Abstract

A computationally efficient dispersion-folded (D-folded) digital backward propagation (DBP) method for nonlinearity compensation of dispersion-managed fiber links is proposed. At the optimum power level of long-haul fiber transmission, the optical waveform evolution along the fiber is dominated by the chromatic dispersion. The optical waveform and, consequently, the nonlinear behavior of the optical signal repeat at locations of identical accumulated dispersion. Hence the DBP steps can be folded according to the accumulated dispersion. Experimental results show that for 6,084 km single channel transmission, the D-folded DBP method reduces the computation by a factor of 43 with negligible penalty in performance. Simulation of inter-channel nonlinearity compensation for 13,000 km wavelength-division multiplexing (WDM) transmission shows that the D-folded DBP method can reduce the computation by a factor of 37.

© 2012 OSA

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[CrossRef]

E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol.28(4), 502–519 (2010).
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L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express18(16), 17075–17088 (2010).
[CrossRef] [PubMed]

L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett.22(5), 320–322 (2010).
[CrossRef]

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
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L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett.46(16), 1140–1141 (2010).
[CrossRef]

2009

2008

2007

2006

E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightwave Technol.24(12), 4697–4710 (2006).
[CrossRef]

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

2004

2003

2001

J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature411(6841), 1007–1010 (2001).
[CrossRef] [PubMed]

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

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B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett.5(10), 1250–1253 (1993).
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1990

Abe, J.

Barros, D. J. F.

Bayvel, P.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007).
[CrossRef] [PubMed]

Behrens, C.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

Bunge, C.-A.

Carena, A.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

Chen, X.

Chugtai, M. N.

Cotter, D.

Curri, V.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

Desurvire, E. B.

Du, L. B.

Ellis, A. D.

Essiambre, R.-J.

Fischer, J. K.

Forghieri, F.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

Forzati, M.

Foschini, G. J.

Fukuchi, K.

Fukumitsu, K.

Gavioli, G.

Goebel, B.

Goldfarb, G.

Gordon, J. P.

Hardcastle, I.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

Hayee, M. I.

Hellerbrand, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

Hirano, S.

Ho, K.-P.

Holzlohner, R.

Imamura, K.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

Ip, E.

Kahn, J. M.

Killey, R. I.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007).
[CrossRef] [PubMed]

Kim, I.

Kisaka, Y.

Kokura, K.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

Komaki, K.

Kramer, G.

Kubo, K.

Kurtzke, B. C.

B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett.5(10), 1250–1253 (1993).
[CrossRef]

Lau, A. P. T.

Li, C.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

Li, G.

Li, X.

L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett.21(5), 292–294 (2009).
[CrossRef]

X. Li, X. Chen, G. Goldfarb, E. F. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16(2), 880–888 (2008).
[CrossRef] [PubMed]

Lowery, A. J.

Makovejs, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

Mårtensson, J.

Mateo, E. F.

Matsui, J.

Matsuoka, S.

Menyuk, C. R.

Millar, D. S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

Miyamoto, Y.

Miyata, Y.

Mizuochi, T.

Mollenauer, L. F.

Mukasa, K.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

Murata, K.

Mussolin, M.

Nakagawa, T.

Nakamura, Y.

Nakashima, H.

Nishimoto, H.

Noguchi, H.

O’Sullivan, M.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

Onaka, H.

Onohara, K.

Petermann, K.

Poggiolini, P.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

Rafique, D.

Roberts, K.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express16(2), 873–879 (2008).
[CrossRef] [PubMed]

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

Sakamoto, Y.

Sakano, T.

Savory, S. J.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007).
[CrossRef] [PubMed]

Shibayama, A.

Shimotakahara, I.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

Sinkin, O. V.

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

Strawczynski, L.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

Sun, H.

Takeuchi, O.

Tomizawa, M.

Winzer, P. J.

Wu, K.-T.

Xie, C.

Yagi, T.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

Yaman, F.

Yamanaka, S.

Yamazaki, E.

Yoshida, E.

Zhang, Q.

Zhao, J.

Zhu, L.

L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express19(7), 5953–5959 (2011).
[CrossRef] [PubMed]

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett.46(16), 1140–1141 (2010).
[CrossRef]

L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett.21(5), 292–294 (2009).
[CrossRef]

E. F. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express16(20), 16124–16137 (2008).
[CrossRef] [PubMed]

Zweck, J.

Electron. Lett.

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett.46(16), 1140–1141 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett.21(5), 292–294 (2009).
[CrossRef]

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett.5(10), 1250–1253 (1993).
[CrossRef]

L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett.22(5), 320–322 (2010).
[CrossRef]

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006).
[CrossRef]

J. Lightwave Technol.

J. Opt. Fiber Commun. Rep.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006).
[CrossRef]

Nature

J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature411(6841), 1007–1010 (2001).
[CrossRef] [PubMed]

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

Opt. Express

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express18(14), 15144–15154 (2010).
[CrossRef] [PubMed]

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express18(16), 17075–17088 (2010).
[CrossRef] [PubMed]

L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express19(7), 5953–5959 (2011).
[CrossRef] [PubMed]

D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express19(10), 9453–9460 (2011).
[CrossRef] [PubMed]

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Express19(14), 13179–13184 (2011).
[CrossRef] [PubMed]

E. F. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express16(20), 16124–16137 (2008).
[CrossRef] [PubMed]

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17(6), 4815–4823 (2009).
[CrossRef] [PubMed]

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007).
[CrossRef] [PubMed]

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Conventional DBP and D-folded DBP for a dispersion-managed coherent fiber link.

Fig. 2
Fig. 2

Experimental demonstration of D-folded DBP. (a) Experimental setup. Inset: constellations after back-to-back detection, EDC and DBP at the corresponding optimum power levels. (b) Q-value as a function of the number of steps using conventional DBP (green line) and D-folded DBP (blue line). (c) Q-value as a function of optical launching power after EDC (red line), 30-step D-folded DBP (blue line) and 1,300-step conventional DBP (green line).

Fig. 3
Fig. 3

Numerical demonstration of D-folded DBP for WDM transmission. (a) Block diagram of the dispersion-managed WDM system. (b) Q-value as a function of the number of steps using D-folded DBP and conventional DBP for SPM + XPM compensation. (c) Q-value as a function of the number of steps using D-folded DBP and conventional DBP for SPM compensation. (d) Q-value as a function of residual dispersion per span.

Tables (2)

Tables Icon

Table 1 Performance and complexity of conventional DBP and D-folded DBP for the single channel system

Tables Icon

Table 2 Performance and complexity of conventional DBP and D-folded DBP for the WDM system

Metrics