Abstract

In this paper, we propose a nonlinear Tomlinson-Harashima pre-coding (THP) scheme for nonlinear distortion suppression in direct-detected double sideband (DSB) PAM-4 transmission systems. Based on the traditional THP, the feedback term is modified by introducing nonlinear components. In this way, more accurate feedback can be obtained to mitigate the signal distortions, especially the nonlinear distortions including the signal-to-signal beating interference and nonlinear power series caused by chromatic dispersion and square-law detection. Meanwhile, we also propose to only reserve the nonlinear kernels with adjacent tap products in nonlinear THP, for the purpose of computation complexity reduction. To verify the effectiveness, transmissions of double sideband (DSB) PAM-4 signal in 1550nm window are experimentally demonstrated. Volterra FFE is adopted on the receiver side to suppress linear and nonlinear pre-cursors. We optimize various parameters of hardware and apply appropriate simplification to the nonlinear THP kernels. The results indicate that, the proposed nonlinear THP can lead to up to three folds BER reduction, compared to the conventional linear THP. Finally, with the combination of proposed nonlinear THP and conventional Volterra FFE, we successfully transmit 84-Gbps PAM-4 and 107-Gbps PAM-4 respectively over 80 km and 40 km under the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10−3.

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

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References

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    [Crossref]
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    [Crossref]
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2019 (1)

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

2018 (5)

2017 (6)

2016 (1)

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

2015 (1)

2013 (1)

E. Batista and R. Seara, “On the performance of adaptive pruned Volterra filters,” Signal Processing 93(7), 1909–1920 (2013).
[Crossref]

1998 (1)

Bai, J.

Batista, E.

E. Batista and R. Seara, “On the performance of adaptive pruned Volterra filters,” Signal Processing 93(7), 1909–1920 (2013).
[Crossref]

Bayvel, P.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Bi, M.

Brandt-Pearce, M.

Buchali, F.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

Bülow, H.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

Chagnon, M.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

Chen, C.

Chen, H. Y.

Chen, J.

Chen, W.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

K. Zhong, X. Zhou, T. Gui, L. Tao, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “Experimental study of PAM-4, CAP-16, and DMT for 100 Gb/s short reach optical transmission systems,” Opt. Express 23(2), 1176–1189 (2015).
[Crossref] [PubMed]

Chen, Y. K.

Clausen, D.

Deng, L.

Dochhan, A.

Eiselt, M. H.

Eiselt, N.

Elbers, J. P.

El-Fiky, E.

M. Xiang, Z. Xing, E. El-Fiky, M. Morsy-Osman, Q. Zhuge, and D. V. Plant, “Single-lane 145 Gbit/s IM/DD transmission with faster-than-Nyquist PAM4 signaling,” IEEE Photonics Technol. Lett. 30(13), 1238–1241 (2018).
[Crossref]

K. Zhang, Q. Zhuge, H. Xin, M. Morsy-Osman, E. El-Fiky, L. Yi, W. Hu, and D. V. Plant, “Intensity directed equalizer for the mitigation of DML chirp induced distortion in dispersion-unmanaged C-band PAM transmission,” Opt. Express 25(23), 28123–28135 (2017).
[Crossref]

Erkilinç, M. S.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Fu, S.

Fu, Y.

Galdino, L.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Gao, F.

Gao, Y.

Griesser, H.

Gui, T.

Guo, Z.

He, H.

He, Z.

Hu, Q.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

Hu, W.

Kaneda, N.

Karinou, F.

Killey, R. I.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Kisaka, Y.

A. Masuda, S. Yamamoto, H. Taniguchi, M. Nakamura, and Y. Kisaka, “255-Gbps PAM-8 transmission under 20-GHz bandwidth limitation using NL-MLSE based on Volterra filter,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper W4I.6.
[Crossref]

Lau, A. P. T.

Le, S. T.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

Lee, J.

Li, L.

Li, X.

Li, Y.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

Li, Z.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Liang, L.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

Liu, D.

Lu, C.

Maher, R.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Man, J.

Masuda, A.

A. Masuda, S. Yamamoto, H. Taniguchi, M. Nakamura, and Y. Kisaka, “255-Gbps PAM-8 transmission under 20-GHz bandwidth limitation using NL-MLSE based on Volterra filter,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper W4I.6.
[Crossref]

Miao, X.

Monroy, I. T.

Morsy-Osman, M.

