Abstract

Spectral efficient frequency division multiplexing (SEFDM) can improve the spectral efficiency for next-generation optical and wireless communications. In this work, we apply SEFDM in beyond 100-Gb/s optical intensity modulation and direct detection transmissions and propose a low-complexity logarithmic-maximum-a-posteriori (log-MAP) Viterbi decoding algorithm to achieve the maximum likelihood (ML) detection. We evaluate the likelihood of detections using a posteriori probability instead of Euclidean distance by taking both noise and inter-carrier interference into consideration. In order to balance the performance and complexity, we then employ Viterbi decoding principle to retain only certain paths with ML detections (a.k.a., the surviving paths) while discarding the others during the decoding procedure. Results show that the proposed log-MAP Viterbi decoding scheme achieves optimal performance due to the precise likelihood evaluation, which guarantees the retention of the global ML detection. By using the proposed decoding scheme, the data rate of SEFDM signals can reach 150-Gb/s in a 2-km standard single mode fiber transmission, using only 28-GHz bandwidth and 16-QAM modulation. Experimental results show that the 16-QAM modulated SEFDM signal with a bandwidth compression factor of 0.8 outperforms 32-QAM modulated OFDM, while both signals have the same bandwidth (28-GHz) and data rate (140-Gb/s), which demonstrate the superiority of SEFDM in optical short reach applications.

© 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. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
    [Crossref]
  2. M. Chagnon, S. Lessard, and D. V. Plant, “336 Gb/s in direct detection below KP4 FEC threshold for intra data center applications,” IEEE Photon. Technol. Lett. 28, 2233–2236 (2016).
    [Crossref]
  3. Y. Zheng, J. Zhang, X. Hong, and C. Guo, “Generation and detection of 170.49-Gb/s single polarization IM/DD optical OFDM signals enabled by Volterra nonlinear equalization,” in Asia Communications and Photonics Conference, (Optical Society of America, 2016), pp. ATh2D-1.
  4. S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.
  5. M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
    [Crossref]
  6. X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).
  7. K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
    [Crossref]
  8. K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
    [Crossref] [PubMed]
  9. I. Kanaras, A. Chorti, M. R. Rodrigues, and I. Darwazeh, “Spectrally efficient FDM signals: bandwidth gain at the expense of receiver complexity,” in Communications, 2009. ICC’09. IEEE International Conference on, (IEEE, 2009), pp. 1–6.
  10. S. J. Heydari, M. F. Naeiny, and F. Marvasti, “Iterative detection with soft decision in spectrally efficient FDM systems,” arXiv preprint arXiv:1304.4003 (2013).
  11. B. Yu, H. Zhang, and X. Dai, “A low-complexity demodulation technique for spectrally efficient FDM systems using decision-feedback,” IET Commun. 11, 2386–2392 (2017).
    [Crossref]
  12. I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
    [Crossref]
  13. J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).
  14. C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.
  15. B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.
  16. Z. Zhang, C. Li, J. Chen, T. Ding, Y. Wang, H. Xiang, Z. Xiao, L. Li, M. Si, and X. Cui, “Coherent transceiver operating at 61-gbaud/s,” Opt. Express 23, 18988–18995 (2015).
    [Crossref] [PubMed]
  17. B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm i. expected complexity,” IEEE Trans. on Signal Process. 53, 2806–2818 (2005).
    [Crossref]
  18. H. C. Myburgh and J. C. Olivier, “Low complexity mlse equalization in highly dispersive rayleigh fading channels,” EURASIP J. on Adv. Signal Process. 2010, 10 (2010).
    [Crossref]

2018 (1)

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

2017 (1)

B. Yu, H. Zhang, and X. Dai, “A low-complexity demodulation technique for spectrally efficient FDM systems using decision-feedback,” IET Commun. 11, 2386–2392 (2017).
[Crossref]

2016 (3)

J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).

M. Chagnon, S. Lessard, and D. V. Plant, “336 Gb/s in direct detection below KP4 FEC threshold for intra data center applications,” IEEE Photon. Technol. Lett. 28, 2233–2236 (2016).
[Crossref]

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

2015 (3)

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Z. Zhang, C. Li, J. Chen, T. Ding, Y. Wang, H. Xiang, Z. Xiao, L. Li, M. Si, and X. Cui, “Coherent transceiver operating at 61-gbaud/s,” Opt. Express 23, 18988–18995 (2015).
[Crossref] [PubMed]

2014 (2)

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

2010 (1)

H. C. Myburgh and J. C. Olivier, “Low complexity mlse equalization in highly dispersive rayleigh fading channels,” EURASIP J. on Adv. Signal Process. 2010, 10 (2010).
[Crossref]

2005 (1)

B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm i. expected complexity,” IEEE Trans. on Signal Process. 53, 2806–2818 (2005).
[Crossref]

Bao, Y.

