Abstract

A blind frequency and phase search algorithm for joint frequency and phase recovery is introduced. The algorithm achieves low complexity due to processing in polar coordinates, which reduces the amount of multiplications. We show an implementation for real-time processing at 32 GBd on FPGA hardware. The hardware design allows for dynamic multi-format operation, where the format can be switched flexibly after each clock cycle (250 MHz, 128 Symbols) between 4QAM, 8QAM, and 16QAM. The performance of the algorithm is evaluated with respect to laser phase noise, carrier frequency offset, and carrier frequency offset drift. The effect of working with limited hardware resources is investigated. An FPGA implementation shows the feasibility of our carrier recovery algorithm with a negligible penalty when compared to a floating point simulation.

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References

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  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), 12–20 (2012).
    [Crossref]
  2. 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]
  3. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
    [Crossref]
  4. 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]
  5. M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC (2009), paper P3.08.
  6. 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(4), 571–577 (2011).
    [Crossref]
  7. A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
    [Crossref]
  8. 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]
  9. 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]
  10. S. M. Bilal, C. R. S. 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]
  11. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
    [Crossref]
  12. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 22(14), 1051–1053 (2010).
    [Crossref]
  13. 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]
  14. H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
    [Crossref]
  15. A. Al-Bermani, C. Wördehoff, K. Puntsri, O. Jan, U. Rückert, and R. Noé, “Real-time synchronous 16-QAM optical transmission system using blind phase search and QPSK partitioning carrier recovery techniques,” in ITG-Fachtagung Photonische Netze (Leipzig, Germany, 2012).
  16. T.-H. Nguyen, M. Joindot, P. Scalart, M. Gay, L. Bramerie, O. Sentieys, J.-C. Simon, and C. Peucheret, “Carrier phase recovery for optical coherent M-QAM communication systems using harmonic decomposition-based maximum loglikelihood estimators,” in Proc. SPPCom, Advanced Photonics (2015), paper SpT4D.3.
  17. T.-h. Nguyen, P. Scalart, M. Gay, L. Bramerie, C. Peucheret, O. Sentieys, J.-C. Simon, and M. Joindot, “Bi-harmonic decomposition-based maximum loglikelihood estimator for carrier phase estimation of coherent optical M-QAM,” in Proc. OFC, (2016), paper Tu3K.3.
    [Crossref]
  18. N. Argyris, S. Dris, C. Spatharakis, and H. Avramopoulos, “High performance carrier phase recovery for coherent optical QAM,” in Proc. OFC, (2015), paper W1E.1.
    [Crossref]
  19. A. Tolmachev, I. Tselniker, M. Meltsin, I. Sigron, D. Dahan, A. Shalom, and M. Nazarathy, “Multiplier-free phase recovery with polar-domain multisymbol-delay-detector,” J. Lightwave Technol. 31(23), 3638–3650 (2013).
    [Crossref]
  20. I. Tselniker, N. Sigron, and M. Nazarathy, “Joint phase noise and frequency offset estimation and mitigation for optically coherent QAM based on adaptive multi-symbol delay detection (MSDD),” Opt. Express 20(10), 10944–10962 (2012).
    [Crossref] [PubMed]
  21. A. Leven, N. Kaneda, and S. Corteselli, “Real-time implementation of digital signal processing for coherent optical digital communication systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (2010).
    [Crossref]
  22. B. Baeuerle, A. Josten, F. C. Abrecht, E. Dornbierer, J. Boesser, M. Dreschmann, J. Becker, J. Leuthold, and D. Hillerkuss, “Multiplier-free, carrier-phase recovery for real-time receivers using processing in polar coordinates,” in Proc. OFC, (2015), paper W1E.2.
    [Crossref]
  23. B. Baeuerle, A. Josten, F. Abrecht, E. Dornbierer, D. Hillerkuss, and J. Leuthold, “Blind real-time multi-format carrier recovery for flexible optical networks,” in Proc. SPPCom, Advanced Photonics, (2015), paper SpT4D.5.
  24. J. E. Volder, “The CORDIC trigonometric computing technique,” IRE Trans. Electron. Comput. EC-8(3), 330–334 (1959).
    [Crossref]
  25. S.-H. Fan, J. Yu, D. Qian, and G.-K. Chang, “A fast and efficient frequency offset correction technique for coherent optical orthogonal frequency division multiplexing,” J. Lightwave Technol. 29(13), 1997–2004 (2011).
    [Crossref]
  26. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
    [Crossref]
  27. L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
    [Crossref]

