Abstract

The Kramers-Kronig (KK) receiver is capable of retrieving the phase information of optical single-sideband (SSB) signal from the optical intensity when the optical signal satisfies the minimum phase condition. Thus, it is possible to direct-detect the optical SSB signal without suffering from the signal-signal beat interference and linear transmission impairments. However, due to the spectral broadening induced by nonlinear operations in the conventional KK algorithm, it is necessary to employ the digital upsampling at the beginning of the digital signal processing (DSP). The increased number of samples at the DSP would hinder the real-time implementation of this attractive receiver. Hence, we propose a new DSP algorithm for KK receiver operable at 2 samples per symbol. We adopt a couple of mathematical approximations to avoid the use of nonlinear operations such as logarithm and exponential functions. By using the proposed algorithm, we demonstrate the transmission of 112-Gb/s SSB orthogonal frequency-division-multiplexed signal over an 80-km fiber link. The results show that the proposed algorithm operating at 2 samples per symbol exhibits similar performance to the conventional KK one operating at 6 samples per symbol. We also present the error analysis of the proposed algorithm for KK receiver in comparison with the conventional one.

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

Full Article  |  PDF Article
OSA Recommended Articles
Kramers–Kronig coherent receiver

Antonio Mecozzi, Cristian Antonelli, and Mark Shtaif
Optica 3(11) 1220-1227 (2016)

Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection

Mingyue Zhu, Jing Zhang, Xingwen Yi, Hao Ying, Xiang Li, Ming Luo, Yingxiong Song, Xiatao Huang, and Kun Qiu
Opt. Express 26(6) 6629-6638 (2018)

Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique

Wei-Ren Peng, Xiaoxia Wu, Kai-Ming Feng, Vahid R. Arbab, Bishara Shamee, Jeng-Yuan Yang, Louis C. Christen, Alan E. Willner, and Sien Chi
Opt. Express 17(11) 9099-9111 (2009)

References

  • View by:
  • |
  • |
  • |

  1. J. C. Cartledge and A. S. Karar, “100 Gb/s intensity modulation and direct detection,” J. Lightwave Technol. 32(16), 2809–2814 (2014).
    [Crossref]
  2. W.-R. Peng, X. Wu, V. R. Arbab, K.-M. Feng, B. Shamee, L. C. Christen, J.-Y. Yang, A. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009).
    [Crossref]
  3. 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 2015 European Conference on Optical Communication (2015), p. 0697.
    [Crossref]
  4. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3(11), 1220–1227 (2016).
    [Crossref]
  5. Z. Li, M. S. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017).
    [Crossref]
  6. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference (2017), paper Th5B.6.
    [Crossref]
  7. Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photonics Technol. Lett. 29(21), 1788–1791 (2017).
    [Crossref]
  8. C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers Kronig receiver,” J. Lightwave Technol. 35(24), 5418–5424 (2017).
    [Crossref]
  9. Z. Li, M. S. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (2017), paper W.2.D.3.
  10. T. Bo and H. Kim, “Kramers-Kronig receiver without digital upsampling,” in Optical Fiber Communication Conference (2018), paper W4E.2.
    [Crossref]
  11. H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14(1), 22–30 (1966).
    [Crossref]
  12. A. A. Poli and M. C. Cirillo, “On the use of the normalized mean square error in evaluating dispersion model performance,” Atmos. Environ., A Gen. Topics 27(15), 2427–2434 (1993).
    [Crossref]

2017 (3)

2016 (1)

2014 (1)

2009 (1)

1993 (1)

A. A. Poli and M. C. Cirillo, “On the use of the normalized mean square error in evaluating dispersion model performance,” Atmos. Environ., A Gen. Topics 27(15), 2427–2434 (1993).
[Crossref]

1966 (1)

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14(1), 22–30 (1966).
[Crossref]

Antonelli, C.

Arbab, V. R.

Bayvel, P.

Cartledge, J. C.

Chandrasekhar, S.

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers Kronig receiver,” J. Lightwave Technol. 35(24), 5418–5424 (2017).
[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 2015 European Conference on Optical Communication (2015), p. 0697.
[Crossref]

Chen, X.

Chi, S.

Christen, L. C.

Cirillo, M. C.

A. A. Poli and M. C. Cirillo, “On the use of the normalized mean square error in evaluating dispersion model performance,” Atmos. Environ., A Gen. Topics 27(15), 2427–2434 (1993).
[Crossref]

Erkilinç, M. S.

Feng, K.-M.

Galdino, L.

Karar, A. S.

Killey, R. I.

Li, Z.

Mecozzi, A.

Peng, W.-R.

Pilori, D.

