Abstract

We present a digital pilot aided carrier frequency offset estimation (FOE) method for coherent optical transmission systems. Unlike the conventional pilot tone insertion scheme, the pilot of the proposed method is generated in a digital manner and can serve as a good FOE indicator. Aided by this kind of digital pilot, the FOE is implemented by determining the location of the digital pilot in the spectrum. Theoretical analysis and numerical simulations show that the proposed method has the advantages in wide range, high accuracy, modulation formats independent, no need to remove the modulation, and high tolerance to the residual chromatic dispersion (CD) and polarization mode dispersion (PMD).

© 2015 Optical Society of America

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References

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2014 (5)

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

X. Zhou and L. Nelson, “Advanced DSP for 400 Gb/s and beyond optical networks,” J. Lightwave Technol. 32(16), 2716–2725 (2014).
[Crossref]

M. Li, J. Zhao, and L. Chen, “Multi-symbol QPSK partitioning for improved frequency offset estimation of 16-QAM signals,” IEEE Photonics Technol. Lett. 27(1), 18–21 (2014).
[Crossref]

Y. Liu, Y. Peng, Y. Zhang, Y. Liu, and Z. Zhang, “Differential phase-based frequency offset estimation for 16-QAM coherent optical systems,” IEEE Photonics Technol. Lett. 26(24), 2492–2494 (2014).
[Crossref]

Y. Liu, Y. Peng, S. Wang, and Z. Chen, “Improved FFT-based frequency offset estimation algorithm for coherent optical systems,” IEEE Photonics Technol. Lett. 26(6), 613–616 (2014).
[Crossref]

2013 (3)

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

X. Zhou, X. Yang, R. Li, and K. Long, “Efficient joint carrier frequency offset and phase noise compensation scheme for high-speed coherent optical OFDM systems,” J. Lightwave Technol. 31(11), 1755–1761 (2013).
[Crossref]

D. Huang, T. Cheng, and C. Yu, “Accurate two-stage frequency offset estimation for coherent optical systems,” IEEE Photonics Technol. Lett. 25(2), 179–182 (2013).
[Crossref]

2012 (2)

S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012).
[Crossref]

X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photonics Technol. Lett. 24(1), 82–84 (2012).
[Crossref]

2011 (3)

J. C. M. Diniz, J. C. R. F. de Oliveira, E. S. Rosa, V. B. Ribeiro, V. E. S. Parahyba, R. da Silva, E. P. da Silva, L. H. H. de Carvalho, A. F. Herbster, and A. C. Bordonalli, “Simple feed-forward wide-range frequency offset estimator for optical coherent receivers,” Opt. Express 19(26), B323–B328 (2011).
[Crossref] [PubMed]

I. Fatadin and S. J. Savory, “Compensation of frequency offset for 16-QAM optical coherent systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 23(17), 1246–1248 (2011).

M. Li and L. Chen, “Blind carrier frequency offset estimation based on eighth-order statistics for coherent optical QAM systems,” IEEE Photonics Technol. Lett. 23(21), 1612–1614 (2011).
[Crossref]

2010 (3)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010).
[Crossref]

2008 (1)

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

2007 (1)

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Adamczyk, O.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Bhandare, S.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Bordonalli, A. C.

Cao, Y.

S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012).
[Crossref]

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010).
[Crossref]

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

Chang, G.-K.

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

Chen, L.

M. Li, J. Zhao, and L. Chen, “Multi-symbol QPSK partitioning for improved frequency offset estimation of 16-QAM signals,” IEEE Photonics Technol. Lett. 27(1), 18–21 (2014).
[Crossref]

M. Li and L. Chen, “Blind carrier frequency offset estimation based on eighth-order statistics for coherent optical QAM systems,” IEEE Photonics Technol. Lett. 23(21), 1612–1614 (2011).
[Crossref]

Chen, X.

X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photonics Technol. Lett. 24(1), 82–84 (2012).
[Crossref]

Chen, Y.-K.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Chen, Z.

Y. Liu, Y. Peng, S. Wang, and Z. Chen, “Improved FFT-based frequency offset estimation algorithm for coherent optical systems,” IEEE Photonics Technol. Lett. 26(6), 613–616 (2014).
[Crossref]

Cheng, T.

D. Huang, T. Cheng, and C. Yu, “Accurate two-stage frequency offset estimation for coherent optical systems,” IEEE Photonics Technol. Lett. 25(2), 179–182 (2013).
[Crossref]

da Silva, E. P.

da Silva, R.

de Carvalho, L. H. H.

de Oliveira, J. C. R. F.

Diniz, J. C. M.

Fatadin, I.

I. Fatadin and S. J. Savory, “Compensation of frequency offset for 16-QAM optical coherent systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 23(17), 1246–1248 (2011).

Gu, W.

S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012).
[Crossref]

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010).
[Crossref]

Herbster, A. F.

Hoffmann, S.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Huang, D.

D. Huang, T. Cheng, and C. Yu, “Accurate two-stage frequency offset estimation for coherent optical systems,” IEEE Photonics Technol. Lett. 25(2), 179–182 (2013).
[Crossref]

Huang, M. F.

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Ji, Y.

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010).
[Crossref]

Kam, P. Y.

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Kaneda, N.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Koc, U.-V.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Leng, H.

S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012).
[Crossref]

Leven, A.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Li, M.

M. Li, J. Zhao, and L. Chen, “Multi-symbol QPSK partitioning for improved frequency offset estimation of 16-QAM signals,” IEEE Photonics Technol. Lett. 27(1), 18–21 (2014).
[Crossref]

M. Li and L. Chen, “Blind carrier frequency offset estimation based on eighth-order statistics for coherent optical QAM systems,” IEEE Photonics Technol. Lett. 23(21), 1612–1614 (2011).
[Crossref]

Li, R.

