Abstract

In this paper, a memory polynomial equalizer combined with decision feedback equalizer (MPE-DFE) is proposed to eliminate channel distortions for intensity modulation and direct detection (IM/DD) systems. Compared with traditional feedforward equalizer and decision feedback equalizer (FFE-DFE), the proposed MPE-DFE introduces extra square terms and cubic terms to jointly equalize chromatic dispersion and nonlinear distortions. We demonstrated a C-band 56-Gb/s four-level pulse-amplitude modulation (PAM4) system over 80-km standard single mode fiber (SSMF) transmission. Experimental results show that the proposed MPE-DFE achieved up to 6.2 dB higher SNR than traditional FFE-DFE. Moreover, the achieved bit error ratio (BER) with MPE-DFE reaches 3.1 × 10−3, which is below 7% feedforward error correction (FEC) threshold of 3.8 × 10−3. To the best of our knowledge, we achieved a record transmission distance for C-band 56-Gb/s PAM4 signal with only electrical equalization at the receiver.

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

Full Article  |  PDF Article
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References

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  1. M. Chagnon, “Optical communications for short reach,” J. Lightwave Technol. 37, 1779–1797 (2019).
    [Crossref]
  2. G. N. Liu, L. Zhang, T. Zuo, and Q. Zhang, “IM/DD Transmission Techniques for Emerging 5G Fronthaul, DCI, and Metro Applications,” J. Lightwave Technol. 36, 560–567 (2018).
    [Crossref]
  3. 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, 1176–1189 (2015).
    [Crossref] [PubMed]
  4. J. Zhou, Y. Qiao, C. Yu, M. Guo, X. Tang, W. Liu, S. Chun, and Z. Li, “Joint Hartley-domain and time-domain equalizer for a 200-G (4 × 56-Gbit/s) optical PAM-4 system using 10G-class optics,” Opt. Express 26, 34451–34460 (2018).
    [Crossref]
  5. L. Zhang, T. Zuo, Y. Mao, Q. Zhang, E. Zhou, G. N. Liu, and X. Xu, “Beyond 100-Gb/s transmission over 80-km SMF using direct-detection SSB-DMT at C-band,” J. Lightwave Technol. 34, 723–729 (2016).
    [Crossref]
  6. J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.
  7. X. Tang, Y. Qiao, J. Zhou, M. Guo, J. Qi, S. Liu, X. Xu, and Y. Lu, “Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON,” Opt. Express 26, 33418–33427 (2018).
    [Crossref]
  8. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “Kramers–Kronig receivers for 100-km datacenter interconnects,” J. Lightwave Technol. 36, 79–89 (2018).
    [Crossref]
  9. X. Tang, S. Liu, X. Xu, J. Qi, M. Guo, J. Zhou, and Y. Qiao, “50-Gb/s PAM4 over 50-km Single Mode Fiber Transmission Using Efficient Equalization Technique,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. W2A–45.
  10. C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. Th4A–5.
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  13. R. Rath, D. Clausen, S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Tomlinson–Harashima precoding for dispersion uncompensated PAM-4 transmission with direct-detection,” J. Lightwave Technol. 35, 3909–3917 (2017).
    [Crossref]
  14. J. Wei, N. Eiselt, H. Griesser, K. Grobe, M. H. Eiselt, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Demonstration of the first real-time end-to-end 40-Gb/s PAM-4 for next-generation access applications using 10-Gb/s transmitter,” J. Lightwave Technol. 34, 1628–1635 (2016).
    [Crossref]
  15. 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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.
  16. H. Xin, K. Zhang, D. Kong, Q. Zhuge, Y. Fu, S. Jia, W. Hu, and H. Hu, “Nonlinear tomlinson-harashima precoding for direct-detected double sideband pam-4 transmission without dispersion compensation,” Opt. Express 27, 19156–19167 (2019).
    [Crossref]
  17. R. F. Fischer, Precoding and signal shaping for digital transmission (John Wiley & Sons, 2005).
  18. A. Li, W.-R. Peng, Y. Cui, and Y. Bai, “Single-λ 112Gbit/s 80-km transmission of PAM4 signal with optical signal-to-signal beat noise cancellation,” in Optical Fiber Communication Conference, (Optical Society of America, 2018), pp. Tu2C–5.
  19. Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35, 5193–5200 (2017).
    [Crossref]
  20. N.-P. Diamantopoulos, H. Nishi, W. Kobayashi, K. Takeda, T. Kakitsuka, and S. Matsuo, “On the Complexity Reduction of the Second-Order Volterra Nonlinear Equalizer for IM/DD Systems,” J. Lightwave Technol. 37, 1214–1224 (2019).
    [Crossref]
  21. B. Farhang-Boroujeny, Adaptive filters: theory and applications (John Wiley & Sons, 2013).
    [Crossref]
  22. J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhou, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27, 6098–6105 (2019).
    [Crossref] [PubMed]

