Abstract

Maximum likelihood sequence estimation (MLSE) offers effective equalizations for bandwidth-limited optical signal on mitigation towards inter-symbol-interference (ISI) impairment. In this paper, we provide the first comprehensive comparisons and analysis of three post-compensation algorithms on the same modeling platform for high spectral-efficiency (SE) optical systems employing the spectral prefiltering. Those algorithms include 1-tap constant modulus algorithm (CMA) and 3-tap MLSE, regular CMA and digital filter with 2-tap MLSE, and constant multi-modulus algorithm (CMMA) with 2-tap MLSE. Furthermore, a novel and effective approach is proposed and verified for the generation of both hard value and soft value at the output of MLSE in order to be compatible with the implementation of soft-decision forward error correction (SD-FEC) decoding process.

© 2014 Optical Society of America

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References

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  1. R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
  4. J. Yu, Z. Dong, H. Chien, Z. Jia, X. Li, D. Huo, M. Gunkel, P. Wagner, H. Mayer, and A. Schippel, “Transmission of 200 G PDM-CSRZ-QPSK and PDM-16 QAM With a SE of 4 b/s/Hz,” J. Lightwave Technol. 31(4), 515–522 (2013).
    [Crossref]
  5. K. Roberts, M. O’Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. J. Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
    [Crossref]
  6. P. J. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1, 200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” in Proc. ECOC, Torino, Italy (2010), paper PDP 2.2.
    [Crossref]
  7. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s reduced-guard-interval CO-OFDM signal with a 60-GHz optical bandwidth over 2000 km of ULAF and five 80-GHz-grid ROADMs,” in Proc. OFC/NFOEC, San Diego, California (2010), paper PDPC2.
    [Crossref]
  8. W.-R. Peng, T. Tsuritani, and I. Morita, “Transmission of high-baud PDM-64QAM signals,” J. Lightwave Technol. 31(13), 2146–2162 (2013).
    [Crossref]
  9. Y. Cai, J.-X. Cai, A. Pilipetskii, G. Mohs, and N. S. Bergano, “Spectral efficiency limits of pre-filtered modulation formats,” Opt. Express 18(19), 20273–20281 (2010).
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  10. J. Li, E. Tipsuwannakul, T. Eriksson, M. Karlsson, and P. A. Andrekson, “Approaching Nyquist limit in WDM systems by low-complexity receiver-side Duobinary shaping,” J. Lightwave Technol. 30(11), 1664–1676 (2012).
    [Crossref]
  11. J. Zhang, J. Yu, Z. Dong, N. Chi, and X. Li, “Multi-modulus blind equalizations for coherent spectrum shaped PolMux Quadrature Duobinary signal processing,” in Proc. OFC/NFOEC, Anaheim, California (2013), paper OW4B.4.
    [Crossref]
  12. J. Yu, J. Zhang, Z. Dong, Z. Jia, H.-C. Chien, Y. Cai, X. Xiao, and X. Li, “Transmission of 8 × 480-Gb/s super-Nyquist-filtering 9-QAM-like signal at 100 GHz-grid over 5000-km SMF-28 and twenty-five 100 GHz-grid ROADMs,” Opt. Express 21(13), 15686–15691 (2013).
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  14. J.-X. Cai, C. R. Davidson, A. J. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. N. Pilipetskii, G. Mohs, and N. S. Bergano, “20Tbit/s transmission over 6860 km with sub-Nyquist channel spacing,” J. Lightwave Technol. 30(4), 651–657 (2012).
    [Crossref]
  15. H.-C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol. 30(24), 3965–3971 (2012).
    [Crossref]
  16. Z. Jia, J. Yu, H.-C. Chien, Z. Dong, and D. Di Huo, “Field transmission of 100 G and beyond: multiple baud rates and mixed line rates using Nyquist-WDM technology,” J. Lightwave Technol. 30(24), 3793–3804 (2012).
    [Crossref]
  17. Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
    [Crossref]
  18. H.-C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “512-Gb/s Quad-carrier PM-QPSK transmission over 2400-km SMF-28 subject to narrowing 100-GHz optical bandwidth,” in ECOC2012, Amsterdam Netherlands (2012), paper Th.2.C.4.
  19. J. Li, M. Karlsson, and P. A. Andrekson, “1.94Tb/s (11x176Gb/s) DP-16QAM Superchannel transmission over 640km EDFA-Only SSMF and two 280GHz WSSs,” ECOC2012, Amsterdam Netherlands (2012), paper Th.2.C.1.
  20. H. Zhang, J.-X. Cai, H. G. Batshon, C. R. Davidson, Y. Sun, M. Mazurczyk, D. G. Foursa, A. Pilipetskii, G. Mohs, and N. S. Bergano, “16QAM transmission with 5.2 bits/s/Hz spectral efficiency over transoceanic distance,” Opt. Express 20(11), 11688–11693 (2012).
    [Crossref] [PubMed]
  21. J. Cho, C. Xie, and P. J. Winzer, “Analysis of soft-decision FEC on non-AWGN channels,” Opt. Express 20(7), 7915–7928 (2012).
    [Crossref] [PubMed]