2014 (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]

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[Crossref]

S. M. Bilal, C. R. S. 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]

2013 (2)

2012 (2)

2011 (3)

2010 (4)

A. Leven, N. Kaneda, and S. Corteselli, “Real-time implementation of digital signal processing for coherent optical digital communication systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (2010).
[Crossref]

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]

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 22(14), 1051–1053 (2010).
[Crossref]

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

2009 (2)

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

L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[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]

1983 (1)

A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

1959 (1)

J. E. Volder, “The CORDIC trigonometric computing technique,” IRE Trans. Electron. Comput. EC-8(3), 330–334 (1959).
[Crossref]

Bilal, S. M.

Birk, M.

Borel, P. I.

Bosco, G.

Cartledge, J. C.

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]

Chang, G.-K.

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]

Corteselli, S.

A. Leven, N. Kaneda, and S. Corteselli, “Real-time implementation of digital signal processing for coherent optical digital communication systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (2010).
[Crossref]

Curri, V.

Dahan, D.

Darwazeh, I.

L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

Dong, J.

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[Crossref]

Fan, S.-H.

Fatadin, I.

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]

Fludger, C. R. S.

Gao, Y.

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]

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]

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), 12–20 (2012).
[Crossref]

Hoffmann, S.

Hoshida, T.

Huang, M.-F.

Ip, E.

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]

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), 12–20 (2012).
[Crossref]

Kahn, J. M.

Kaneda, N.

A. Leven, N. Kaneda, and S. Corteselli, “Real-time implementation of digital signal processing for coherent optical digital communication systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (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]

Ke, J. 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]

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]

Leven, A.

A. Leven, N. Kaneda, and S. Corteselli, “Real-time implementation of digital signal processing for coherent optical digital communication systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (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]

Li, J.

Li, L.

Lingle, R.

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), 12–20 (2012).
[Crossref]

Lu, C.

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]

Magill, P.

Meltsin, M.

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]

Nazarathy, M.

Nelson, L.

Noe, R.

Peckham, D. W.

Pessoa, L. M.

L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

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]

Qian, D.

Rasmussen, J. C.

Salgado, H. M.

L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

Savory, S. J.

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]

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

Shalom, A.

Shao, Y.

Sigron, I.

Sigron, N.

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]

Tao, Z.

Tolmachev, A.

Tselniker, I.

Viterbi, A. M.

A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

Volder, J. E.

J. E. Volder, “The CORDIC trigonometric computing technique,” IRE Trans. Electron. Comput. EC-8(3), 330–334 (1959).
[Crossref]

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]

Wang, T.

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]

Yan, S.

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[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), 12–20 (2012).
[Crossref]

Yu, J.

Zhang, X.

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[Crossref]

Zhong, K. P.

Zhou, H.

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[Crossref]

Zhou, X.

Zhou, Y.

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[Crossref]

Zhu, B.

Zhuge, 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]

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), 12–20 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

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

A. Leven, N. Kaneda, and S. Corteselli, “Real-time implementation of digital signal processing for coherent optical digital communication systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (5)

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 22(14), 1051–1053 (2010).
[Crossref]

L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[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, 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]

H. Zhou, J. Dong, S. Yan, Y. Zhou, and X. Zhang, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photonics Technol. Lett. 26(18), 1 (2014).
[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]

IEEE Trans. Inf. Theory (1)

A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

IRE Trans. Electron. Comput. (1)

