Abstract

A novel carrier recovery scheme for demodulating optical M-ary quadrature amplitude modulation (M-QAM) signals is proposed and demonstrated. The proposed scheme treats a certain number of consecutive symbols as a processing block for which linear evolution of the carrier phases in time is assumed. The Kalman filter algorithm is employed to simultaneously estimate the carrier-frequency offset and carrier phases of the symbols in each block from the observation result. Consequently, an optimal carrier recovery operation with minimum mean squared error can be obtained, and large phase errors due to optical noise and large carrier-frequency offsets can be tolerated. We experimentally demonstrate the proposed scheme in demodulating optical 16- and 64-QAM signals, confirming its stable operation for carrier-frequency offsets even larger than 10% of the symbol rate of the signal. We also demonstrate 160-km transmission of a single-channel, single-polarization 64-QAM signal by using the proposed scheme in the demodulation process.

© 2014 Optical Society of America

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References

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  1. A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.
  2. X. Zhou, J. Yu, M.-F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, R. Lingle, and B. Zhu, “64-Tb/s, 8 b/s/Hz, PDM-36QAM transmission over 320 km using both pre- and post-transmission digital signal processing,” J. Lightwave Technol. 29, 571–577 (2011).
    [Crossref]
  3. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008).
    [Crossref] [PubMed]
  4. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” J. Sel. Top. Quantum Electron. 16, 1164–1179 (2010).
    [Crossref]
  5. X. Zhou, “Efficient clock and carrier recovery algorithms for single-carrier coherent optical systems: A systematic review on challenges and recent progress,” IEEE Signal Process. Mag. 31, 35–45 (2014).
    [Crossref]
  6. M. Selmi, Y. Jaouën, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” inEuropean Conference and Exhibition of Optical Communication (ECOC) (2009), P3.08.
  7. T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.
  8. S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, “Phase entropy-based frequency offset estimation for coherent optical QAM systems,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2012), OTu2G.4.
  9. E. Ip and J. Kahn, “Feedforward carrier recovery for optical communication,” J. Lightwave Technol. 25, 2675–2692 (2007).
    [Crossref]
  10. I. Fatadin, D. Ives, and S. J. Savory, “Compensation of frequency offset for differentially encoded 16 and 64-QAM in the presence of laser phase noise,” IEEE Photon. Technol. Lett. 22, 176–178 (2010).
    [Crossref]
  11. 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, 989–999 (2009).
    [Crossref]
  12. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receiver with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22, 1051–1053 (2010).
    [Crossref]
  13. S. Haykin, ed., Kalman Filtering and Neural Networks, 4th ed. (Wiley-Interscience, 2001)
    [Crossref]
  14. W.-T. Lin and D.-C. Chang, “Adaptive carrier synchronization using decision-aided Kalman filtering algorithms,” IEEE Trans. Consum. Electron. 53, 1260–1267 (2007).
    [Crossref]
  15. B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31, 648–663 (2013).
    [Crossref]
  16. J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2008).
  17. B. C. Thomsen, R. Maher, D. S. Millar, and S. J. Savory, “Burst mode receiver for 112 Gb/s DP-QPSK with parallel DSP,” Opt. Express 19, B770–B776 (2011).
    [Crossref]
  18. Y. R. Shayan and T. Le-Ngoc, “All digital phase-locked loop: concepts, design and applications,” IEE Proc. 136F, 53–56 (1989).
  19. M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

2014 (1)

X. Zhou, “Efficient clock and carrier recovery algorithms for single-carrier coherent optical systems: A systematic review on challenges and recent progress,” IEEE Signal Process. Mag. 31, 35–45 (2014).
[Crossref]

2013 (1)

2011 (2)

2010 (3)

I. Fatadin, D. Ives, and S. J. Savory, “Compensation of frequency offset for differentially encoded 16 and 64-QAM in the presence of laser phase noise,” IEEE Photon. Technol. Lett. 22, 176–178 (2010).
[Crossref]

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receiver with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22, 1051–1053 (2010).
[Crossref]

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

2009 (1)

2008 (1)

2007 (2)

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

W.-T. Lin and D.-C. Chang, “Adaptive carrier synchronization using decision-aided Kalman filtering algorithms,” IEEE Trans. Consum. Electron. 53, 1260–1267 (2007).
[Crossref]

1989 (1)

Y. R. Shayan and T. Le-Ngoc, “All digital phase-locked loop: concepts, design and applications,” IEE Proc. 136F, 53–56 (1989).

Avramopoulos, H.

S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, “Phase entropy-based frequency offset estimation for coherent optical QAM systems,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2012), OTu2G.4.

Bakopoulos, P.

S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, “Phase entropy-based frequency offset estimation for coherent optical QAM systems,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2012), OTu2G.4.

Barros, D. J. F.

Birk, M.

Borel, P. I.