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

Chagnon, M.

M. Chagnon, S. Lessard, and D. V. Plant, “336 Gb/s in direct detection below KP4 FEC threshold for intra data center applications,” IEEE Photon. Technol. Lett. 28, 2233–2236 (2016).
[Crossref]

Chen, J.

Chen, W.

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Chorti, A.

I. Kanaras, A. Chorti, M. R. Rodrigues, and I. Darwazeh, “Spectrally efficient FDM signals: bandwidth gain at the expense of receiver complexity,” in Communications, 2009. ICC’09. IEEE International Conference on, (IEEE, 2009), pp. 1–6.

Cui, X.

Dai, X.

B. Yu, H. Zhang, and X. Dai, “A low-complexity demodulation technique for spectrally efficient FDM systems using decision-feedback,” IET Commun. 11, 2386–2392 (2017).
[Crossref]

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Darwazeh, I.

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

I. Kanaras, A. Chorti, M. R. Rodrigues, and I. Darwazeh, “Spectrally efficient FDM signals: bandwidth gain at the expense of receiver complexity,” in Communications, 2009. ICC’09. IEEE International Conference on, (IEEE, 2009), pp. 1–6.

Ding, T.

Fujisawa, T.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Gao, Y.

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Gui, T.

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

Guo, C.

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

Y. Zheng, J. Zhang, X. Hong, and C. Guo, “Generation and detection of 170.49-Gb/s single polarization IM/DD optical OFDM signals enabled by Volterra nonlinear equalization,” in Asia Communications and Photonics Conference, (Optical Society of America, 2016), pp. ATh2D-1.

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Hassibi, B.

B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm i. expected complexity,” IEEE Trans. on Signal Process. 53, 2806–2818 (2005).
[Crossref]

Heydari, S. J.

S. J. Heydari, M. F. Naeiny, and F. Marvasti, “Iterative detection with soft decision in spectrally efficient FDM systems,” arXiv preprint arXiv:1304.4003 (2013).

Hong, X.

Y. Zheng, J. Zhang, X. Hong, and C. Guo, “Generation and detection of 170.49-Gb/s single polarization IM/DD optical OFDM signals enabled by Volterra nonlinear equalization,” in Asia Communications and Photonics Conference, (Optical Society of America, 2016), pp. ATh2D-1.

Huang, J.

J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).

Huo, J.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

Ishii, H.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Jensen, J. B.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Ji, F.

J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).

Kanaras, I.

I. Kanaras, A. Chorti, M. R. Rodrigues, and I. Darwazeh, “Spectrally efficient FDM signals: bandwidth gain at the expense of receiver complexity,” in Communications, 2009. ICC’09. IEEE International Conference on, (IEEE, 2009), pp. 1–6.

Kanazawa, S.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Kobayashi, W.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Lau, A.

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Lau, A. P. T.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

Lessard, S.

M. Chagnon, S. Lessard, and D. V. Plant, “336 Gb/s in direct detection below KP4 FEC threshold for intra data center applications,” IEEE Photon. Technol. Lett. 28, 2233–2236 (2016).
[Crossref]

Li, C.

Li, F.

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

Li, L.

Li, Z.

J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

Liu, J.

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

Long, K.

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

Lu, C.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Man, J.

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Marvasti, F.

S. J. Heydari, M. F. Naeiny, and F. Marvasti, “Iterative detection with soft decision in spectrally efficient FDM systems,” arXiv preprint arXiv:1304.4003 (2013).

Monroy, I. T.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Muramoto, Y.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Myburgh, H. C.

H. C. Myburgh and J. C. Olivier, “Low complexity mlse equalization in highly dispersive rayleigh fading channels,” EURASIP J. on Adv. Signal Process. 2010, 10 (2010).
[Crossref]

Naeiny, M. F.

S. J. Heydari, M. F. Naeiny, and F. Marvasti, “Iterative detection with soft decision in spectrally efficient FDM systems,” arXiv preprint arXiv:1304.4003 (2013).

Nakanishi, Y.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Olivier, J. C.

H. C. Myburgh and J. C. Olivier, “Low complexity mlse equalization in highly dispersive rayleigh fading channels,” EURASIP J. on Adv. Signal Process. 2010, 10 (2010).
[Crossref]

Olmedo, M. I.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Plant, D. V.

