Abstract

Due to the non-rectangular distribution of the constellation points, traditional fast Fourier transform based frequency offset estimation (FFT-FOE) is no longer suitable for 32-QAM signal. Here, we report a modified FFT-FOE technique by selecting and digitally amplifying the inner QPSK ring of 32-QAM after the adaptive equalization, which is defined as QPSK-selection assisted FFT-FOE. Simulation results show that no FOE error occurs with a FFT size of only 512 symbols, when the signal-to-noise ratio (SNR) is above 17.5 dB using our proposed FOE technique. However, the error probability of traditional FFT-FOE scheme for 32-QAM is always intolerant. Finally, our proposed FOE scheme functions well for 10 Gbaud dual polarization (DP)-32-QAM signal to reach 20% forward error correction (FEC) threshold of BER=2×102, under the scenario of back-to-back (B2B) transmission.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  28. M. Oerder and H. Mery, “Digital Filter and Square Timing Recovery,” IEEE Trans. Commun. 34(10), 605–612 (1988).
    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (1)

2016 (2)

2014 (1)

2013 (2)

2012 (5)

2011 (2)

2010 (3)

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 22(9), 631–633 (2010).
[Crossref]

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[Crossref]

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

2009 (1)

2008 (2)

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

2007 (2)

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
[Crossref]

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]

1997 (1)

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. 45(12), 1613–1621 (1997).
[Crossref]

1988 (1)

M. Oerder and H. Mery, “Digital Filter and Square Timing Recovery,” IEEE Trans. Commun. 34(10), 605–612 (1988).
[Crossref]

1974 (1)

D. C. Rife and R. R. Boorstyn, “Single-tone parameter estimation from discrete-time observations,” IEEE Trans. Inf. Theory 20(5), 591–598 (1974).
[Crossref]

Alam, S. U.

Alouini, M. S.

P. K. Vitthaladevuni and M. S. Alouini, “Exact BER computation for the cross 32-QAM constellation,” in International Symposium on Control, Communications and Signal Processing (2004), pp. 643–646.
[Crossref]

Boorstyn, R. R.

D. C. Rife and R. R. Boorstyn, “Single-tone parameter estimation from discrete-time observations,” IEEE Trans. Inf. Theory 20(5), 591–598 (1974).
[Crossref]

Borel, P.

Borel, P. I.

Calabrò, S.

Carlson, K.

Chandrasekhar, S.

Chen, X.

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]

Cheng, J.

Chien, H.-C.

Ciblat, P.

Y. Wang, E. Serpedin, P. Ciblat, and P. Loubaton, “Non-data aided feedforward cyclostationary statistics based carrier frequency offset estimators for linear modulations,” in Proc. GLOBECOM’01, 1386–1390.
[Crossref]

M. Selmi, Y. Jaouën, P. Ciblat, and B. Lankl, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC’09 (2009), paper P3.08.

Corbett, B.

Cox, D. C.

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. 45(12), 1613–1621 (1997).
[Crossref]

de Waardt, H.

Di Huo, D.

Dimarcello, F. V.

Dong, Z.

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).

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 22(9), 631–633 (2010).
[Crossref]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Feng, Z.

Fini, J. M.

Fishteyn, M.

Fu, S.

Grüner-Nielsen, L.

Hirooka, T.

K. Kasai, D. O. Otuya, M. Yoshida, T. Hirooka, and M. Nakazawa, “Single-Carrier 800-Gb/s 32 RZ/QAM Coherent Transmission Over 225 km Employing a Novel RZ-CW Conversion Technique,” IEEE Photonics Technol. Lett. 24(5), 416–418 (2012).
[Crossref]

Hoffmann, S.

Igarashi, K.

Y. Mori, C. Zhang, M. Usui, K. Igarashi, K. Katoh, and K. Kikuchi, “200-km transmission of 100-Gbit/s 32-QAM Dual-Polarization Signals using a Digital Coherent Receiver,” in Proc. ECOC’09 (2009), paper 8.4.6.

Ip, E.

Isaac, R.

Ives, D.

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 22(9), 631–633 (2010).
[Crossref]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Jaouën, Y.

M. Selmi, Y. Jaouën, P. Ciblat, and B. Lankl, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC’09 (2009), paper P3.08.

