrier SCM systems and SC systems at the optimized launch power.
Fig. 10
Fig. 10 The required number of complex multiplications per sample for various DBP schemes in 16-subcarrier SCM systems.

Tables (1)

Tables Icon

Table 1 The complexity calculation of DBP schemes with 10 spans/step.

Equations (18)

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

H N (ω)= n= N 2 +1 N 2 exp(jΔβωn L span ) × H 1 (ω)
H 1 (ω)= 8γ 9 × 1exp(α L span +jΔβω L span ) αjΔβω
H 1 (ω)= 8γ 9 × 1exp(α L span +jΔβω L span ) αjΔβω 8γ 9 1 αjΔβω = 8γ 9 α 2 + (Δβω) 2 α 2 + (Δβω) 2 exp(j tan 1 ( Δβω α ))
H N (ω)= 8γ 9 sin( N 2 Δβω L span ) α 2 + (Δβω) 2 sin( 1 2 Δβω L span )[ α 2 + (Δβω) 2 ] exp(j( 1 2 Δβω L span tan 1 ( Δβω α ))
| H B (ω)|=1/ 1+ (ω/ ω 0 ) 2n
| H B (ω)|=1/ 1+ (ξ( ω I ω P )ω) 2n
(M+1) K CD,R ( log 2 K CD,R +1) K CD,R P CD,R +M[6.5+ 1.5 K NL,R ( log 2 K NL,R + N RS 2 + N RS 2 4 N SCM + N RS 2 N SCM ) ( K NL,R P NL,R ) ]
(M+1) K CD,R ( log 2 K CD,R +1) K CD,R P CD,R +M[6.5+3 N RS ]
(M+1) K CD,L ( log 2 K CD,L +1) K CD,L P CD,L +M[3.5+ 1.5 K NL,L ( log 2 K NL,L +1) K NL,L P NL,L ]
K CD,R ( log 2 K CD,R +1) K CD,R P CD,R
6.5+ 1.5 K NL,R ( log 2 K NL,R + N SCM 1) K NL,R P NL,R
6.5+ 1.5 K NL,R ( log 2 K NL,R + N RS ) K NL,R P NL,R
6.5+ 1.5 K NL,R ( log 2 K NL,R + N RS /2+ N RS 2 /4 N SCM + N RS /2 N SCM ) ( K NL,R P NL,R )
(M+1) K CD,R ( log 2 K CD,R +1) K CD,R P CD,R +M[6.5+ 1.5 K NL,R ( log 2 K NL,R + N RS 2 + N RS 2 4 N SCM + N RS 2 N SCM ) ( K NL,R P NL,R ) ]
(M+1) K CD,A ( log 2 K CD,A +1) K CD,A P CD,A +M[6.5+3 N RS ]
K CD,L ( log 2 K CD,L +1) K CD,L P CD,L
3.5+ 1.5 K NL,L ( log 2 K NL,L +1) K NL,L P NL,L
(M+1) K CD,L ( log 2 K CD,L +1) K CD,L P CD,L +M[3.5+ 1.5 K NL,L ( log 2 K NL,L +1) K NL,L P NL,L ]

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