M. Chagnon, S. Lessard, and D. V. Plant, “336 Gb/s in direct detection below KP4 FEC threshold for intra data center applications,” IEEE Photon. Technol. Lett. 28, 2233–2236 (2016).
[Crossref]

Popov, S.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Rodrigues, M. R.

I. Kanaras, A. Chorti, M. R. Rodrigues, and I. Darwazeh, “Spectrally efficient FDM signals: bandwidth gain at the expense of receiver complexity,” in Communications, 2009. ICC’09. IEEE International Conference on, (IEEE, 2009), pp. 1–6.

Sanjoh, H.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Si, M.

Sui, Q.

J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).

Takahata, K.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Ueda, Y.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Vikalo, H.

B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm i. expected complexity,” IEEE Trans. on Signal Process. 53, 2806–2818 (2005).
[Crossref]

Wang, L.

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

Wang, Y.

Wu, X.

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

Xiang, H.

Xiao, Z.

Xu, T.

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

Xu, X.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Xu, Y.

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

Yamazaki, H.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

Yi, L.

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Yu, B.

B. Yu, H. Zhang, and X. Dai, “A low-complexity demodulation technique for spectrally efficient FDM systems using decision-feedback,” IET Commun. 11, 2386–2392 (2017).
[Crossref]

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Yu, C.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

Yuan, J.

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

Zeng, L.

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Zhang, H.

B. Yu, H. Zhang, and X. Dai, “A low-complexity demodulation technique for spectrally efficient FDM systems using decision-feedback,” IET Commun. 11, 2386–2392 (2017).
[Crossref]

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

Zhang, J.

Y. Zheng, J. Zhang, X. Hong, and C. Guo, “Generation and detection of 170.49-Gb/s single polarization IM/DD optical OFDM signals enabled by Volterra nonlinear equalization,” in Asia Communications and Photonics Conference, (Optical Society of America, 2016), pp. ATh2D-1.

Zhang, Z.

Zheng, Y.

Y. Zheng, J. Zhang, X. Hong, and C. Guo, “Generation and detection of 170.49-Gb/s single polarization IM/DD optical OFDM signals enabled by Volterra nonlinear equalization,” in Asia Communications and Photonics Conference, (Optical Society of America, 2016), pp. ATh2D-1.

Zhong, K.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Zhong, Q.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Zhou, X.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

K. Zhong, X. Zhou, Y. Wang, L. Wang, J. Yuan, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of 608Gbit/s short reach transmission employing half-cycle 16QAM Nyquist-SCM signal and direct detection with 25Gbps EML,” Opt. Express 24, 25057–25067 (2016).
[Crossref] [PubMed]

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

Zuo, T.

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

EURASIP J. on Adv. Signal Process. (1)

H. C. Myburgh and J. C. Olivier, “Low complexity mlse equalization in highly dispersive rayleigh fading channels,” EURASIP J. on Adv. Signal Process. 2010, 10 (2010).
[Crossref]

IEEE Photon. J. (2)

J. Huang, Q. Sui, Z. Li, and F. Ji, “Experimental Demonstration of 16-QAM DD-SEFDM with cascaded BPSK iterative detection,” IEEE Photon. J. 8, 1–9 (2016).

X. Zhou, K. Zhong, J. Huo, J. Yuan, F. Li, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarization-multiplexed DMT with IM-DD using 2× 2 MIMO processing based on SOP estimation and MPBI elimination,” IEEE Photon. J. 7, 1–12 (2015).

IEEE Photon. Technol. Lett. (3)

K. Zhong, X. Zhou, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “140 Gbit/s 20km transmission of PAM-4 signal at 1.3 µ m for short reach communications,” IEEE Photon. Technol. Lett. 27, 1757–1760 (2015).
[Crossref]

M. Chagnon, S. Lessard, and D. V. Plant, “336 Gb/s in direct detection below KP4 FEC threshold for intra data center applications,” IEEE Photon. Technol. Lett. 28, 2233–2236 (2016).
[Crossref]

I. Darwazeh, T. Xu, T. Gui, Y. Bao, and Z. Li, “Optical SEFDM system; bandwidth saving using non-orthogonal sub-carriers,” IEEE Photon. Technol. Lett. 26, 352–355 (2014).
[Crossref]

IEEE Trans. on Signal Process. (1)

B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm i. expected complexity,” IEEE Trans. on Signal Process. 53, 2806–2818 (2005).
[Crossref]

IET Commun. (1)

B. Yu, H. Zhang, and X. Dai, “A low-complexity demodulation technique for spectrally efficient FDM systems using decision-feedback,” IET Commun. 11, 2386–2392 (2017).
[Crossref]

J. Light. Technol. (2)

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Light. Technol. 36, 377–400 (2018).
[Crossref]

M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Light. Technol. 32, 798–804 (2014).
[Crossref]

Opt. Express (2)

Other (6)

C. Guo, B. Yu, L. Yi, Y. Xu, X. Wu, J. Liu, and H. Zhang, “98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions,” in Asia Communications and Photonics Conference, (Optical Society of America, 2017), pp. S4B–2.