Liu, C.

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

Liu, X.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

Liu, Y.

Y. Liu, Y. Peng, S. Wang, and Z. Chen, “Improved FFT-based frequency offset estimation algorithm for coherent optical systems,” IEEE Photonics Technol. Lett. 26(6), 613–616 (2014).
[Crossref]

Y. Liu, Y. Peng, Y. Zhang, Y. Liu, and Z. Zhang, “Differential phase-based frequency offset estimation for 16-QAM coherent optical systems,” IEEE Photonics Technol. Lett. 26(24), 2492–2494 (2014).
[Crossref]

Y. Liu, Y. Peng, Y. Zhang, Y. Liu, and Z. Zhang, “Differential phase-based frequency offset estimation for 16-QAM coherent optical systems,” IEEE Photonics Technol. Lett. 26(24), 2492–2494 (2014).
[Crossref]

Long, K.

X. Zhou, X. Yang, R. Li, and K. Long, “Efficient joint carrier frequency offset and phase noise compensation scheme for high-speed coherent optical OFDM systems,” J. Lightwave Technol. 31(11), 1755–1761 (2013).
[Crossref]

X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photonics Technol. Lett. 24(1), 82–84 (2012).
[Crossref]

Nelson, L.

Noe, R.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Parahyba, V. E. S.

Peng, Y.

Y. Liu, Y. Peng, S. Wang, and Z. Chen, “Improved FFT-based frequency offset estimation algorithm for coherent optical systems,” IEEE Photonics Technol. Lett. 26(6), 613–616 (2014).
[Crossref]

Y. Liu, Y. Peng, Y. Zhang, Y. Liu, and Z. Zhang, “Differential phase-based frequency offset estimation for 16-QAM coherent optical systems,” IEEE Photonics Technol. Lett. 26(24), 2492–2494 (2014).
[Crossref]

Peveling, R.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Pfau, T.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Porrmann, M.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Ribeiro, V. B.

Rosa, E. S.

Savory, S. J.

I. Fatadin and S. J. Savory, “Compensation of frequency offset for 16-QAM optical coherent systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 23(17), 1246–1248 (2011).

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

Shen, J.

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010).
[Crossref]

Wang, J.

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

Wang, S.

Y. Liu, Y. Peng, S. Wang, and Z. Chen, “Improved FFT-based frequency offset estimation algorithm for coherent optical systems,” IEEE Photonics Technol. Lett. 26(6), 613–616 (2014).
[Crossref]

Wang, T.

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Winzer, P. J.

X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014).
[Crossref]

Wordehoff, C.

S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008).
[Crossref]

Wu, G.

S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012).
[Crossref]

Xu, L.

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Yan, L.-S.

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

Yang, X.

Ye, C.-H.

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

Yi, A.-L.

A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013).
[Crossref]

Yu, C.

D. Huang, T. Cheng, and C. Yu, “Accurate two-stage frequency offset estimation for coherent optical systems,” IEEE Photonics Technol. Lett. 25(2), 179–182 (2013).
[Crossref]

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Yu, J.

S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010).
[Crossref]

Yu, S.

S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012).
[Crossref]

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010).
[Crossref]

Zhang, L.

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Figures (9)

Fig. 1
Fig. 1 Frame structure. (a) The frame structure for both polarizations; (b) The common constellation diagrams.
Fig. 2
Fig. 2 System block diagram of the single polarization coherent optical transmission system.
Fig. 3
Fig. 3 Power spectral density of the pilot and the payload under zero carrier frequency offset (solid lines) and carrier frequency offset equals ∆f (dashed lines).
Fig. 4
Fig. 4 The simulation setup. AWG: arbitrary waveform generator; IQM: IQ modulator; PBC: polarization beam combiner; OBPF: optical band-pass filter; PMD: polarization mode dispersion; OSNR: optical signal to noise ratio; LPF: low-pass filter; ADC: analog to digital converter; DSP: digital signal processing
Fig. 5
Fig. 5 The DSP module. FFT: fast Fourier transform; CFR: carrier frequency offset recovery; CPR: carrier phase recovery.
Fig. 6
Fig. 6 The absolute mean FOE error vs FFT length NFFT for NRZ-QPSK.
Fig. 7
Fig. 7 The absolute mean FOE error under different OSNR for (a) NRZ-QPSK; (b) Nyquist-QPSK; (c) NRZ-16QAM; (d) Nyquist-16QAM.
Fig. 8
Fig. 8 The absolute mean FOE error vs the residual CD for (a) NRZ-QPSK; (b) Nyquist-QPSK; (c) NRZ-16QAM; (d) Nyquist-16QAM.
Fig. 9
Fig. 9 The absolute mean FOE error vs the DGD for (a) NRZ-QPSK; (b) Nyquist-QPSK; (c) NRZ-16QAM; (d) Nyquist-16QAM.

Equations (9)

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r ( t ) = n = a n g ( t n T s ) exp ( j 2 π Δ f t ) = r b ( t ) exp ( j 2 π Δ f t )
P r b ( f ) = 1 T s P a ( f ) | G ( f ) | 2
R a , p a [ k ] = σ a , p a 2 δ [ k ] < k <
P a , p a ( f ) = σ a , p a 2
P r , p a ( f ) = σ a , p a 2 T s | G ( f ) | 2
R a , p i [ k ] = | S | 2 < k <
P a , p i ( f ) = | S | 2 T s m = δ ( f m T s )
P r , p i ( f ) = | S | 2 T s 2 m = | G ( m T s ) | 2 δ ( f m T s )
P r , p i ( f ) = | S | 2 T s 2 | G ( 0 ) | 2 δ ( f )

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