Jia, Z.

Jung, Y.

Kahn, J. M.

Kam, P.

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]

Kasai, K.

K. Kasai, D. O. Otuya, M. Yoshida, T. Hirooka, and M. Nakazawa, “Single-Carrier 800-Gb/s 32 RZ/QAM Coherent Transmission Over 225 km Employing a Novel RZ-CW Conversion Technique,” IEEE Photonics Technol. Lett. 24(5), 416–418 (2012).
[Crossref]

Katoh, K.

Y. Mori, C. Zhang, M. Usui, K. Igarashi, K. Katoh, and K. Kikuchi, “200-km transmission of 100-Gbit/s 32-QAM Dual-Polarization Signals using a Digital Coherent Receiver,” in Proc. ECOC’09 (2009), paper 8.4.6.

Kikuchi, K.

Y. Mori, C. Zhang, M. Usui, K. Igarashi, K. Katoh, and K. Kikuchi, “200-km transmission of 100-Gbit/s 32-QAM Dual-Polarization Signals using a Digital Coherent Receiver,” in Proc. ECOC’09 (2009), paper 8.4.6.

Kim, H.

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]

Kuschnerov, M.

Lankl, B.

M. Selmi, Y. Jaouën, P. Ciblat, and B. Lankl, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC’09 (2009), paper P3.08.

Lau, A. P. T.

Leoni, P.

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, B.

Li, X.

Liu, D.

Liu, X.

Loubaton, P.

Y. Wang, E. Serpedin, P. Ciblat, and P. Loubaton, “Non-data aided feedforward cyclostationary statistics based carrier frequency offset estimators for linear modulations,” in Proc. GLOBECOM’01, 1386–1390.
[Crossref]

Lu, C.

Lu, J.

Luo, M.

Magill, P.

Meiyappan, A.

Mery, H.

M. Oerder and H. Mery, “Digital Filter and Square Timing Recovery,” IEEE Trans. Commun. 34(10), 605–612 (1988).
[Crossref]

Monberg, E. M.

Mori, Y.

Y. Mori, C. Zhang, M. Usui, K. Igarashi, K. Katoh, and K. Kikuchi, “200-km transmission of 100-Gbit/s 32-QAM Dual-Polarization Signals using a Digital Coherent Receiver,” in Proc. ECOC’09 (2009), paper 8.4.6.

Nakazawa, M.

K. Kasai, D. O. Otuya, M. Yoshida, T. Hirooka, and M. Nakazawa, “Single-Carrier 800-Gb/s 32 RZ/QAM Coherent Transmission Over 225 km Employing a Novel RZ-CW Conversion Technique,” IEEE Photonics Technol. Lett. 24(5), 416–418 (2012).
[Crossref]

Nelson, L.

Nelson, L. E.

Noé, R.

Oerder, M.

M. Oerder and H. Mery, “Digital Filter and Square Timing Recovery,” IEEE Trans. Commun. 34(10), 605–612 (1988).
[Crossref]

Otuya, D. O.

K. Kasai, D. O. Otuya, M. Yoshida, T. Hirooka, and M. Nakazawa, “Single-Carrier 800-Gb/s 32 RZ/QAM Coherent Transmission Over 225 km Employing a Novel RZ-CW Conversion Technique,” IEEE Photonics Technol. Lett. 24(5), 416–418 (2012).
[Crossref]

Pan, Y.

Peckham, D.

Peckham, D. W.

Pfau, T.

Plant, D. V.

Qiu, M.

Richardson, D. J.

Rife, D. C.

D. C. Rife and R. R. Boorstyn, “Single-tone parameter estimation from discrete-time observations,” IEEE Trans. Inf. Theory 20(5), 591–598 (1974).
[Crossref]

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).

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 22(9), 631–633 (2010).
[Crossref]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

Schmidl, T. M.

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. 45(12), 1613–1621 (1997).
[Crossref]

Selmi, M.

M. Selmi, Y. Jaouën, P. Ciblat, and B. Lankl, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC’09 (2009), paper P3.08.

Serpedin, E.