Chang, D.-C.

W.-T. Lin and D.-C. Chang, “Adaptive carrier synchronization using decision-aided Kalman filtering algorithms,” IEEE Trans. Consum. Electron. 53, 1260–1267 (2007).
[Crossref]

Ciblat, P.

M. Selmi, Y. Jaouën, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” inEuropean Conference and Exhibition of Optical Communication (ECOC) (2009), P3.08.

Dou, L.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Dris, S.

S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, “Phase entropy-based frequency offset estimation for coherent optical QAM systems,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2012), OTu2G.4.

Fatadin, I.

I. Fatadin, D. Ives, and S. J. Savory, “Compensation of frequency offset for differentially encoded 16 and 64-QAM in the presence of laser phase noise,” IEEE Photon. Technol. Lett. 22, 176–178 (2010).
[Crossref]

Hoffmann, S.

Hoshida, T.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Huang, M.-F.

Ip, E.

Ishihara, K.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

Ives, D.

I. Fatadin, D. Ives, and S. J. Savory, “Compensation of frequency offset for differentially encoded 16 and 64-QAM in the presence of laser phase noise,” IEEE Photon. Technol. Lett. 22, 176–178 (2010).
[Crossref]

Jaouën, Y.

M. Selmi, Y. Jaouën, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” inEuropean Conference and Exhibition of Optical Communication (ECOC) (2009), P3.08.

Kahn, J.

Kahn, J. M.

Kobayashi, T.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Kudo, R.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

Lau, A. P. T.

Lazarou, I.

S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, “Phase entropy-based frequency offset estimation for coherent optical QAM systems,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2012), OTu2G.4.

Le-Ngoc, T.

Y. R. Shayan and T. Le-Ngoc, “All digital phase-locked loop: concepts, design and applications,” IEE Proc. 136F, 53–56 (1989).

Li, L.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Lin, W.-T.

W.-T. Lin and D.-C. Chang, “Adaptive carrier synchronization using decision-aided Kalman filtering algorithms,” IEEE Trans. Consum. Electron. 53, 1260–1267 (2007).
[Crossref]

Lingle, R.

Magill, P.

Maher, R.

Marshall, T. S.

Matsui, M.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

Matsuura, A.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Millar, D. S.

Miyamoto, Y.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

Mizoguchi, M.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Mizuno, T.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Nakagawa, T.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

Nebendahl, B.

Nelson, L.

Noé, R.

Peckham, D. W.

Pfau, T.

Proakis, J. G.

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2008).

Rasmussen, J. C.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Salehi, M.

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2008).

Sano, A.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Savory, S. J.

B. C. Thomsen, R. Maher, D. S. Millar, and S. J. Savory, “Burst mode receiver for 112 Gb/s DP-QPSK with parallel DSP,” Opt. Express 19, B770–B776 (2011).
[Crossref]

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

I. Fatadin, D. Ives, and S. J. Savory, “Compensation of frequency offset for differentially encoded 16 and 64-QAM in the presence of laser phase noise,” IEEE Photon. Technol. Lett. 22, 176–178 (2010).
[Crossref]

Selmi, M.

M. Selmi, Y. Jaouën, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” inEuropean Conference and Exhibition of Optical Communication (ECOC) (2009), P3.08.

Shao, Y.

Shayan, Y. R.

Y. R. Shayan and T. Le-Ngoc, “All digital phase-locked loop: concepts, design and applications,” IEE Proc. 136F, 53–56 (1989).

Szafraniec, B.

Tao, Z.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Thomsen, B. C.

Wang, T.

Yamamoto, S.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Yamanaka, S.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Yan, M.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Yoshida, E.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

Yu, J.

Zhao, Y.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

Zhou, X.

X. Zhou, “Efficient clock and carrier recovery algorithms for single-carrier coherent optical systems: A systematic review on challenges and recent progress,” IEEE Signal Process. Mag. 31, 35–45 (2014).
[Crossref]

X. Zhou, J. Yu, M.-F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, R. Lingle, and B. Zhu, “64-Tb/s, 8 b/s/Hz, PDM-36QAM transmission over 320 km using both pre- and post-transmission digital signal processing,” J. Lightwave Technol. 29, 571–577 (2011).
[Crossref]

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receiver with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22, 1051–1053 (2010).
[Crossref]

Zhu, B.

IEE Proc. (1)

Y. R. Shayan and T. Le-Ngoc, “All digital phase-locked loop: concepts, design and applications,” IEE Proc. 136F, 53–56 (1989).

