Abstract

Multi-format and linewidth-tolerant carrier phase estimation (CPE) is a vital part of digital signal processing (DSP) units for future elastic optical transmissions to relax the laser linewidth limitation. In this paper, an innovative CPE scheme outperforming existing CPEs in both universality and performance is presented and verified for multiple quadrature amplitude modulation (QAM) formats. Based on the technique of extended QPSK partitioning and quasi-linear approximation, accurate phase estimation is determined by calculating the intersection of two symmetric straight lines with very low complexity. Comprehensive simulation results of square 4/16/32/64-QAM not only demonstrate that the scheme can be applied to different modulation formats with a universal structure, i.e., indicate its flexibility in the format-adaptive elastic optical networks (EONs), but also show that the linewidth tolerance is greatly enhanced even in comparison with traditional BPS schemes. In addition, taking 64-QAM as an example, the computational efforts can be significantly reduced by a factor of 15.7 (or 10.3) in the form of multipliers (or adders). The slightly better OSNR performance is experimentally validated in polarization multiplexing 16GBaud 4/16-QAM systems respectively, which shows the potential application for flexible receiver-side DSP unit in EONs.

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

Full Article  |  PDF Article
OSA Recommended Articles
Low-complexity feed-forward carrier phase estimation for M-ary QAM based on phase search acceleration by quadratic approximation

Meng Xiang, Songnian Fu, Lei Deng, Ming Tang, Perry Shum, and Deming Liu
Opt. Express 23(15) 19142-19153 (2015)

Low-complexity and phase noise tolerant carrier phase estimation for dual-polarization 16-QAM systems

Yuliang Gao, Alan Pak Tao Lau, Shuangyi Yan, and Chao Lu
Opt. Express 19(22) 21717-21729 (2011)

Phase noise tolerance study in coherent optical circular QAM transmissions with Viterbi-Viterbi carrier phase estimation

Sebastian Ortega Zafra, Xiaodan Pang, Gunnar Jacobsen, Sergei Popov, and Sergey Sergeyev
Opt. Express 22(25) 30579-30585 (2014)