2013 (3)

2012 (8)

H. Zhang, J.-X. Cai, H. G. Batshon, C. R. Davidson, Y. Sun, M. Mazurczyk, D. G. Foursa, A. Pilipetskii, G. Mohs, and N. S. Bergano, “16QAM transmission with 5.2 bits/s/Hz spectral efficiency over transoceanic distance,” Opt. Express 20(11), 11688–11693 (2012).
[Crossref] [PubMed]

J. Cho, C. Xie, and P. J. Winzer, “Analysis of soft-decision FEC on non-AWGN channels,” Opt. Express 20(7), 7915–7928 (2012).
[Crossref] [PubMed]

J.-X. Cai, C. R. Davidson, A. J. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. N. Pilipetskii, G. Mohs, and N. S. Bergano, “20Tbit/s transmission over 6860 km with sub-Nyquist channel spacing,” J. Lightwave Technol. 30(4), 651–657 (2012).
[Crossref]

H.-C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol. 30(24), 3965–3971 (2012).
[Crossref]

Z. Jia, J. Yu, H.-C. Chien, Z. Dong, and D. Di Huo, “Field transmission of 100 G and beyond: multiple baud rates and mixed line rates using Nyquist-WDM technology,” J. Lightwave Technol. 30(24), 3793–3804 (2012).
[Crossref]

J. Li, E. Tipsuwannakul, T. Eriksson, M. Karlsson, and P. A. Andrekson, “Approaching Nyquist limit in WDM systems by low-complexity receiver-side Duobinary shaping,” J. Lightwave Technol. 30(11), 1664–1676 (2012).
[Crossref]

R. J. Essiambre and R. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

X. Zhou and L. E. Nelson, “400G WDM transmission on the 50 GHz grid for future optical networks,” J. Lightwave Technol. 30(24), 3779–3792 (2012).
[Crossref]

2011 (2)

2010 (2)

2009 (1)

Andrekson, P. A.

Awadalla, A.

Batshon, H. G.

Bergano, N.

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

Bergano, N. S.

Cai, J.-X.

Cai, Y.

Chien, H.

Chien, H.-C.

Cho, J.

Davidson, C.

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

Davidson, C. R.

Di Huo, D.

Dong, Z.

Eriksson, T.

Essiambre, R. J.

R. J. Essiambre and R. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

Foursa, D.

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

Foursa, D. G.

Gunkel, M.

Huo, D.

Jia, Z.

Karlsson, M.

Krause, D. J.

Laperle, C.

Li, J.

Li, X.

Lucero, A.

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

Lucero, A. J.

Mayer, H.

Mazurczyk, M.

Mohs, G.

Morita, I.

Nelson, L. E.

O’Sullivan, M.

Patterson, W. W.

Peng, W.-R.

Pilipetskii, A.

Pilipetskii, A. N.

Roberts, K.

Schippel, A.

Sinkin, O.

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

Sinkin, O. V.

Sun, H.

Sun, Y.

H. Zhang, J.-X. Cai, H. G. Batshon, C. R. Davidson, Y. Sun, M. Mazurczyk, D. G. Foursa, A. Pilipetskii, G. Mohs, and N. S. Bergano, “16QAM transmission with 5.2 bits/s/Hz spectral efficiency over transoceanic distance,” Opt. Express 20(11), 11688–11693 (2012).
[Crossref] [PubMed]

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

Tipsuwannakul, E.

Tkach, R.

R. J. Essiambre and R. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

Tsuritani, T.

Wagner, P.

Winzer, P. J.

Wu, K.-T.

Xiao, X.

Xie, C.

Yu, J.

Zhang, H.

Zhang, J.

Zhou, X.

Bell Labs Tech. J. (1)

R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

IEICE Trans. Commun. (1)

Y. Cai, J.-X. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, Y. Sun, A. Pilipetskii, G. Mohs, and N. Bergano, “Ultra-long-haul WDM transmission with high spectral efficiency,” IEICE Trans. Commun. E94-B(2), 392–399 (2011).
[Crossref]

J. Lightwave Technol. (9)

J. Li, E. Tipsuwannakul, T. Eriksson, M. Karlsson, and P. A. Andrekson, “Approaching Nyquist limit in WDM systems by low-complexity receiver-side Duobinary shaping,” J. Lightwave Technol. 30(11), 1664–1676 (2012).
[Crossref]

W.-R. Peng, T. Tsuritani, and I. Morita, “Transmission of high-baud PDM-64QAM signals,” J. Lightwave Technol. 31(13), 2146–2162 (2013).
[Crossref]

K. Roberts, M. O’Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. J. Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
[Crossref]

J.-X. Cai, Y. Cai, C. R. Davidson, D. G. Foursa, A. J. Lucero, O. V. Sinkin, W. W. Patterson, A. N. Pilipetskii, G. Mohs, and N. S. Bergano, “Transmission of 96x100-Gb/s bandwidth-constrained PDM-RZ-QPSK channels with 300% spectral efficiency over 10610 km and 400% spectral efficiency over 4370 km,” J. Lightwave Technol. 29(3), 491–498 (2011).

