Abstract

Fiber nonlinearity has become a major limiting factor to realize ultra-high-speed optical communications. We propose a fractionally-spaced equalizer which exploits a trained high-order statistics to deal with data-pattern dependent nonlinear impairments in fiber-optic communications. The computer simulation reveals that the proposed 3-tap equalizer improves Q-factor by more than 2 dB for long-haul transmissions of 5,230 km distance and 40 Gbps data rate. We also demonstrate that the joint use of a digital backpropagation (DBP) and the proposed equalizer offers an additional 1–2 dB performance improvement due to the channel shortening gain. A performance in high-speed transmissions of 100 Gbps and beyond is evaluated as well.

© 2012 OSA

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References

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  1. J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).
  2. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol.28, 423–433 (2010).
    [CrossRef]
  3. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16, 880–888 (2008).
    [CrossRef] [PubMed]
  4. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol.26, 3416–3425 (2008).
    [CrossRef]
  5. E. Ip, N. Bai, and T. Wang, “Complexity versus performance tradeoff in fiber nonlinearity compensation using frequency-shaped, multi-subband backpropagation,” in Proceedings of OFC’11, OThF4 (2011).
  6. T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
    [PubMed]
  7. 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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
    [PubMed]
  8. F. P. Guiomar, J. D. Reis, A. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” in Proceedings of ECOC’11, Tu.6.B.1 (2011).
    [PubMed]
  9. N. Alić, G. C. Papen, R. E. Saperstein, L. B. Milstein, and Y. Fainman, “Signal statistics and maximum likelihood sequence estimation in intensity modulated fiber optic links containing a single optical preamplifier,” Opt. Express13, 4568–4579 (2005).
    [CrossRef]
  10. Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).
  11. T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).
  12. J. B. Anderson and S. Mohan, “Sequential coding algorithms: a survey and cost analysis,” IEEE Trans. Commun.32, 169–176 (1984).
    [CrossRef]
  13. A. Azzalini and A. Capitanio, “Statistical applications of the multivariate skew normal distribution,” J. R. Stat. Soc.61, 579–602 (1999).
    [CrossRef]
  14. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).
  15. C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).
  16. I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, “Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization,” IEEE J. Sel. Areas Commun.26, 73–83 (2008).
    [CrossRef]
  17. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
    [CrossRef]

2012

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

2010

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
[CrossRef]

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol.28, 423–433 (2010).
[CrossRef]

2008

2005

1999

A. Azzalini and A. Capitanio, “Statistical applications of the multivariate skew normal distribution,” J. R. Stat. Soc.61, 579–602 (1999).
[CrossRef]

1984

J. B. Anderson and S. Mohan, “Sequential coding algorithms: a survey and cost analysis,” IEEE Trans. Commun.32, 169–176 (1984).
[CrossRef]

Alic, N.

Anderson, J. B.

J. B. Anderson and S. Mohan, “Sequential coding algorithms: a survey and cost analysis,” IEEE Trans. Commun.32, 169–176 (1984).
[CrossRef]

Annavajjala, R.

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

Azzalini, A.

A. Azzalini and A. Capitanio, “Statistical applications of the multivariate skew normal distribution,” J. R. Stat. Soc.61, 579–602 (1999).
[CrossRef]

Bai, N.

E. Ip, N. Bai, and T. Wang, “Complexity versus performance tradeoff in fiber nonlinearity compensation using frequency-shaped, multi-subband backpropagation,” in Proceedings of OFC’11, OThF4 (2011).

Batshon, H. G.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
[CrossRef]

I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, “Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization,” IEEE J. Sel. Areas Commun.26, 73–83 (2008).
[CrossRef]

Bigo, S.

J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).

Cai, J. X.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Cai, Y.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Capitanio, A.

A. Azzalini and A. Capitanio, “Statistical applications of the multivariate skew normal distribution,” J. R. Stat. Soc.61, 579–602 (1999).
[CrossRef]

Charlet, G.