J. E. Volder, “The CORDIC trigonometric computing technique,” IRE Trans. Electron. Comput. EC-8(3), 330–334 (1959).
[Crossref]

J. Lightwave Technol. (8)

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]

A. Tolmachev, I. Tselniker, M. Meltsin, I. Sigron, D. Dahan, A. Shalom, and M. Nazarathy, “Multiplier-free phase recovery with polar-domain multisymbol-delay-detector,” J. Lightwave Technol. 31(23), 3638–3650 (2013).
[Crossref]

S. M. Bilal, C. R. S. 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]

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

T. Pfau, S. Hoffmann, and R. Noe, “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, 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(4), 571–577 (2011).
[Crossref]

S.-H. Fan, J. Yu, D. Qian, and G.-K. Chang, “A fast and efficient frequency offset correction technique for coherent optical orthogonal frequency division multiplexing,” J. Lightwave Technol. 29(13), 1997–2004 (2011).
[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]

Opt. Express (1)

Other (7)

B. Baeuerle, A. Josten, F. C. Abrecht, E. Dornbierer, J. Boesser, M. Dreschmann, J. Becker, J. Leuthold, and D. Hillerkuss, “Multiplier-free, carrier-phase recovery for real-time receivers using processing in polar coordinates,” in Proc. OFC, (2015), paper W1E.2.
[Crossref]

B. Baeuerle, A. Josten, F. Abrecht, E. Dornbierer, D. Hillerkuss, and J. Leuthold, “Blind real-time multi-format carrier recovery for flexible optical networks,” in Proc. SPPCom, Advanced Photonics, (2015), paper SpT4D.5.

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

A. Al-Bermani, C. Wördehoff, K. Puntsri, O. Jan, U. Rückert, and R. Noé, “Real-time synchronous 16-QAM optical transmission system using blind phase search and QPSK partitioning carrier recovery techniques,” in ITG-Fachtagung Photonische Netze (Leipzig, Germany, 2012).

T.-H. Nguyen, M. Joindot, P. Scalart, M. Gay, L. Bramerie, O. Sentieys, J.-C. Simon, and C. Peucheret, “Carrier phase recovery for optical coherent M-QAM communication systems using harmonic decomposition-based maximum loglikelihood estimators,” in Proc. SPPCom, Advanced Photonics (2015), paper SpT4D.3.

T.-h. Nguyen, P. Scalart, M. Gay, L. Bramerie, C. Peucheret, O. Sentieys, J.-C. Simon, and M. Joindot, “Bi-harmonic decomposition-based maximum loglikelihood estimator for carrier phase estimation of coherent optical M-QAM,” in Proc. OFC, (2016), paper Tu3K.3.
[Crossref]