References

  • View by:
  • |
  • |
  • |

  1. O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
    [Crossref]
  2. X. Zhou and L. Nelson, “Advanced DSP for 400 Gb/s and Beyond Optical Networks,” J. Lightwave Technol. 32(16), 2716–2725 (2014).
    [Crossref]
  3. A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
    [Crossref]
  4. D. A. Morero, M. A. Castrillón, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design Tradeoffs and Challenges in Practical Coherent Optical Transceiver Implementations,” J. Lightwave Technol. 34(1), 121–136 (2016).
    [Crossref]
  5. Q. Zhuge, M. Morsy-Osman, X. Xu, M. Chagnon, M. Qiu, and D. V. Plant, “Spectral Efficiency-Adaptive Optical Transmission Using Time Domain Hybrid QAM for Agile Optical Networks,” J. Lightwave Technol. 31(15), 2621–2628 (2013).
    [Crossref]
  6. P. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(8), 3824–3835 (2012).
    [Crossref]
  7. S. Zhang and F. Yaman, “Design and Comparison of Advanced Modulation Formats Based on Generalized Mutual Information,” J. Lightwave Technol. 36(2), 416–423 (2018).
    [Crossref]
  8. Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).
  9. M. Xiang, S. Fu, L. Deng, M. Tang, P. Shum, and D. Liu, “Low-complexity feed-forward carrier phase estimation for M-ary QAM based on phase search acceleration by quadratic approximation,” Opt. Express 23(15), 19142–19153 (2015).
    [Crossref] [PubMed]
  10. B. Baeuerle, A. Josten, F. Abrecht, M. Eppenberger, E. Dornbierer, D. Hillerkuss, and J. Leuthold, “Multi-format carrier recovery for coherent real-time reception with processing in polar coordinates,” Opt. Express 24(22), 25629–25640 (2016).
    [Crossref] [PubMed]
  11. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
    [Crossref]
  12. Y. Gao, A. P. T. Lau, S. Yan, and C. Lu, “Low-complexity and phase noise tolerant carrier phase estimation for dual-polarization 16-QAM systems,” Opt. Express 19(22), 21717–21729 (2011).
    [Crossref] [PubMed]
  13. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 14(14), 1051–1053 (2010).
    [Crossref]
  14. S. M. Bilal, C. R. Fludger, V. Curri, and G. Bosco, “Multistage carrier phase estimation algorithms for phase noise mitigation in 64-quadrature amplitude modulation optical systems,” J. Lightwave Technol. 32(17), 2973–2980 (2014).
    [Crossref]
  15. X. Zhou, K. Zhong, Y. Gao, C. Lu, A. P. T. Lau, and K. Long, “Modulation-format-independent blind phase search algorithm for coherent optical square M-QAM systems,” Opt. Express 22(20), 24044–24054 (2014).
    [Crossref] [PubMed]
  16. M. Xiang, Q. Zhuge, M. Qiu, X. Zhou, M. Tang, D. Liu, S. Fu, and D. V. Plant, “RF-pilot aided modulation format identification for hitless coherent transceiver,” Opt. Express 25(1), 463–471 (2017).
    [Crossref] [PubMed]
  17. G. Liu, R. Proietti, K. Zhang, H. Lu, and S. J. Ben Yoo, “Blind modulation format identification using nonlinear power transformation,” Opt. Express 25(25), 30895–30904 (2017).
    [Crossref] [PubMed]
  18. Q. Zhuge, C. Chen, and D. V. Plant, “Low computation complexity two-stage feedforward carrier recovery algorithm for M-QAM,” in Proceedings of OFC (2011), paper OMJ5.
    [Crossref]
  19. K. P. Zhong, J. H. Ke, Y. Gao, and J. C. Cartledge, “Linewidth tolerant and low-complexity two-stage carrier phase estimation based on modified QPSK partitioning for dual-polarization 16-QAM systems,” J. Lightwave Technol. 31(1), 50–57 (2013).
    [Crossref]
  20. I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
    [Crossref]
  21. J. Li, L. Li, Z. Tao, T. Hoshida, and J. C. Rasmussen, “Laser-Linewidth-Tolerant Feed-Forward Carrier Phase Estimator with Reduced Complexity for QAM,” J. Lightwave Technol. 29(16), 2358–2364 (2011).
    [Crossref]
  22. J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
    [Crossref]
  23. J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
    [Crossref]
  24. T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
    [Crossref]
  25. J. H. Ke, K. P. Zhong, Y. Gao, J. C. Cartledge, A. S. Karar, and M. A. Rezania, “Linewidth-Tolerant and Low-Complexity Two-Stage Carrier Phase Estimation for Dual-Polarization 16-QAM Coherent Optical Fiber Communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012).
    [Crossref]
  26. J. D. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2008).

2018 (2)

S. Zhang and F. Yaman, “Design and Comparison of Advanced Modulation Formats Based on Generalized Mutual Information,” J. Lightwave Technol. 36(2), 416–423 (2018).
[Crossref]

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

2017 (2)

2016 (4)

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

B. Baeuerle, A. Josten, F. Abrecht, M. Eppenberger, E. Dornbierer, D. Hillerkuss, and J. Leuthold, “Multi-format carrier recovery for coherent real-time reception with processing in polar coordinates,” Opt. Express 24(22), 25629–25640 (2016).
[Crossref] [PubMed]

D. A. Morero, M. A. Castrillón, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design Tradeoffs and Challenges in Practical Coherent Optical Transceiver Implementations,” J. Lightwave Technol. 34(1), 121–136 (2016).
[Crossref]

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

2015 (2)

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

M. Xiang, S. Fu, L. Deng, M. Tang, P. Shum, and D. Liu, “Low-complexity feed-forward carrier phase estimation for M-ary QAM based on phase search acceleration by quadratic approximation,” Opt. Express 23(15), 19142–19153 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (2)

2012 (3)

2011 (2)

2010 (1)

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 14(14), 1051–1053 (2010).
[Crossref]

2009 (1)

Abrecht, F.

Agazzi, O. E.

Aguirre, A.

Baeuerle, B.

Ben Yoo, S. J.

Bilal, S. M.

Bosco, G.

Cartledge, J. C.

Castrillón, M. A.

