Abstract

We present the design and optimization of the optical single side-band (SSB) Nyquist four-level pulse amplitude modulation (PAM-4) transmission using dual-drive Mach-Zehnder modulator (DDMZM)modulation and direct detection (DD), aiming at the C-band cost-effective, high-speed and long-distance transmission. At the transmitter, the laser line width should be small to avoid the phase noise to amplitude noise conversion and equalization-enhanced phase noise due to the large chromatic dispersion (CD). The optical SSB signal is generated after optimizing the optical modulation index (OMI) and hence the minimum phase condition which is required by the Kramers-Kronig (KK) receiver can also be satisfied. At the receiver, a simple AC-coupled photodiode (PD) is used and a virtual carrier is added for the KK operation to alleviate the signal-to-signal beating interference (SSBI).A Volterra filter (VF) is cascaded for remaining nonlinearities mitigation. When the fiber nonlinearity becomes significant, we elect to use an optical band-pass filter with offset filtering. It can suppress the simulated Brillouin scattering and the conjugated distortion by filtering out the imaging frequency components. With our design and optimization, we achieve single-channel, single polarization 102.4-Gb/s Nyquist PAM-4 over 800-km standard single-mode fiber (SSMF).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
    [Crossref]
  2. 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]
  3. B. J. Lin, J. H. Li, H. Yang, Y. S. Wan, Y. Q. He, and Z. Y. Chen, “Comparison of DSB and SSB transmission for OFDM-PON,” in Proceedings of Optical Fiber Communication Conference (2012), paper NTu1J.7.
    [Crossref]
  4. L. Zhang, Q. Zhang, T. J. Zuo, E. B. Zhou, G. N. Liu, and X. G. Xu, “C-band Single Wavelength 100-Gb/s IM-DD Transmissionover 80-km SMF without CD compensation using SSB-DMT,” in Proceedings of Optical Fiber Communication Conference (2015), paper Th4A.2.
    [Crossref]
  5. L. Zhang, T. J. Zuo, Y. Mao, Q. Zhang, E. B. Zhou, G. N. Liu, and X. G. Xu, “Beyond 100-Gb/s Transmission Over 80-km SMFUsing Direct-Detection SSB-DMT at C-Band,” J. Lightwave Technol. 34(2), 723–729 (2016).
    [Crossref]
  6. H. Y. Chen, N. Kaneda, J. Lee, J. Chen, and Y. K. Chen, “Optical filter requirements in an EML-based single-sideband PAM4 intensity-modulation and direct-detection transmission system,” Opt. Express 25(6), 5852–5860 (2017).
    [Crossref] [PubMed]
  7. D. Pilori, C. Fludger, and R. Gaudino, “Comparing DMT Variants in Medium-Reach 100G Optically Amplified Systems,” J. Lightwave Technol. 34(14), 3389–3399 (2016).
    [Crossref]
  8. M. Xu, J. Y. Shi, J. W. Zhang, J. J. Yu, and G. K. Chang, “High-Capacity Tier-II Fronthaul Network with SSB-DD Multiband OQAM/QAM-CAP,” in Proceedings of European Conference and Exhibition on Optical Communication (2017), paper P2.SC8.58.
  9. M. S. Erkılınç, Z. Li, S. Pachnicke, H. Griesser, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally Efficient WDM Nyquist Pulse-Shaped 16-QAM Subcarrier Modulation Transmission With Direct Detection,” J. Lightwave Technol. 33(15), 3147–3155 (2015).
    [Crossref]
  10. N. Eiselt, H. Griesser, J. L. Wei, A. Dochhan, M. Eiselt, J. P. Elbers, J. J. V. Olmos, and I. T. Monroy, “Real-Time Evaluation of 26-GBaud PAM-4 Intensity Modulation and Direct Detection Systems for Data-Center Interconnects,” in Proceedings of Optical Fiber Communication Conference (2016), paper Th1G.3.
    [Crossref]
  11. J. King, D. Leyba, and G. D. LeCheminant, “TDECQ (Transmitter Dispersion Eye Closure Quaternary) Replaces Historic Eye-mask and TDP Test for 400 Gb/s PAM4 Optical Transmitters,” in Proceedings of Optical Fiber Communication Conference (2017), paper W4D.1.
    [Crossref]
  12. M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
    [Crossref]
  13. M. Y. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, Y. X. Song, F. Li, X. T. Huang, X. W. Yi, and K. Qiu, “56-Gb/s Optical SSB PAM-4 Transmission over 800-km SSMF Using DDMZM Transmitter and Simplified Direct Detection Kramers-Kronig Receiver,”in Proceedings of Optical Fiber Communication Conference (2018), paper M2C.5.
  14. M. Y. Zhu, X. W. Yi, J. Zhang, X. Li, M. Luo, F. Li, Z. H. Li, X. T. Huang, and K. Qiu, “102.4-Gb/s Optical SSB Nyquist-PAM-4 Transmission over 800-km SSMF at C-band Using Direct-Detection Kramers-KronigReceiver,” in Proceedings ofAsia Communications and Photonics Conference(2017), paper Su2B.3.
    [Crossref]
  15. F. Gao, S. Zhou, X. Li, S. Fu, L. Deng, M. Tang, D. Liu, and Q. Yang, “2 × 64 Gb/s PAM-4 transmission over 70 km SSMF using O-band 18G-class directly modulated lasers (DMLs),” Opt. Express 25(7), 7230–72372017).
    [Crossref] [PubMed]
  16. S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
    [Crossref]
  17. Z. Li, M. S. Erkilinc, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24(25), 29176–29189 (2016).
    [Crossref] [PubMed]
  18. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3(11), 1220–1227 (2016).
    [Crossref]
  19. C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers Kronig transceiver,” J. Lightwave Technol. 36(2), 468–475 (2018).
  20. C. Antonelli, M. Shtaif, and A. Mecozzi, “Kramers-Kronig PAM Transceiver,” in Proceedings of Optical Fiber Communication Conference (2017), paper Tu3I.5.
    [Crossref]
  21. A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” https://arxiv.org/abs/1606.04861 .
  22. Q. Zhang, N. Stojanovic, C. Xie, C. Prodaniuc, and P. Laskowski, “Transmission of single lane 128 Gbit/s PAM-4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation,” Opt. Express 24(21), 24580–24591 (2016).
    [Crossref] [PubMed]
  23. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008).
    [Crossref] [PubMed]
  24. Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017).
    [Crossref]