Y. Wang, E. Serpedin, P. Ciblat, and P. Loubaton, “Non-data aided feedforward cyclostationary statistics based carrier frequency offset estimators for linear modulations,” in Proc. GLOBECOM’01, 1386–1390.
[Crossref]

Shum, P. P.

Sleiffer, V. A. J. M.

Sun, Y.

Surof, J.

Tang, M.

Taunay, T. F.

Tkach, R. W.

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

Usui, M.

Y. Mori, C. Zhang, M. Usui, K. Igarashi, K. Katoh, and K. Kikuchi, “200-km transmission of 100-Gbit/s 32-QAM Dual-Polarization Signals using a Digital Coherent Receiver,” in Proc. ECOC’09 (2009), paper 8.4.6.

Veljanovski, V.

Vitthaladevuni, P. K.

P. K. Vitthaladevuni and M. S. Alouini, “Exact BER computation for the cross 32-QAM constellation,” in International Symposium on Control, Communications and Signal Processing (2004), pp. 643–646.
[Crossref]

Wang, Y.

Y. Wang, E. Serpedin, P. Ciblat, and P. Loubaton, “Non-data aided feedforward cyclostationary statistics based carrier frequency offset estimators for linear modulations,” in Proc. GLOBECOM’01, 1386–1390.
[Crossref]

Winfield, R.

Winzer, P. J.

Xiang, M.

Yan, M. F.

Yoshida, M.

K. Kasai, D. O. Otuya, M. Yoshida, T. Hirooka, and M. Nakazawa, “Single-Carrier 800-Gb/s 32 RZ/QAM Coherent Transmission Over 225 km Employing a Novel RZ-CW Conversion Technique,” IEEE Photonics Technol. Lett. 24(5), 416–418 (2012).
[Crossref]

Yu, J.

Zhang, C.

Y. Mori, C. Zhang, M. Usui, K. Igarashi, K. Katoh, and K. Kikuchi, “200-km transmission of 100-Gbit/s 32-QAM Dual-Polarization Signals using a Digital Coherent Receiver,” in Proc. ECOC’09 (2009), paper 8.4.6.

Zhang, F.

Zhong, K.

Zhou, H.

Zhou, X.

Zhu, B.

Zhuge, Q.

Bell Labs Tech. J. (1)

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

IEEE Commun. Mag. (1)

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (5)

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 22(9), 631–633 (2010).
[Crossref]

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]

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).

K. Kasai, D. O. Otuya, M. Yoshida, T. Hirooka, and M. Nakazawa, “Single-Carrier 800-Gb/s 32 RZ/QAM Coherent Transmission Over 225 km Employing a Novel RZ-CW Conversion Technique,” IEEE Photonics Technol. Lett. 24(5), 416–418 (2012).
[Crossref]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

IEEE Trans. Commun. (2)

M. Oerder and H. Mery, “Digital Filter and Square Timing Recovery,” IEEE Trans. Commun. 34(10), 605–612 (1988).
[Crossref]

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. 45(12), 1613–1621 (1997).
[Crossref]

IEEE Trans. Inf. Theory (1)

D. C. Rife and R. R. Boorstyn, “Single-tone parameter estimation from discrete-time observations,” IEEE Trans. Inf. Theory 20(5), 591–598 (1974).
[Crossref]

J. Lightwave Technol. (9)

X. Zhou, L. Nelson, P. Magill, R. Isaac, B. Zhu, D. Peckham, P. Borel, and K. Carlson, “High spectral efficiency 400 Gb/s transmission using PDM time-domain hybrid 32–64 QAM and training-assisted carrier recovery,” J. Lightwave Technol. 31(7), 999–1005 (2013).
[Crossref]

A. Meiyappan, P. Kam, and H. Kim, “On decision aided carrier phase and frequency offset estimation in coherent optical receivers,” J. Lightwave Technol. 31(13), 2055–2069 (2013).
[Crossref]

H. Zhou, B. Li, M. Tang, K. Zhong, Z. Feng, J. Cheng, A. P. T. Lau, C. Lu, S. Fu, P. P. Shum, and D. Liu, “Fractional Fourier Transformation-Based Blind Chromatic Dispersion Estimation for Coherent Optical Communications,” J. Lightwave Technol. 34(10), 2371–2380 (2016).
[Crossref]