Chagnon, M.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Q. Zhuge, M. Morsy-Osman, X. Xu, M. Chagnon, M. Qiu, and D. V. Plant, “Spectral Efficiency-Adaptive Optical Transmission Using Time Domain Hybrid QAM for Agile Optical Networks,” J. Lightwave Technol. 31(15), 2621–2628 (2013).
[Crossref]

Chen, X.

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Curri, V.

Deng, L.

Dornbierer, E.

Eppenberger, M.

Fatadin, I.

Feng, J.

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

Fludger, C. R.

Fu, S.

Gao, X.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Gao, Y.

Gerstel, O.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Han, J.

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

He, Z.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Hillerkuss, D.

Hoffmann, S.

Hoshida, T.

Hu, Q.

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

Huang, L.

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

Hueda, M. R.

Ives, D.

Ji, Y.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Jinno, M.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Josten, A.

Karar, A. S.

Ke, J. H.

Lau, A.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Lau, A. P. T.

Leuthold, J.

Li, H.

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

Li, J.

Li, L.

Li, W.

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

Liu, D.

Liu, G.

Liu, W.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Liu, Y.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Long, K.

Lord, A.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Lu, C.

Lu, H.

Morero, D. A.

Morsy-Osman, M.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Q. Zhuge, M. Morsy-Osman, X. Xu, M. Chagnon, M. Qiu, and D. V. Plant, “Spectral Efficiency-Adaptive Optical Transmission Using Time Domain Hybrid QAM for Agile Optical Networks,” J. Lightwave Technol. 31(15), 2621–2628 (2013).
[Crossref]

Nelson, L.

Noe, R.

Pfau, T.

Plant, D.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Plant, D. V.

Proietti, R.

Qiu, M.

Rasmussen, J. C.

Rezania, M. A.

Savory, S. J.

Shang, D.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Shen, B.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Shi, C.

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

Shi, S.

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Shum, P.

Sui, Q.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Sun, E.

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

Tang, M.

Tao, Z.

Wang, D.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Winzer, P.

Xiang, M.

Xiao, J.

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

Xu, X.

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

Q. Zhuge, M. Morsy-Osman, X. Xu, M. Chagnon, M. Qiu, and D. V. Plant, “Spectral Efficiency-Adaptive Optical Transmission Using Time Domain Hybrid QAM for Agile Optical Networks,” J. Lightwave Technol. 31(15), 2621–2628 (2013).
[Crossref]

Yaman, F.

Yan, S.

Yang, T.

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

Yoo, S. J. B.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Yu, S.

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

Zhang, K.

Zhang, Q.

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

Zhang, S.

Zheng, Y.

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

Zhong, K.

Zhong, K. P.

Zhou, X.

Zhuge, Q.

Chin. Opt. Lett. (1)

Z. He, W. Liu, B. Shen, X. Chen, X. Gao, S. Shi, Q. Zhang, D. Shang, Y. Ji, and Y. Liu, “Flexible multidimensional modulation formats based on PM-QPSK constellations for elastic optical networks,” Chin. Opt. Lett. 14(4), 20–23 (2016).

IEEE Commun. Mag. (1)

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (3)

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 14(14), 1051–1053 (2010).
[Crossref]

J. Han, W. Li, L. Huang, H. Li, Q. Hu, and S. Yu, “Carrier Phase Estimation Based on Error Function Calculation for 16-QAM Systems,” IEEE Photonics Technol. Lett. 28(22), 2561–2564 (2016).
[Crossref]

J. Feng, W. Li, J. Xiao, J. Han, H. Li, L. Huang, and Y. Zheng, “Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK partitioning Algorithm,” IEEE Photonics Technol. Lett. 28(1), 75–78 (2015).
[Crossref]

IEEE Signal Process. Mag. (1)

A. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. Plant, “Advanced DSP techniques enabling high spectral efficiency and flexible transmissions: toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014).
[Crossref]

J. Lightwave Technol. (11)

D. A. Morero, M. A. Castrillón, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design Tradeoffs and Challenges in Practical Coherent Optical Transceiver Implementations,” J. Lightwave Technol. 34(1), 121–136 (2016).
[Crossref]