2018 (2)

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers Kronig transceiver,” J. Lightwave Technol. 36(2), 468–475 (2018).

2017 (4)

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

H. Y. Chen, N. Kaneda, J. Lee, J. Chen, and Y. K. Chen, “Optical filter requirements in an EML-based single-sideband PAM4 intensity-modulation and direct-detection transmission system,” Opt. Express 25(6), 5852–5860 (2017).
[Crossref] [PubMed]

F. Gao, S. Zhou, X. Li, S. Fu, L. Deng, M. Tang, D. Liu, and Q. Yang, “2 × 64 Gb/s PAM-4 transmission over 70 km SSMF using O-band 18G-class directly modulated lasers (DMLs),” Opt. Express 25(7), 7230–72372017).
[Crossref] [PubMed]

Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017).
[Crossref]

2016 (5)

2015 (2)

2008 (1)

Antonelli, C.

Bayvel, P.

Cartledge, J. C.

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

Chandrasekhar, S.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
[Crossref]

Chen, H. Y.

Chen, J.

Chen, W.

Chen, Y. K.

Deng, L.

Erkilinc, M. S.

Erkilinç, M. S.

Fludger, C.

Fu, S.

Galdino, L.

Gao, F.

Gao, Y.

Gao, Y. L.

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

Gaudino, R.

Griesser, H.

Gui, T.