B. Yu, L. Yi, C. Guo, J. Liu, X. Dai, A. Lau, and C. Lu, “Dispersion Tolerant 66.7-Gb/s SEFDM IM/DD Transmission over 77-km SSMF,” in Optical Communication (ECOC), 2018 European Conference on, (IEEE, 2018), pp. We2.25-1.

Y. Zheng, J. Zhang, X. Hong, and C. Guo, “Generation and detection of 170.49-Gb/s single polarization IM/DD optical OFDM signals enabled by Volterra nonlinear equalization,” in Asia Communications and Photonics Conference, (Optical Society of America, 2016), pp. ATh2D-1.

S. Kanazawa, H. Yamazaki, Y. Nakanishi, T. Fujisawa, K. Takahata, Y. Ueda, W. Kobayashi, Y. Muramoto, H. Ishii, and H. Sanjoh, “Transmission of 214-Gbit/s 4-PAM signal using an ultra-broadband lumped-electrode EADFB laser module,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. Th5B-3.

I. Kanaras, A. Chorti, M. R. Rodrigues, and I. Darwazeh, “Spectrally efficient FDM signals: bandwidth gain at the expense of receiver complexity,” in Communications, 2009. ICC’09. IEEE International Conference on, (IEEE, 2009), pp. 1–6.

S. J. Heydari, M. F. Naeiny, and F. Marvasti, “Iterative detection with soft decision in spectrally efficient FDM systems,” arXiv preprint arXiv:1304.4003 (2013).

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Figures (7)

Fig. 1
Fig. 1 SEFDM transceiver diagram using IFFT method.
Fig. 2
Fig. 2 Tree diagram of the proposed log-MAP Viterbi decoding algorithm. The solid dots denote the retained ML detections, while the others denote the discarded ones.
Fig. 3
Fig. 3 (a) Simulated BER performance of the proposed log-MAP Viterbi decoding algorithm with various values of C for SEFDM with α = 0.80 using 4-QAM and 16-QAM modulations in AWGN channel; (b) comparison between the proposed log-MAP Viterbi decoding scheme with conventional CBID-FSD for SEFDM with various values of α; (c) comparison of performance between SEFDM with OFDM.
Fig. 4
Fig. 4 Experimental setup.
Fig. 5
Fig. 5 (a) BER performance of the proposed log-MAP Viterbi decoding algorithm with various values of C for SEFDM with α = 0.80 using 16-QAM modulation after 2-km SSMF transmission; (b) calculated SNR after ICI cancellation using the proposed decoding scheme, compared with the real SNR obtained via OFDM training.
Fig. 6
Fig. 6 Received signal distributions of SEFDM before (left) and after (right) ICI cancellation using the proposed log-MAP Viterbi decoding algorithm.
Fig. 7
Fig. 7 (a) BER performance of the proposed log-MAP Viterbi decoding algorithm with C = 16 for SEFDM with various values of α using 16-QAM modulations after 2-km SSMF transmission, compared with CBID; (b) BER comparison between OFDM and SEFDM with α = 0.80 after 2-km SSMF transmission.

Tables (2)

Tables Icon

Table 1 Parameters used for experiments and simulations

Tables Icon

Table 2 General computational complexity comparison

Equations (10)

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

x ( t ) = k = 0 N 1 S k exp ( j 2 π k Δ f t ) ,
x n : = x ( n T N 1 ) = k = 0 N 1 S k exp ( j 2 π α k n N 1 ) , n = 0 , 1 , , N 1 1 ,
x n = k = 0 N f f t 1 S k exp ( j 2 π k n N f f t ) , n = 0 , 1 , , N 1 1 ,
Y k = W k , k S k + i = 0 , i k N 1 W k , i S i + Z k ,
W k , i = 1 N f f t n = 0 N 1 1 exp ( j 2 π n ( k i ) N f f t ) .
γ k = i = P N 1 W k , i S i + Z k , k = 0 , 1 , , P 1 ,
Γ k , l = E { γ k * γ l } = i = P N 1 j = P N 1 W k , i W j , l + A k , l ,
A k , l = { σ 2 k = l 0 k l .
P = d H Γ 1 d ,
d k = Y k i = 0 P 1 W k , i S i ,

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