M. Xiang, Z. Xing, E. El-Fiky, M. Morsy-Osman, Q. Zhuge, and D. V. Plant, “Single-lane 145 Gbit/s IM/DD transmission with faster-than-Nyquist PAM4 signaling,” IEEE Photonics Technol. Lett. 30(13), 1238–1241 (2018).
[Crossref]

K. Zhang, Q. Zhuge, H. Xin, M. Morsy-Osman, E. El-Fiky, L. Yi, W. Hu, and D. V. Plant, “Intensity directed equalizer for the mitigation of DML chirp induced distortion in dispersion-unmanaged C-band PAM transmission,” Opt. Express 25(23), 28123–28135 (2017).
[Crossref]

Nakamura, M.

A. Masuda, S. Yamamoto, H. Taniguchi, M. Nakamura, and Y. Kisaka, “255-Gbps PAM-8 transmission under 20-GHz bandwidth limitation using NL-MLSE based on Volterra filter,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper W4I.6.
[Crossref]

Ohlendorf, S.

Olmos, J. J. V.

Pachnicke, S.

Peddanarappagari, K. V.

Plant, D. V.

Prodaniuc, C.

Qiang, Z.

Rath, R.

Rosenkranz, W.

Schuh, K.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

Seara, R.

E. Batista and R. Seara, “On the performance of adaptive pruned Volterra filters,” Signal Processing 93(7), 1909–1920 (2013).
[Crossref]

Shi, K.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Song, Y.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

Stojanovic, N.

Tan, A.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

Tang, M.

Taniguchi, H.

A. Masuda, S. Yamamoto, H. Taniguchi, M. Nakamura, and Y. Kisaka, “255-Gbps PAM-8 transmission under 20-GHz bandwidth limitation using NL-MLSE based on Volterra filter,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper W4I.6.
[Crossref]

Tao, L.

Thomsen, B. C.

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

Wei, J.

Xiang, M.

M. Xiang, Z. Xing, E. El-Fiky, M. Morsy-Osman, Q. Zhuge, and D. V. Plant, “Single-lane 145 Gbit/s IM/DD transmission with faster-than-Nyquist PAM4 signaling,” IEEE Photonics Technol. Lett. 30(13), 1238–1241 (2018).
[Crossref]

Xie, C.

Xin, H.

Xing, Z.

M. Xiang, Z. Xing, E. El-Fiky, M. Morsy-Osman, Q. Zhuge, and D. V. Plant, “Single-lane 145 Gbit/s IM/DD transmission with faster-than-Nyquist PAM4 signaling,” IEEE Photonics Technol. Lett. 30(13), 1238–1241 (2018).
[Crossref]

Xu, T.

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

Yamamoto, S.

A. Masuda, S. Yamamoto, H. Taniguchi, M. Nakamura, and Y. Kisaka, “255-Gbps PAM-8 transmission under 20-GHz bandwidth limitation using NL-MLSE based on Volterra filter,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper W4I.6.
[Crossref]

Yang, Z.

Yi, L.

Zeng, L.

Zhang, K.

Zhang, Q.

Zhong, K.

Zhou, X.

Zhuge, Q.

IEEE Photonics J. (1)

A. Tan, Z. Li, T. Xu, L. Liang, W. Chen, Y. Li, and Y. Song, “50-km C-Band transmission of 50-Gb/s PAM4 using 10-G EML and complexity-reduced adaptive equalization,” IEEE Photonics J. 11(1), 17200410 (2019).

IEEE Photonics Technol. Lett. (2)

Z. Li, M. S. Erkılınç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016).
[Crossref]

M. Xiang, Z. Xing, E. El-Fiky, M. Morsy-Osman, Q. Zhuge, and D. V. Plant, “Single-lane 145 Gbit/s IM/DD transmission with faster-than-Nyquist PAM4 signaling,” IEEE Photonics Technol. Lett. 30(13), 1238–1241 (2018).
[Crossref]

J. Lightwave Technol. (4)

Opt. Express (5)

Opt. Lett. (3)

Signal Processing (1)

E. Batista and R. Seara, “On the performance of adaptive pruned Volterra filters,” Signal Processing 93(7), 1909–1920 (2013).
[Crossref]

Other (8)

N. Kikuchi, R. Hirai, T. Fukui, and S. Takashima, “Modulator non-linearity compensation in Tomlinson-Harashima precoding (THP) for short-reach Nyquist- and faster-than-Nyquist (FTN) IM/DD PAM signaling,” in Proceedings of European conference on optical communications (ECOC, 2018), paper Th.2.34.
[Crossref]

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, and H. Bülow, “Up to 94 GBd THP PAM-4 transmission with 33 GHz bandwidth limitation,” in Proceedings of European conference on optical communications (ECOC, 2018), paper Th3F.6.
[Crossref]

M. Chagnon, “Optical communications for short reach,” J. Lightwave Technol. Early access, (2019).
[Crossref]

A. Masuda, S. Yamamoto, H. Taniguchi, M. Nakamura, and Y. Kisaka, “255-Gbps PAM-8 transmission under 20-GHz bandwidth limitation using NL-MLSE based on Volterra filter,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper W4I.6.
[Crossref]

IEEE P802.3bs 400 Gb/s Ethernet Task Force, accessed on Dec. 19, 2016. [Online]. Available: http://www.ieee802.org/3/bs/

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9 bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers Kronig receiver without optical CD compensation,” in Optical Fiber communications conference (Optical Society of America, 2018), paper Tu2D.3.