Ho, K. P.

Kaneda, N.

Kashi, A. S.

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

Killey, R. I.

Laskowski, P.

Lau, A. P. T.

Lee, J.

Li, X.

Li, Z.

Liu, D.

Liu, G. N.

Lu, C.

Man, J.

Mao, Y.

Matsui, Y.

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

Mecozzi, A.

Pachnicke, S.

Pilori, D.

D. Pilori, C. Fludger, and R. Gaudino, “Comparing DMT Variants in Medium-Reach 100G Optically Amplified Systems,” J. Lightwave Technol. 34(14), 3389–3399 (2016).
[Crossref]

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
[Crossref]

Prodaniuc, C.

Qiu, K.

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

Randel, S.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
[Crossref]

Raybon, G.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
[Crossref]

Shi, K.

Shieh, W.

Shtaif, M.

Stojanovic, N.

Tang, M.

Tao, L.

Thomsen, B. C.

Winzer, P.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
[Crossref]

Xie, C.

Xu, X. G.

Yam, S. S. H.

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

Yang, Q.

Yi, X. W.

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

Ying, H.

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

Zeng, L.

Zhang, F.

Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017).
[Crossref]

Zhang, J.

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

Zhang, L.

Zhang, Q.

Zhong, K.

Zhou, E. B.

Zhou, S.

Zhou, X.

Zhu, M. Y.

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

Zhu, Y. X.

Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017).
[Crossref]

Zou, K. H.

Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017).
[Crossref]

Zuo, T. J.

IEEE Photonics Technol. Lett. (2)

Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017).
[Crossref]

Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017).
[Crossref]

J. Lightwave Technol. (4)

Opt. Commun. (1)

M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018).
[Crossref]

Opt. Express (6)

F. Gao, S. Zhou, X. Li, S. Fu, L. Deng, M. Tang, D. Liu, and Q. Yang, “2 × 64 Gb/s PAM-4 transmission over 70 km SSMF using O-band 18G-class directly modulated lasers (DMLs),” Opt. Express 25(7), 7230–72372017).
[Crossref] [PubMed]

Z. Li, M. S. Erkilinc, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24(25), 29176–29189 (2016).
[Crossref] [PubMed]

H. Y. Chen, N. Kaneda, J. Lee, J. Chen, and Y. K. Chen, “Optical filter requirements in an EML-based single-sideband PAM4 intensity-modulation and direct-detection transmission system,” Opt. Express 25(6), 5852–5860 (2017).
[Crossref] [PubMed]

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]

Q. Zhang, N. Stojanovic, C. Xie, C. Prodaniuc, and P. Laskowski, “Transmission of single lane 128 Gbit/s PAM-4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation,” Opt. Express 24(21), 24580–24591 (2016).
[Crossref] [PubMed]

W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008).
[Crossref] [PubMed]

Optica (1)

Other (10)

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697.
[Crossref]

M. Y. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, Y. X. Song, F. Li, X. T. Huang, X. W. Yi, and K. Qiu, “56-Gb/s Optical SSB PAM-4 Transmission over 800-km SSMF Using DDMZM Transmitter and Simplified Direct Detection Kramers-Kronig Receiver,”in Proceedings of Optical Fiber Communication Conference (2018), paper M2C.5.

M. Y. Zhu, X. W. Yi, J. Zhang, X. Li, M. Luo, F. Li, Z. H. Li, X. T. Huang, and K. Qiu, “102.4-Gb/s Optical SSB Nyquist-PAM-4 Transmission over 800-km SSMF at C-band Using Direct-Detection Kramers-KronigReceiver,” in Proceedings ofAsia Communications and Photonics Conference(2017), paper Su2B.3.
[Crossref]

N. Eiselt, H. Griesser, J. L. Wei, A. Dochhan, M. Eiselt, J. P. Elbers, J. J. V. Olmos, and I. T. Monroy, “Real-Time Evaluation of 26-GBaud PAM-4 Intensity Modulation and Direct Detection Systems for Data-Center Interconnects,” in Proceedings of Optical Fiber Communication Conference (2016), paper Th1G.3.
[Crossref]