J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).

Chen, X.

Cotter, D.

Davidson, C. R.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Djordjevic, I. B.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
[CrossRef]

I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, “Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization,” IEEE J. Sel. Areas Commun.26, 73–83 (2008).
[CrossRef]

Dou, L.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Duan, C.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

Ellis, A. D.

Fainman, Y.

Foursa, D. G.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Goldfarb, G.

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

Goto, H.

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

Guiomar, F. P.

F. P. Guiomar, J. D. Reis, A. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” in Proceedings of ECOC’11, Tu.6.B.1 (2011).
[PubMed]

Hoshida, T.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Ip, E.

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

E. Ip, N. Bai, and T. Wang, “Complexity versus performance tradeoff in fiber nonlinearity compensation using frequency-shaped, multi-subband backpropagation,” in Proceedings of OFC’11, OThF4 (2011).

Ishida, K.

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

Kahn, J. M.

Kim, I.

Koike-Akino, T.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

Kojima, K.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

Li, G.

Li, L.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Li, X.

Mateo, E.

Milstein, L. B.

Minkov, L. L.

I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, “Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization,” IEEE J. Sel. Areas Commun.26, 73–83 (2008).
[CrossRef]

Mizuochi, T.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

Mohan, S.

J. B. Anderson and S. Mohan, “Sequential coding algorithms: a survey and cost analysis,” IEEE Trans. Commun.32, 169–176 (1984).
[CrossRef]

Nissov, M.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Oda, S.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Papen, G. C.

Parsons, K.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

Pilipetskii, A.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Pinto, A. N.

F. P. Guiomar, J. D. Reis, A. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” in Proceedings of ECOC’11, Tu.6.B.1 (2011).
[PubMed]

Rasmussen, J. C.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Reis, J. D.

F. P. Guiomar, J. D. Reis, A. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” in Proceedings of ECOC’11, Tu.6.B.1 (2011).
[PubMed]

Renaudier, J.

J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).

Salsi, M.

J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).

Saperstein, R. E.

Sinkin, O.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

Sugihara, T.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

Tanimura, T.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Tao, Z.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Teixeira, A.

F. P. Guiomar, J. D. Reis, A. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” in Proceedings of ECOC’11, Tu.6.B.1 (2011).
[PubMed]

Tokura, T.

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

Tran, P.

J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

Wang, T.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
[CrossRef]

E. Ip, N. Bai, and T. Wang, “Complexity versus performance tradeoff in fiber nonlinearity compensation using frequency-shaped, multi-subband backpropagation,” in Proceedings of OFC’11, OThF4 (2011).

Xu, L.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
[CrossRef]

Yaman, F.

Yan, W.

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

Yoshida, T.

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

Zhao, J.

IEEE J. Sel. Areas Commun.

I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, “Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization,” IEEE J. Sel. Areas Commun.26, 73–83 (2008).
[CrossRef]

IEEE Photon. J.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2, 593–599 (2010).
[CrossRef]

IEEE Trans. Commun.

J. B. Anderson and S. Mohan, “Sequential coding algorithms: a survey and cost analysis,” IEEE Trans. Commun.32, 169–176 (1984).
[CrossRef]

J. Lightwave Technol.

J. R. Stat. Soc.

A. Azzalini and A. Capitanio, “Statistical applications of the multivariate skew normal distribution,” J. R. Stat. Soc.61, 579–602 (1999).
[CrossRef]

Opt. Express

Proceedings of OFC’12 OTh3C.3

T. Koike-Akino, C. Duan, K. Kojima, K. Parsons, T. Yoshida, T. Sugihara, and T. Mizuochi, “Fractionally-spaced statistical equalizer for fiber nonlinearity mitigation in digital coherent optical systems,” in Proceedings of OFC’12 OTh3C.3 (2012).