K. Matsumoto, Y. Yoshida, A. Maruta, A. Kanno, N. Yamamoto, and K.-I. Kitayama, “On the impact of Tomlinson–Harashima precoding in optical PAM transmissions for intra-DCN communication,” in Optical Fiber communications conference (Optical Society of America, 2017), paper Th3D.7.

Q. Hu, K. Schuh, M. Chagnon, F. Buchali, S. T. Le, and H. Bülow, “50 Gb/s PAM-4 transmission over 80-km SSMF without dispersion compensation,” in Proceedings of European conference on optical communications (ECOC, 2018), pp. 1–3.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Principle of nonlinear THP pre-coding and decoding. (i) Frequency response after CD of 1360ps/nm (80 km SSMF at 1550nm window). (ii) Occurrence of samples after receiver side equalization. (iii) Occurrence of samples after modulo operation.
Fig. 2
Fig. 2 Experimental setup and DSP flows. When THP coefficients need to be obtained or optimized, the original PAM-4 without pre-coding is transmitted, and joint FFE and DFE is adopted in the receiver side. When THP performance needs to be tested, the THP pre-coded PAM-4 signal is transmitted, and only FFE is adopted in the receiver side.
Fig. 3
Fig. 3 BER results as a function of driving Vpp and OMI. (a) 84-Gbps PAM-4 over 80 km using linear DFE. (b) 84-Gbps PAM-4 over 80 km using Volterra DFE. (c) 107-Gbps PAM-4 over 40 km using linear DFE. (d) 107-Gbps PAM-4 over 40 km using Volterra DFE.
Fig. 4
Fig. 4 BER results as a function of roll off factor. (a) 84-Gbps PAM-4 over 80 km. (b) 107-Gbps PAM-4 over 40 km.
Fig. 5
Fig. 5 BER results as a function of the 2nd tap number L 2 and the product memory lengthP. (a) and (b): 84 Gbps PAM-4 over 80 km. (c) and (d): 107 Gbps PAM-4 over 40 km.
Fig. 6
Fig. 6 Received signal with nonlinear THP. (a)~(c): Eye diagram, electrical spectrum and occurrences of decisions samples before equalization. (d)~(f): Eye diagram, electrical spectrum and occurrences of decision samples after equalization. For (f), linear THP result is attached as a reference.
Fig. 7
Fig. 7 BER results as a function of PIN-PD input optical power. (a): 84-Gbps PAM-4 over 80 km. (b): 107-Gbps PAM-4 over 40 km.

Equations (9)

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P Tx = P o +ηm(t),
E Tx (t)= P Tx (t) = P o 1+ηm(t)/ P o .
E Tx (t)=1+ n=1 c n m' (t) n =1+ 1 2 m'(t)+ n=2 c n m' (t) n ,
E Rx (t)= E Tx (t) h CD (t)=1+ 1 2 m'(t) h CD (t)+ n=2 c n m' (t) n h CD (t).
P Rx (t)= | E Rx (t) | 2 = 1 DC + m'(t)R{ h CD (t)} signal of interest + 2 n=2 c n m' (t) n R{ h CD (t) } received power series of the applied current + | 1 2 m'(t) h CD (t)+ n=2 c n m' (t) n h CD (t) | 2 SSBI ,
H CD (f)=f( h CD (t))= cos 2 (2 π 2 β 2 L f 2 ),
m'(t)R{ h CD (t)} | t=kT = m'(kT) ideal signal + q= R{ h CD (qT)}m'(kTqT) power fading induced ISI = m'[k] ideal signal + q= R{ h CD [q]}m'[kq] power fading induced ISI ,
e[k]= l 1 =1 L 1 h( l 1 ) x[k l 1 ]+ l 1 =1 L 2 l 2 = l 1 L 2 h( l 1 , l 2 ) x[k l 1 ]x[k l 2 ]+... + l 1 =1 L n l 2 = l 1 L n ... l n = l n1 L n h( l 1 , l 2 ... l n ) x[k l 1 ]x[k l 2 ]...x[k l n ],
e[k]= l 1 =1 L 1 h( l 1 ) x[k l 1 ]+ l 1 =1 L 2 l 2 = l 1 min( L 2 , l 2 +P) h( l 1 , l 2 ) x[k l 1 ]x[k l 2 ],

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