N. Argyris, S. Dris, C. Spatharakis, and H. Avramopoulos, “High performance carrier phase recovery for coherent optical QAM,” in Proc. OFC, (2015), paper W1E.1.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of the carrier recovery operation principle. The two important blocks are the carrier frequency recovery (CFR) and the carrier phase recovery (CPR). The CFO varies slowly with time so that testing of the proper frequency may be performed in a serial manner, i.e. with one test frequency at a time. The CFR algorithm then evaluates a cost function with the defined test frequency to select the correct frequency offset and corrects the CFO. The CPR adds test phases in parallel, evaluates the cost function for each and corrects the phase. (b) The three modulation formats (4QAM, 8QAM, and 16QAM) that are subsequently recovered by the proposed algorithm. The different constellation points are subdivided into groups with identical magnitude (r0, r1, and r2).
Fig. 2
Fig. 2 The proposed carrier frequency recovery corrects the frequency offset in four steps. To provide the samples in polar coordinates, the CORDIC algorithm [21] transforms LCFR complex time samples rl from Cartesian to polar coordinates. (1) In the first step, K test frequencies fk are applied sequentially to the incoming signal by adding the corresponding linear phase ramp (φk,1,…, φk,L). (2) In the second step, the cost function JCFR(fk) is calculated for the current test frequency fk. (3) In the third step, the results are stored in a buffer and evaluated by the min(∙) block, which selects for the correct CFO among the K test-frequencies. An exponential average function is applied to improve the estimation. (4) The frequency offset is corrected by applying the correction with a vector of linearly increasing phase from the selected CFO.
Fig. 3
Fig. 3 Partitioning and remapping of the symbols to remove data information from the signal and therefore align the symbols to an axis with identical relative phase φref. Here, the reference phase φref is π / 4. The process is adapted for (a) 4QAM, (b) 8QAM, and (c) 16QAM. For 4QAM, a modulo π / 2 suffices to align all symbols to one phase. For 8QAM and 16QAM, the constellation points have to be separated in groups with identical magnitude (r0, r1, and r2). Subsequently, the grayed out constellation points in (b) and (c) are either shifted by π / 4 for 8QAM (b) or neglected for 16QAM (c).
Fig. 4
Fig. 4 Performance of the CFR for different formats. (a) Normalized JCFR as a function of test frequencies fk for 4QAM, 8QAM, and 16QAM and for LCFR = 64 and LCFR = 128. (b) The estimated carrier frequency offset (CFO) as a function over time for 16QAM. The red curve shows the actual CFO which drifts by 1 MHz/μs. The blue dots represent the estimated CFO values without exponential average and the green dots represent the estimated CFO value with exponential average.
Fig. 5
Fig. 5 Block diagram of the proposed carrier phase recovery (CPR) algorithm consisting of four steps. (1) Parallel summation of B test phases φb to the received phase ∠rl, (2) computation of the cost function JCPR(φb), (3) selection of the smallest cost function value to determine the optimum test phase, and (4) correction of the received phase ∠rl with the optimal test phase φb.
Fig. 6
Fig. 6 Performance of the CPR for different formats and the partitioning for 16QAM. (a) Normalized JCPR as a function of the test phases φb for 4QAM, 8QAM and 16QAM. (b) Portioning concept for 16QAM to calculate the cost function JCPR(φb). Symbols are mapped to the first quadrant and are partitioned according to their amplitude and phase (dotted red lines).
Fig. 7
Fig. 7 Simulation results for the CPR processing 32 GBd signals with 4QAM, 8QAM, and 16QAM. SNR penalty at a BER of 10-3 as a function of (a) the block size LCPR under influence of a laser linewidth of 100 kHz and 1 MHz, (b) the laser linewidth with block sizes of LCPR=32, 64, (c) the number of test angles B under the influence of a laser linewidth of 100 kHz, (d) the ADC word width in number of bits under the influence of a laser linewidth of 100 kHz.
Fig. 8
Fig. 8 Simulation results for the CFR processing 32 GBd signals with 4QAM, 8QAM, and 16QAM. (a) SNR penalty as a function of carrier frequency offsets (CFOs) with CFR and without CFR. (b) SNR penalty as a function of carrier frequency offset (CFO) drifts for processing lengths of LCFR = 128 and LCFR = 256.
Fig. 9
Fig. 9 Results of software simulation and hardware realization for 4QAM, 8QAM, and 16QAM (a) BER performance as a function of SNR of the software (SW) and hardware (HW) implementation compared to the theoretical limit of differential encoding. (b) Constellation diagrams which are modulated by the carrier recovery hardware implementation

Tables (1)

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Table 1 FPGA chip utilization (% of Xilinx xc7vx690t).

Equations (5)

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ϑ test,k,l =mod( r l + φ k,l , π 2 ).
Δ φ k,l =| ϑ test,k,l φ ref |,
J CFR ( f k )= 1 L CFR 2 i=1 L CFR l=1 L CFR 1 2 ( Δ φ k,i Δ φ k,l ) 2 .
J CFR ( f k )= i=1 I< L CFR l=1 L CFR | Δ φ k,i Δ φ k,l | .
J CPR ( φ b )= 1 L CPR l=1 L CPR ( | ϑ test,l,b φ ref ( | r l |, ϑ test,l,b ) | ) with ϑ test,l,b =mod( r l + φ b , π 2 )

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