J. King, D. Leyba, and G. D. LeCheminant, “TDECQ (Transmitter Dispersion Eye Closure Quaternary) Replaces Historic Eye-mask and TDP Test for 400 Gb/s PAM4 Optical Transmitters,” in Proceedings of Optical Fiber Communication Conference (2017), paper W4D.1.
[Crossref]

B. J. Lin, J. H. Li, H. Yang, Y. S. Wan, Y. Q. He, and Z. Y. Chen, “Comparison of DSB and SSB transmission for OFDM-PON,” in Proceedings of Optical Fiber Communication Conference (2012), paper NTu1J.7.
[Crossref]

L. Zhang, Q. Zhang, T. J. Zuo, E. B. Zhou, G. N. Liu, and X. G. Xu, “C-band Single Wavelength 100-Gb/s IM-DD Transmissionover 80-km SMF without CD compensation using SSB-DMT,” in Proceedings of Optical Fiber Communication Conference (2015), paper Th4A.2.
[Crossref]

M. Xu, J. Y. Shi, J. W. Zhang, J. J. Yu, and G. K. Chang, “High-Capacity Tier-II Fronthaul Network with SSB-DD Multiband OQAM/QAM-CAP,” in Proceedings of European Conference and Exhibition on Optical Communication (2017), paper P2.SC8.58.

C. Antonelli, M. Shtaif, and A. Mecozzi, “Kramers-Kronig PAM Transceiver,” in Proceedings of Optical Fiber Communication Conference (2017), paper Tu3I.5.
[Crossref]

A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” https://arxiv.org/abs/1606.04861 .

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Figures (10)

Fig. 1
Fig. 1 The operation structure of the simplified DD-KK receiver.
Fig. 2
Fig. 2 Optical SSB Nyquist PAM-4 experimental setup.
Fig. 3
Fig. 3 The B2B results (a) The optimized OMI; (b) The spectrum of optical SSB Nyquist PAM-4 signal.
Fig. 4
Fig. 4 BER performance at 80-km SSMF with different laser line width.
Fig. 5
Fig. 5 (a) Spectrum of optical SSB NPAM-4 with sweeping filter wavelength over 80-km SSMF; (b) The system performance and signal CSPR with sweeping filter wavelength over 80-km SSMF.
Fig. 6
Fig. 6 (a) Simulation of the order of Gaussian filter. (b) Optimal filter bandwidth with different filter center wavelength.
Fig. 7
Fig. 7 Signal traces of received NPAM-4. The solid lines are the mean values.
Fig. 8
Fig. 8 (a) Detected DSB spectrum and the reconstructed SSB signal spectrum by the KK scheme; (b) BER at the optimum launch power versus resampling rate at 640 and 800km.
Fig. 9
Fig. 9 (a) BER with different SSBI mitigation schemes with 56-Gb/s PAM-4; (b) Transmission performance of KK receiver cascades FFE and VF with 56-Gb/s PAM-4. Insets: (I) ratio of the Volterra kernels, (II)-(IV) eye diagrams after VF, SSLF and KK at 3-dBm optical launch power after 640-km transmission.
Fig. 10
Fig. 10 (a) Transmission performance at 720 km. Insets (I) and (II) are the histograms with and without KK operation at 5 dBm. (b) BER versus transmission distance. Insets (III) and (IV) are the histograms with and without KK operation at 400-km SSMF.

Equations (4)

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V ( n ) = π V π [ s ( n ) s ^ ( n ) ] + π 2 2 V π 2 [ s 2 ( n ) + s ^ 2 ( n ) ]
r ( n ) = α | ( V ( n ) ) min | + V ( n )
ϕ ( n ) = H { log [ r ( n ) ] } / 2
r ( n ) = r ( n ) e j ϕ ( n )

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