2019 (5)

2018 (4)

2017 (2)

2016 (2)

2015 (2)

Antonelli, C.

Bai, Y.

A. Li, W.-R. Peng, Y. Cui, and Y. Bai, “Single-λ 112Gbit/s 80-km transmission of PAM4 signal with optical signal-to-signal beat noise cancellation,” in Optical Fiber Communication Conference, (Optical Society of America, 2018), pp. Tu2C–5.

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

Chagnon, M.

M. Chagnon, “Optical communications for short reach,” J. Lightwave Technol. 37, 1779–1797 (2019).
[Crossref]

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

Chandrasekhar, S.

Chen, C.

C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. Th4A–5.
[Crossref]

Chen, H.-Y.

Chen, J.

Chen, W.

Chen, X.

Chen, Y.-C.

Chien, H.

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

Chu, H.-H.

Chun, S.

Clausen, D.

Cui, Y.

A. Li, W.-R. Peng, Y. Cui, and Y. Bai, “Single-λ 112Gbit/s 80-km transmission of PAM4 signal with optical signal-to-signal beat noise cancellation,” in Optical Fiber Communication Conference, (Optical Society of America, 2018), pp. Tu2C–5.

Dai, Y.

Diamantopoulos, N.-P.

Eiselt, M. H.

Eiselt, N.

Elbers, J.-P.

Fan, Y.

Farhang-Boroujeny, B.

B. Farhang-Boroujeny, Adaptive filters: theory and applications (John Wiley & Sons, 2013).
[Crossref]

Fischer, R. F.

R. F. Fischer, Precoding and signal shaping for digital transmission (John Wiley & Sons, 2005).

Fu, S.

Fu, Y.

Gao, Y.

Griesser, H.

Grobe, K.

Gui, T.

Guo, M.

Hu, H.

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

Hu, W.

Jia, S.

Kakitsuka, T.

Kang, H.-S.

Kobayashi, W.

Kong, D.

Kong, M.

J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhou, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27, 6098–6105 (2019).
[Crossref] [PubMed]

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

Lee, J.

Li, A.

A. Li, W.-R. Peng, Y. Cui, and Y. Bai, “Single-λ 112Gbit/s 80-km transmission of PAM4 signal with optical signal-to-signal beat noise cancellation,” in Optical Fiber Communication Conference, (Optical Society of America, 2018), pp. Tu2C–5.

Li, J.

Li, X.

Li, Z.

Liu, B.

Liu, G. N.

Liu, S.

X. Tang, Y. Qiao, J. Zhou, M. Guo, J. Qi, S. Liu, X. Xu, and Y. Lu, “Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON,” Opt. Express 26, 33418–33427 (2018).
[Crossref]

X. Tang, S. Liu, X. Xu, J. Qi, M. Guo, J. Zhou, and Y. Qiao, “50-Gb/s PAM4 over 50-km Single Mode Fiber Transmission Using Efficient Equalization Technique,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. W2A–45.

Liu, W.

Lu, C.

Lu, I.-C.

Lu, Y.

Man, J.

Mao, Y.

Matsuo, S.

Mecozzi, A.

Monroy, I. T.

Moon, S.-R.

Nishi, H.

Ohlendorf, S.

Olmos, J. J. V.

Pachnicke, S.

Pan, X.

Peng, W.-R.

A. Li, W.-R. Peng, Y. Cui, and Y. Bai, “Single-λ 112Gbit/s 80-km transmission of PAM4 signal with optical signal-to-signal beat noise cancellation,” in Optical Fiber Communication Conference, (Optical Society of America, 2018), pp. Tu2C–5.

Qi, J.