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
[Crossref]

X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P. I. Borel, and K. Carlson, “PDM-Nyquist-32QAM for 450-Gb/s Per-Channel WDM Transmission on the 50 GHz ITU-T Grid,” J. Lightwave Technol. 30(4), 553–559 (2012).
[Crossref]

P. J. Winzer, “High-Spectral-Efficiency Optical Modulation Formats,” J. Lightwave Technol. 30(24), 3824–3835 (2012).
[Crossref]

P. J. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(8), 3824–3835 (2012).
[Crossref]

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
[Crossref]

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C. Malouin, M. Arabaci, P. Thomas, B. Zhang, T. Schmidt, and R. Marcoccia, “Efficient, non-data-aided chromatic dispersion estimation via generalized, FFT-based sweep,” in Proc. OFC’13 (2013), paper JW2A.45.
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Figures (11)

Fig. 1
Fig. 1

Constellations of (a) QPSK, (b) 16-QAM, (c) 32-QAM, (d) 64-QAM.

Fig. 2
Fig. 2

Block diagram of QPSK-selection assisted FFT-FOE scheme.

Fig. 3
Fig. 3

Constellations of received 32-QAM signals r(k) (a) before selection and digital amplification of the inner QPSK ring, SNR = 24 dB, (b) after selection and digital amplification of the inner QPSK ring, SNR = 24 dB, (c) before selection and digital amplification of the inner QPSK ring, SNR = 21 dB, (d) after selection and digital amplification of the inner QPSK ring, SNR = 21 dB. The symbol rate is 10G Baud, FO is set to 0.35GHz.

Fig. 4
Fig. 4

4th power spectrum of received 32-QAM signals r 4 (k) using (a) traditional FFT-FOE, SNR = 24 dB, (b) QPSK-selection assisted FFT-FOE, SNR = 24 dB, (c) traditional FFT-FOE, SNR = 21 dB, (d) QPSK-selection assisted FFT-FOE, SNR = 21 dB. The symbol rate is 10G Baud, FO is set to 0.35GHz.

Fig. 5
Fig. 5

(a) Simulation setup. FOE error probability as a function of SNR under the condition of (b) Δf = 0 GHz, (c) Δf = 0.35 GHz and (d) Δf = 1 GHz.

Fig. 6
Fig. 6

Theoretical BER calculation as a function of SNR.

Fig. 7
Fig. 7

(a) Performance of QPSK-selection assisted FFT-FOE under various SNRs. (b) FOE error of QPSK-selection assisted FFT-FOE under various SNRs.

Fig. 8
Fig. 8

(a) Experimental setup and DSP flow for 10 Gbaud DP-32-QAM system. OBPF: optical band-width pass filter, PC: polarization controller, PBS: polarization beam splitter, PBC: polarization beam combiner, ASE: amplified spontaneous emission. (b) Frame structure.

Fig. 9
Fig. 9

FOE error probability and BER with respect to various OSNRs, (a) FO = 0 GHz, (b) FO = 1 GHz.

Fig. 10
Fig. 10

Experimental distributions of FOE at (a) OSNR = 13.0 dB, FO = 0 GHz; (b) OSNR = 16.7 dB, FO = 0 GHz; (c) OSNR = 19.6 dB, FO = 0 GHz; (d) OSNR = 13.0 dB, FO = 1 GHz; (e) OSNR = 16.7 dB, FO = 1 GHz; (f) OSNR = 19.6 dB, FO = 1 GHz. QS-FFT-FOE: QPSK-selection assisted FFT-FOE.

Fig. 11
Fig. 11

BER performance as a function of OSNR, (a) FO 0 GHz, (b) FO is 1 GHz. QT-FFT-FOE: QPSK training symbol assisted FFT-FOE, QS-FFT-FOE: QPSK-selection assisted FFT-FOE.

Tables (1)

Tables Icon

Table 1 Complexity comparison of two methods

Equations (2)

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r(k)=m(k)exp(j(Δωk+θ(k)))+n(k),k=0,1,2,
Δ f ^ = 1 4 arg max | Δ f ^ |<1/2T | k=0 N1 r 4 (k) e j2πΔ f ^ Tk |