Q. Zhuge, M. Morsy-Osman, X. Xu, M. Chagnon, M. Qiu, and D. V. Plant, “Spectral Efficiency-Adaptive Optical Transmission Using Time Domain Hybrid QAM for Agile Optical Networks,” J. Lightwave Technol. 31(15), 2621–2628 (2013).
[Crossref]

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

S. Zhang and F. Yaman, “Design and Comparison of Advanced Modulation Formats Based on Generalized Mutual Information,” J. Lightwave Technol. 36(2), 416–423 (2018).
[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]

S. M. Bilal, C. R. Fludger, V. Curri, and G. Bosco, “Multistage carrier phase estimation algorithms for phase noise mitigation in 64-quadrature amplitude modulation optical systems,” J. Lightwave Technol. 32(17), 2973–2980 (2014).
[Crossref]

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
[Crossref]

K. P. Zhong, J. H. Ke, Y. Gao, and J. C. Cartledge, “Linewidth tolerant and low-complexity two-stage carrier phase estimation based on modified QPSK partitioning for dual-polarization 16-QAM systems,” J. Lightwave Technol. 31(1), 50–57 (2013).
[Crossref]

I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
[Crossref]

J. Li, L. Li, Z. Tao, T. Hoshida, and J. C. Rasmussen, “Laser-Linewidth-Tolerant Feed-Forward Carrier Phase Estimator with Reduced Complexity for QAM,” J. Lightwave Technol. 29(16), 2358–2364 (2011).
[Crossref]

J. H. Ke, K. P. Zhong, Y. Gao, J. C. Cartledge, A. S. Karar, and M. A. Rezania, “Linewidth-Tolerant and Low-Complexity Two-Stage Carrier Phase Estimation for Dual-Polarization 16-QAM Coherent Optical Fiber Communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012).
[Crossref]

Opt. Commun. (1)

T. Yang, X. Chen, S. Shi, E. Sun, and C. Shi, “Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks,” Opt. Commun. 410, 376–384 (2018).
[Crossref]

Opt. Express (6)

Other (2)

Q. Zhuge, C. Chen, and D. V. Plant, “Low computation complexity two-stage feedforward carrier recovery algorithm for M-QAM,” in Proceedings of OFC (2011), paper OMJ5.
[Crossref]

J. D. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2008).

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 (11)

Fig. 1
Fig. 1 (a) The constellation partitioning of the ideal 64-QAM in conventional QPSK partitioning scheme, (b) the principle of the proposed extended QPSK partitioning scheme. Symbols used for conventional QPSK partitioning are highlighted by the red points, while those used for extended QPSK partitioning are highlighted by the red and blue points.
Fig. 2
Fig. 2 Normalized offset distance as a function of phase compensation error for QPSK, 16-QAM, 32-QAM and 64-QAM respectively, in (a) the first stage, (b) the second stage.
Fig. 3
Fig. 3 Block diagram of the proposed two-stage CPE scheme. (1) course stage using introduced QPSK-like symbols and fixed two rotation angles to obtain a coarse phase estimation, (2) fine stage using all current symbols and dynamically adaptive four rotation angles to determine the optimum phase estimation.
Fig. 4
Fig. 4 Three possible distributions of normalized offset distance versus rotation angle.
Fig. 5
Fig. 5 The effect of block length on linewidth tolerance for (a) QPSK, (b) 16-QAM, (c) 32-QAM and (d) 64-QAM in the first stage. (e) The optimum block length in the second stage QLA.
Fig. 6
Fig. 6 Required OSNR versus the linewidth tolerance Δv T s   at a target BER of 1 × 10−2 for (a) QPSK, (b) 16-QAM, (c) 32-QAM and (d) 64-QAM systems.
Fig. 7
Fig. 7 Deviations to the actual phase of different CPE schemes, (a) 16-QAM at OSNR = 18 dB and  Δv T s =2× 10 4 , (b) 64-QAM at OSNR = 28 dB and  Δv T s =8× 10 5 .
Fig. 8
Fig. 8 BER as a function of OSNR for (a) QPSK with of 3 × 10−4 and 32-QAM with Δv T s of 6 × 10−5, (b) 16-QAM with Δv T s of 1.25 × 10−4 and 64-QAM with Δv T s of 4 × 10−5.
Fig. 9
Fig. 9 Constellation diagrams recovered by BPS (upper) and the proposed two-stage QLA scheme (bottom) for (a) QPSK at OSNR = 12.5 dB and  Δv T s =8× 10 4 , (b) 16-QAM at OSNR = 19.2 dB and  Δv T s =4× 10 4 , (c) 32-QAM at OSNR = 22.4 dB and  Δv T s =9× 10 5 , (d) 64-QAM at OSNR = 25.4 dB and  Δv T s =6× 10 5 .
Fig. 10
Fig. 10 Experiment setup for 16 GBaud PM-QPSK and PM-16QAM coherent systems.
Fig. 11
Fig. 11 BER as a function of OSNR for 16GBaud (a) PM-QPSK, (b) PM-16QAM systems.