IEEE Photon. Technol. Lett. (2)

I. Fatadin, D. Ives, and S. J. Savory, “Compensation of frequency offset for differentially encoded 16 and 64-QAM in the presence of laser phase noise,” IEEE Photon. Technol. Lett. 22, 176–178 (2010).
[Crossref]

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receiver with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22, 1051–1053 (2010).
[Crossref]

IEEE Signal Process. Mag. (1)

X. Zhou, “Efficient clock and carrier recovery algorithms for single-carrier coherent optical systems: A systematic review on challenges and recent progress,” IEEE Signal Process. Mag. 31, 35–45 (2014).
[Crossref]

IEEE Trans. Consum. Electron. (1)

W.-T. Lin and D.-C. Chang, “Adaptive carrier synchronization using decision-aided Kalman filtering algorithms,” IEEE Trans. Consum. Electron. 53, 1260–1267 (2007).
[Crossref]

J. Lightwave Technol. (4)

J. Sel. Top. Quantum Electron. (1)

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

Opt. Express (2)

Other (7)

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2008).

S. Haykin, ed., Kalman Filtering and Neural Networks, 4th ed. (Wiley-Interscience, 2001)
[Crossref]

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” in European Conference and Exhibition of Optical Communication (ECOC) (2010), paper PD2.4.

M. Selmi, Y. Jaouën, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” inEuropean Conference and Exhibition of Optical Communication (ECOC) (2009), P3.08.

T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2011), OMJ1.

S. Dris, I. Lazarou, P. Bakopoulos, and H. Avramopoulos, “Phase entropy-based frequency offset estimation for coherent optical QAM systems,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2012), OTu2G.4.

M. Yan, Z. Tao, L. Dou, L. Li, Y. Zhao, T. Hoshida, and J. C. Rasmussen, “Digital clock recovery algorithm for Nyquist signal,” in Optical Fiber Communication Conference and Exposition (OFC) and National Fiber Optic Engineers Conference (NFOEC) (Optical Society of America, 2013), OTu2I.7.

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Figures (7)

Fig. 1
Fig. 1 Time evolution of carrier phases φ (circles) and their linear fitting (dashed line) for N symbols in each block.
Fig. 2
Fig. 2 Schematic diagram of proposed carrier recovery scheme with block size N.
Fig. 3
Fig. 3 Experimental setup with selectable three conditions of (a) back-to-back, (b) single-span 30-km SSMF transmission, and (c) two-span 80-km SSMF transmission.
Fig. 4
Fig. 4 Measured BER against received OSNR for 16- and 64-QAM signals demodulated with the proposed carrier recovery scheme of various block sizes N. The dotted curves are reference data obtained by previously proposed demodulation scheme [6, 12].
Fig. 5
Fig. 5 (a) Q factor against block size N and some constellation diagrams for 16-QAM signals. (b) The same for 64-QAM signals. The dotted lines are reference data obtained by previously proposed demodulation scheme [6, 12].
Fig. 6
Fig. 6 Q factor against carrier-frequency offset for (a) 16- and (b) 64-QAM signals.
Fig. 7
Fig. 7 (a) Q factor against launch power for 64-QAM signal after 30-km SSMF transmission. (b) BER against received OSNR for 64-QAM signals in back-to-back condition and after 160-km SSMF transmission.

Equations (24)

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

φ n , k = θ k + ( n N + 1 2 ) ω k ,
ω k + 1 = ω k .
θ k + 1 = N ω k + θ k .
ω k + 1 = ω k + n f ,
[ θ k + 1 ω k + 1 ] = [ 1 N 0 1 ] [ θ k ω k ] + [ 0 0 0 1 ] [ 0 n f ] ,
A = [ 1 N 0 1 ] , B = [ 0 0 0 1 ] , n s = [ 0 n f ] .
[ θ ˜ k ω ˜ k ] = [ θ k ω k ] + [ n θ n ω ] ,
y k = [ θ ˜ k ω ˜ k ] , C = I = [ 1 0 0 1 ] , n o = [ n θ n ω ] .
x ^ k = A x ^ k 1 ,
P k = AP k 1 A T + BQB T ,
BQB T = [ 0 0 0 σ f 2 ] .
x ^ k = x ^ k + G k ( y k x ^ k ) x ^ k + G k e k ,
P k = ( I G k ) P k .
G k = P k ( P k + R ) 1 ,
δ θ k = tan 1 { Im [ n = 1 N s n d n * ] Re [ n = 1 N s n d n * ] } ,
δ ω k = Im [ n = 1 N ( n N + 1 2 ) s n d n * ] Re [ n = 1 N ( n N + 1 2 ) 2 s n d n * ] .
Λ ( ω ) = Re [ n = 1 N s n d n * e i ( n N + 1 2 ) ω ] ,
x k + 1 = A x k + B n s .
y k = C x k + n o .
x ^ k = A x ^ k 1 ,
P k = A P k 1 A T + BQB T .
G k = P k C T ( CP k C T + R ) 1 ,
x ^ k = x ^ k + G k ( y k C x ^ k ) x ^ k + G k e k ,
P k = ( I G k C ) P k ,

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