X. Tang, Y. Qiao, J. Zhou, M. Guo, J. Qi, S. Liu, X. Xu, and Y. Lu, “Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON,” Opt. Express 26, 33418–33427 (2018).
[Crossref]

X. Tang, S. Liu, X. Xu, J. Qi, M. Guo, J. Zhou, and Y. Qiao, “50-Gb/s PAM4 over 50-km Single Mode Fiber Transmission Using Efficient Equalization Technique,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. W2A–45.

Qiao, Y.

Rath, R.

Raybon, G.

Rha, H.

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

Shtaif, M.

Shu, L.

Takeda, K.

Tang, X.

X. Tang, Y. Qiao, J. Zhou, M. Guo, J. Qi, S. Liu, X. Xu, and Y. Lu, “Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON,” Opt. Express 26, 33418–33427 (2018).
[Crossref]

J. Zhou, Y. Qiao, C. Yu, M. Guo, X. Tang, W. Liu, S. Chun, and Z. Li, “Joint Hartley-domain and time-domain equalizer for a 200-G (4 × 56-Gbit/s) optical PAM-4 system using 10G-class optics,” Opt. Express 26, 34451–34460 (2018).
[Crossref]

C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. Th4A–5.
[Crossref]

X. Tang, S. Liu, X. Xu, J. Qi, M. Guo, J. Zhou, and Y. Qiao, “50-Gb/s PAM4 over 50-km Single Mode Fiber Transmission Using Efficient Equalization Technique,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. W2A–45.

Tao, L.

Wan, Z.

Wang, K.

Wei, C.-C.

Wei, J.

Wei, Y.

Wey, J. S.

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

Winzer, P.

Xin, H.

Xin, X.

J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhou, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27, 6098–6105 (2019).
[Crossref] [PubMed]

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

Xu, K.

Xu, X.

Yin, F.

Yu, C.

Yu, J.

J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhou, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27, 6098–6105 (2019).
[Crossref] [PubMed]

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

Zeng, L.

Zhang, J.

J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhou, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27, 6098–6105 (2019).
[Crossref] [PubMed]

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

Zhang, K.

Zhang, L.

Zhang, Q.

Zhang, Y.

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

Zhang, Z.

C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. Th4A–5.
[Crossref]

Zhao, L.

Zhong, K.

Zhou, E.

Zhou, J.

Zhou, W.

Zhou, X.

Zhou, Y.

Zhuge, Q.

Zuo, T.

J. Lightwave Technol. (8)

M. Chagnon, “Optical communications for short reach,” J. Lightwave Technol. 37, 1779–1797 (2019).
[Crossref]

G. N. Liu, L. Zhang, T. Zuo, and Q. Zhang, “IM/DD Transmission Techniques for Emerging 5G Fronthaul, DCI, and Metro Applications,” J. Lightwave Technol. 36, 560–567 (2018).
[Crossref]

L. Zhang, T. Zuo, Y. Mao, Q. Zhang, E. Zhou, G. N. Liu, and X. Xu, “Beyond 100-Gb/s transmission over 80-km SMF using direct-detection SSB-DMT at C-band,” J. Lightwave Technol. 34, 723–729 (2016).
[Crossref]

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “Kramers–Kronig receivers for 100-km datacenter interconnects,” J. Lightwave Technol. 36, 79–89 (2018).
[Crossref]

R. Rath, D. Clausen, S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Tomlinson–Harashima precoding for dispersion uncompensated PAM-4 transmission with direct-detection,” J. Lightwave Technol. 35, 3909–3917 (2017).
[Crossref]

J. Wei, N. Eiselt, H. Griesser, K. Grobe, M. H. Eiselt, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Demonstration of the first real-time end-to-end 40-Gb/s PAM-4 for next-generation access applications using 10-Gb/s transmitter,” J. Lightwave Technol. 34, 1628–1635 (2016).
[Crossref]

Z. Wan, J. Li, L. Shu, S. Fu, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “64-Gb/s SSB-PAM4 transmission over 120-km dispersion-uncompensated SSMF with blind nonlinear equalization, adaptive noise-whitening postfilter and MLSD,” J. Lightwave Technol. 35, 5193–5200 (2017).
[Crossref]

N.-P. Diamantopoulos, H. Nishi, W. Kobayashi, K. Takeda, T. Kakitsuka, and S. Matsuo, “On the Complexity Reduction of the Second-Order Volterra Nonlinear Equalizer for IM/DD Systems,” J. Lightwave Technol. 37, 1214–1224 (2019).
[Crossref]

J. Opt. Commun. Netw. (1)

Opt. Express (6)

Other (7)

X. Tang, S. Liu, X. Xu, J. Qi, M. Guo, J. Zhou, and Y. Qiao, “50-Gb/s PAM4 over 50-km Single Mode Fiber Transmission Using Efficient Equalization Technique,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. W2A–45.