Tables (1)

Tables Icon

Table 1 Computational complexity comparison of different CPE schemes

Equations (13)

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

r( k )=A(k) e j( θ k +ϕ) +n(k), k=0,1,2,
Z( k,b )=r(k) e j ϕ b
{ Z I ( k,b )=Z( k,b )cos( θ k +ϕ φ b ) Z Q ( k,b )=Z( k,b )sin( θ k +ϕ φ b )
d( k,b )=| | Z (k,b) I || Z Q (k,b) | |
e b,1 ( k )= n=ceil(N1/2)+1 floor(N1/2) d(kn,b) = ceil(N1/2)+1 floor(N1/2) [ | | Z(kn,b) || cos( θ kn +ϕ φ b ) || Z(kn,b) || sin( θ kn +ϕ φ b ) | | ] = n=ceil(N1/2)+1 floor(N1/2) [ | Z(kn,b) || sin( ( θ kn π 4 )+(ϕ φ b ) ) | ] = n=ceil(N1/2)+1 floor(N1/2) [ | Z(kn,b) || sin( ϕ φ b ) | ]
{ e I,b,2 ( k )= n=kceil(N2/2)+1 k+floor(N2/2) [ | | | | y I ( kn,b ) |4 |2 |1 | ] e Q,b,2 ( k )= n=kceil(N2/2)+1 k+floor(N2/2) [ | | | | y Q ( kn,b ) |4 |2 |1 | ] e b,2 ( k )= e I,b,2 ( k )+ e Q,b,2 ( k )
{ y e 3,1 = e 3,1 e 1,1 (π/3)(π/6) ( x( π/3 ) ) y e 2,1 = ( e 3,1 e 1,1 ) (π/3)(π/6) ( x0 )
φ est,1 ={ π( e 3,1 e 2,1 ) 12( e 3,1 e 1,1 ) π 6 , e 3,1 > e 2,1 π( e 3,1 e 2,1 ) 12( e 2,1 e 1,1 ) π 6 , e 3,1 e 2,1
φ est,1 ={ π( e 1,1 e 3,1 ) 12( e 3,1 e 2,1 ) , e 3,1 > e 1,1 π( e 1,1 e 3,1 ) 12( e 1,1 e 2,1 ) , e 3,1 e 1,1
φ est,1 ={ π( e 2,1 e 1,1 ) 12( e 2,1 e 3,1 ) + π 6 , e 2,1 > e 1,1 π( e 2,1 e 1,1 ) 12( e 1,1 e 3,1 ) + π 6 , e 2,1 e 1,1
φ i,2 = φ est,1 +iQLI/45QLI/8,i=1,2,3,4
φ est,2 ={ ( φ s+1,2 + φ s,2 )( e s1,2 e s+1,2 ) 2( e s+1,2 e s,2 ) + φ s+1,2 + φ s1,2 2 , e s+1,2 > e 1,2 ( φ s1,2 + φ s,2 )( e s+1,2 e s-1,2 ) 2( e s-1,2 e s,2 ) + φ s+1,2 + φ s1v2 2 , e s+1,2 e 1,2
{ BER= 2 log 2 M ( 1 1 M )erfc[ 3 log 2 M 2( M1 ) E b N 0 ] OSNR= E b N 0 R b 2 B ref

Metrics