Other

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

C. Duan, K. Parsons, T. Koike-Akino, R. Annavajjala, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “A low-complexity sliding-window turbo equalizer for nonlinearity compensation,” in Proceedings of OFC’12, JW2A.59 (2012).

J. Renaudier, G. Charlet, P. Tran, M. Salsi, and S. Bigo, “A performance comparison of differential and coherent detections over ultra long haul transmission of 10Gb/s BPSK,” in Proceedings of OFC’07, OWM1 (2007).

E. Ip, N. Bai, and T. Wang, “Complexity versus performance tradeoff in fiber nonlinearity compensation using frequency-shaped, multi-subband backpropagation,” in Proceedings of OFC’11, OThF4 (2011).

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proceedings of ECOC’11, Tu.3.A.1 (2011).
[PubMed]

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 Proceedings of ECOC’11, Tu.3.A.2 (2011).
[PubMed]

F. P. Guiomar, J. D. Reis, A. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” in Proceedings of ECOC’11, Tu.6.B.1 (2011).
[PubMed]

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Pilipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmissions,” in Proceedings of OFC’10, OTuE1 (2010).

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Figures (8)

Fig. 1
Fig. 1

Fractionally-spaced statistical sequence equalizer (FS-SSE) which exploits high-order statistics of nonlinearity distortion in coherent fiber-optic systems.

Fig. 2
Fig. 2

Examples of received I-Q constellation with nonlinear distortion (launching power: −4 dBm, wavelength: 1551 nm, fiber distance: 5,230 km).

Fig. 3
Fig. 3

Fiber channel dispersion maps (wavelength: 1551 nm and 1561 nm).

Fig. 4
Fig. 4

Simulation results of Q-factor performance as a function of launching power for 40 Gbps DP-DQPSK (5,230 km). (a) Low local dispersion channel (1551.32 nm). (b) High local dispersion channel (1561.01 nm).

Fig. 5
Fig. 5

Simulation results of Q-factor performance as a function of launching power for 40 Gbps DP-QPSK (5,230 km). (a) Low local dispersion channel (1551.32 nm). (b) High local dispersion channel (1561.01 nm).

Fig. 6
Fig. 6

Simulation results of Q-factor performance as a function of fiber distance for 40 Gbps DP-DQPSK/DP-QPSK (−7 dBm). (a) DP-DQPSK. (b) DP-QPSK.

Fig. 7
Fig. 7

Simulation results of Q-factor performance as a function of launching power for 10 GBd DP-DQPSK/DP-16QAM (high local dispersion channel: 1561.01 nm, 5,230 km). (a) Tap length effect for DP-DQPSK. (b) M-algorithm effect for DP-16QAM.

Fig. 8
Fig. 8

Simulation results of Q-factor performance as a function of launching power and fiber distance for 28 GBd high-speed DP-DQPSK/DP-16QAM. (a) Q vs power for 1551.32 nm. (b) Q vs power for 1561.01 nm. (c) Q vs distance for −3 dBm. (d) Q vs power for DP-16QAM.

Equations (7)

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μ ( s ) = 1 𝒩 ( s ) j : s j = s r j ,
Σ ( s ) = 1 𝒩 ( s ) 1 j : s j = s ( r j μ ( s ) ) ( r j μ ( s ) ) T ,
Pr ( r k | s ) = 1 det [ 2 π Σ ( s ) ] exp ( 1 2 ( r k μ ( s ) ) T Σ ( s ) 1 ( r k μ ( s ) ) ) .
lnPr ( r k | s ) = 1 2 ( r k μ ( s ) ) T Σ ( s ) 1 ( r k μ ( s ) ) 1 2 lndet [ 2 π Σ ( s ) ] .
lndet [ Σ ( s ) ] lndet [ Σ ( s ) ] + 2 N ln ν + ln c ,
Σ ( s ) 1 1 ν Σ ( s ) 1 1 c b b T ,
b 1 ν Σ ( s ) 1 ( r j μ ( s ) ) , c 1 + b T ( r j μ ( s ) ) .

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