C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. Th4A–5.
[Crossref]

J. Zhang, J. Yu, H. Chien, J. S. Wey, M. Kong, X. Xin, and Y. Zhang, “Demonstration of 100-Gb/s/λ PAM-4 TDM-PON Supporting 29-dB Power Budget with 50-km Reach Using 10G-class O-band DML Transmitters,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. Th4C–3.

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 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

R. F. Fischer, Precoding and signal shaping for digital transmission (John Wiley & Sons, 2005).

A. Li, W.-R. Peng, Y. Cui, and Y. Bai, “Single-λ 112Gbit/s 80-km transmission of PAM4 signal with optical signal-to-signal beat noise cancellation,” in Optical Fiber Communication Conference, (Optical Society of America, 2018), pp. Tu2C–5.

B. Farhang-Boroujeny, Adaptive filters: theory and applications (John Wiley & Sons, 2013).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of the proposed equalizer structure.
Fig. 2
Fig. 2 (a). Experimental setup of 56-Gb/s PAM4 signal over 80-km SSMF transmission. (b). Experimental measured transfer function of MZM. DAC: Digital to analog converter; MZM: Mach-Zehnder modulator; SSMF: Standard single-mode fiber; EDFA: Erbium-doped fiber amplifier; OBPF: Optical bandpass filter; VOA: Variable optical attenuator; PD: Photo-detector; DPO: Digital phosphor oscilloscope.
Fig. 3
Fig. 3 (a). Frequency response of system for optical back to back transmission. (b). Normalized power spectrum of signal at back to back transmission and after 80-km transmission.
Fig. 4
Fig. 4 (a). CSPR versus DC Bias. (b). SNR versus CSPR with different equalizers at the received optical power of 0 dBm for 80-km transmission.
Fig. 5
Fig. 5 Convergence condition in terms of (a) signal amplitude and (b) square error.
Fig. 6
Fig. 6 (a). BER versus received optical power with different equalizers for 80-km SSMF transmission. (b)–(e): Eye diagrams with different equalizers at received optical power of 0 dBm.
Fig. 7
Fig. 7 BER performance and multiplications per symbol versus MPE-DFE with different taps.

Equations (11)

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

r ( t ) = s ( t ) + c ( t )
y ( t ) = c 2 ( t ) + | s ( t ) h ( t ) | 2 + 2 c ( t ) s ( t ) 1 ( Re { H ( f ) } )
Re { H ( f ) } = cos ( 2 π 2 β 2 L f 2 )
X ( k ) = [ X 1 ( k ) X 2 ( k ) X 3 ( k ) ] X 1 ( k ) = [ x ( k T + N F 1 T / 2 ) x ( k T ) x ( k T N F 1 T / 2 ) ] X 2 ( k ) = [ x 2 ( k T + N F 2 T / 2 ) x 2 ( k T ) x 2 ( k T N F 2 T / 2 ) ] X 3 ( k ) = [ x 3 ( k T + N F 3 T / 2 ) x 3 ( k T ) x 3 ( k T N F 3 T / 2 ) ]
D ( k ) = [ d ( k 1 ) d ( k 2 ) d ( k N B ) ]
y ( k ) = W F X ( k ) + W B D ( k )
W ( k ) = W ( k 1 ) + e ( k ) G * ( k )
e ( k ) = d ( k ) S T ( k ) W ( k 1 )
G ( k ) = P ( k 1 ) S * ( k ) [ λ + S T ( k ) P ( k 1 ) S * ( k ) ] 1
P ( k ) = λ 1 P ( k 1 ) G ( k ) S T ( k ) λ 1 P ( k 1 )
C MPE DFE = l 1 + 2 l 2 + 3 l 3 + d

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