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 2015 European Conference on Optical Communication (2015), p. 0697.
[Crossref]

Poli, A. A.

A. A. Poli and M. C. Cirillo, “On the use of the normalized mean square error in evaluating dispersion model performance,” Atmos. Environ., A Gen. Topics 27(15), 2427–2434 (1993).
[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 2015 European Conference on Optical Communication (2015), p. 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 2015 European Conference on Optical Communication (2015), p. 0697.
[Crossref]

Ruan, X.

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photonics Technol. Lett. 29(21), 1788–1791 (2017).
[Crossref]

Shamee, B.

Shi, K.

Shtaif, M.

Sillekens, E.

Thomsen, B. C.

Voelcker, H.

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14(1), 22–30 (1966).
[Crossref]

Willner, A.

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 2015 European Conference on Optical Communication (2015), p. 0697.
[Crossref]

Winzer, P. J.

Wu, X.

Yang, J.-Y.

Zhang, F.

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photonics Technol. Lett. 29(21), 1788–1791 (2017).
[Crossref]

Zhu, Y.

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photonics Technol. Lett. 29(21), 1788–1791 (2017).
[Crossref]

Zou, K.

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photonics Technol. Lett. 29(21), 1788–1791 (2017).
[Crossref]

Atmos. Environ., A Gen. Topics (1)

A. A. Poli and M. C. Cirillo, “On the use of the normalized mean square error in evaluating dispersion model performance,” Atmos. Environ., A Gen. Topics 27(15), 2427–2434 (1993).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photonics Technol. Lett. 29(21), 1788–1791 (2017).
[Crossref]

IEEE Trans. Commun. Technol. (1)

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14(1), 22–30 (1966).
[Crossref]

J. Lightwave Technol. (4)

Optica (1)

Other (4)

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference (2017), paper Th5B.6.
[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 2015 European Conference on Optical Communication (2015), p. 0697.
[Crossref]

Z. Li, M. S. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (2017), paper W.2.D.3.

T. Bo and H. Kim, “Kramers-Kronig receiver without digital upsampling,” in Optical Fiber Communication Conference (2018), paper W4E.2.
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Block diagrams of (a) the conventional KK receiver [5] and (b) proposed KK receiver.
Fig. 2
Fig. 2 (a). Experiment setup. ECL: external-cavity laser, AWG: arbitrary waveform generator, EDFA: Er-doped fiber amplifier, BPF: band-pass filter, PD: photodetector. (b) Optical spectrum measured before the PD.
Fig. 3
Fig. 3 BER performance as a function of the magnitude of optical carrier.
Fig. 4
Fig. 4 Experimental results. (a) Measured receiver sensitivity (@BER = 3.8 × 10−3) versus CSPR after 80-km transmission, (b) BER curves.
Fig. 5
Fig. 5 The normalized mean square error between the original and approximated waveforms.
Fig. 6
Fig. 6 Effect of the sampling rate on the performance of the proposed algorithm. The sensitivity penalty is measured with respect to the conventional KK algorithm operating at 6 SPSs.

Equations (11)

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

E(t)= E 0 +s( t )+j s ^ ( t )
I( t )= | E( t ) | 2 =η | E 0 +s( t )+j s ^ ( t ) | 2
ϕ( t )=H[ ln I( t ) ]
E( t )= I( t ) exp[ jϕ( t ) ]
I( t ) = E 0 1+ 2s( t ) E 0 + s 2 ( t )+ s ^ 2 ( t ) E 0 2 = E 0 { 1+ 1 2 [ 2s( t ) E 0 + s 2 ( t )+ s ^ 2 ( t ) E 0 2 ] 1 8 [ 2s( t ) E 0 + s 2 ( t )+ s ^ 2 ( t ) E 0 2 ] 2 +O( E 0 5 ) } = E 0 +s( t )+ s ^ 2 ( t ) 2 E 0 +O( E 0 2 )
ϕ( t )= tan 1 s ^ ( t ) E 0 +s( t ) = s ^ ( t ) E 0 +O( E 0 2 )
s ^ ( t ) E 0 H[ ln I( t ) ]
ln I( t ) =ln{ E 0 [ ( I( t ) E 0 1 )+1 ] }=2 I( t ) E 0 1 2 I( t ) E 0 2 +ln E 0 3 2 +O( E 0 3 )
E 0 +s( t ) I( t ) E 0 2 { H[ 2 I( t ) E 0 1 2 I( t ) E 0 2 ] } 2
E 0 = DC×( 1 1 1+CSPR )
NMSE=10 log 10 E{ [ x( n ) x ˜ ( n ) ] 2 } E{ x( n ) }E{ x ˜ ( n ) }