X. Zhou and L. E. Nelson, “400G WDM transmission on the 50 GHz grid for future optical networks,” J. Lightwave Technol. 30(24), 3779–3792 (2012).
[Crossref]

J. Yu, Z. Dong, H. Chien, Z. Jia, X. Li, D. Huo, M. Gunkel, P. Wagner, H. Mayer, and A. Schippel, “Transmission of 200 G PDM-CSRZ-QPSK and PDM-16 QAM With a SE of 4 b/s/Hz,” J. Lightwave Technol. 31(4), 515–522 (2013).
[Crossref]

H.-C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol. 30(24), 3965–3971 (2012).
[Crossref]

Z. Jia, J. Yu, H.-C. Chien, Z. Dong, and D. Di Huo, “Field transmission of 100 G and beyond: multiple baud rates and mixed line rates using Nyquist-WDM technology,” J. Lightwave Technol. 30(24), 3793–3804 (2012).
[Crossref]

J.-X. Cai, C. R. Davidson, A. J. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. N. Pilipetskii, G. Mohs, and N. S. Bergano, “20Tbit/s transmission over 6860 km with sub-Nyquist channel spacing,” J. Lightwave Technol. 30(4), 651–657 (2012).
[Crossref]

Opt. Express (4)

Proc. IEEE (1)

R. J. Essiambre and R. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

Other (5)

P. J. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1, 200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” in Proc. ECOC, Torino, Italy (2010), paper PDP 2.2.
[Crossref]

X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s reduced-guard-interval CO-OFDM signal with a 60-GHz optical bandwidth over 2000 km of ULAF and five 80-GHz-grid ROADMs,” in Proc. OFC/NFOEC, San Diego, California (2010), paper PDPC2.
[Crossref]

J. Zhang, J. Yu, Z. Dong, N. Chi, and X. Li, “Multi-modulus blind equalizations for coherent spectrum shaped PolMux Quadrature Duobinary signal processing,” in Proc. OFC/NFOEC, Anaheim, California (2013), paper OW4B.4.
[Crossref]

H.-C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “512-Gb/s Quad-carrier PM-QPSK transmission over 2400-km SMF-28 subject to narrowing 100-GHz optical bandwidth,” in ECOC2012, Amsterdam Netherlands (2012), paper Th.2.C.4.

J. Li, M. Karlsson, and P. A. Andrekson, “1.94Tb/s (11x176Gb/s) DP-16QAM Superchannel transmission over 640km EDFA-Only SSMF and two 280GHz WSSs,” ECOC2012, Amsterdam Netherlands (2012), paper Th.2.C.1.

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Figures (12)

Fig. 1
Fig. 1 Spectral prefiltering in (a) optical and (b) digital domains, O-MUX: optical multiplexing, WSS: wavelength selective switch.
Fig. 2
Fig. 2 System setup. CW: continuous wave, PBS/C: polarization beam splitter/combiner, LO: local oscillator, O/E: optical to electrical conversion, CD: chromatic dispersion, TOF: tunable optical filter, CMA1: 1-tap CMA, CMA2: multi-tap CMA.
Fig. 3
Fig. 3 DSP flow chart of 1-tap CMA and 3-tap MLSE scheme.
Fig. 4
Fig. 4 DSP flow chart of digital filter and 2-tap MLSE scheme.
Fig. 5
Fig. 5 DSP flow chart of CMMA and 2-tap MLSE scheme.
Fig. 6
Fig. 6 Signal constellation plot evolutions at different processing schemes.
Fig. 7
Fig. 7 BER curves at (a) 22-GHz, (b) 25-GHz, and (c) 28-GHz 3rd-order Gaussian filter in single-channel case.
Fig. 8
Fig. 8 BER curves for performance comparison between single-channel and WDM cases.
Fig. 9
Fig. 9 Performance comparison vs. channel spacing between Nyquist pulse shaping and post-compensation schemes.
Fig. 10
Fig. 10 Trellis search for the minimization of Euclidean distance.
Fig. 11
Fig. 11 Constellations before (a) and after (b) soft-decision MLSE recovery.
Fig. 12
Fig. 12 BER performances of soft and hard output of MLSE w/ SD FEC as a function of OSNR. Spectral prefiltering with (a) 3rd-order 22-GHz optical Gaussian filter; (b) 3rd-order 25-GHz optical Gaussian filter.

Equations (2)

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S o f t V a l u e = a b s ( min ( D 3 , D 1 ) min ( D 2 , D 4 ) )
S o f t   D e c i s i o n   O u t p u t = S o f t   V a l u e * H a r d   D e c i s i o n   V a l u e  

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