Abstract

An all-digital timing recovery loop is employed in optical coherent receivers, which depends on the number-controlled oscillator and the interpolator to complete timing adjustment in an all-digital way instead of the traditional hybrid way using an analog device (a voltage-controlled oscillator) to adjust the sampling frequency. Therefore it avoids introducing the nonideal characteristics of an analog device and is beneficial to all-digital implementation of optical coherent receivers. Furthermore, in order to meet the requirements of low complexity and sampling rate, the Gardner timing error detector is adopted in the all-digital timing recovery loop. However, it has low tolerance of dispersion, which requires another device to compensate the large residual dispersion prior to it. Although the adaptive equalizer can compensate signal for dispersion impairment, its effective operation must rely upon synchronized signals. For solving the incompatible problem without any extra cost, a joint scheme that embeds an adaptive equalizer into the all-digital timing recovery loop is proposed to accomplish synchronization and compensation of linear transmission impairments. Finally, the feasibility and effectiveness of the proposed scheme are demonstrated in a 112Gbits polarization-multiplexing non-return-to-zero differential-quadrature phase-shift-keying (POLMUX-NRZ-DQPSK) optical coherent receiver by simulation.

© 2010 Optical Society of America

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  1. K. Kikuchi, “Coherent transmission system,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 6, pp. 145–183.
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    [CrossRef]
  3. M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.
  4. M. Oerder, H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun., vol. 36, no. 5, pp. 605–612, May 1998.
    [CrossRef]
  5. T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.
  6. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.
  7. L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.
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  18. K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.
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    [CrossRef] [PubMed]

2009

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

2008

2007

A. Leven, N. Kaneda, U.-V. Koc, Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett., vol. 19, no. 6, pp. 366–368, Mar. 2007.
[CrossRef]

G. Goldfarb, G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett., vol. 19, no. 13, pp. 969–971, July 2007.
[CrossRef]

1998

M. Oerder, H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun., vol. 36, no. 5, pp. 605–612, May 1998.
[CrossRef]

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

1993

F. M. Gardner, “Interpolation in digital modems—part I: fundamentals,” IEEE Trans. Commun., vol. 41, no. 3, pp. 501–507, Mar. 1993.
[CrossRef]

L. Erup, F. M. Gardner, R. A. Harris, “Interpolation in digital modems—part II: implementation and performance,” IEEE Trans. Commun., vol. 41, no. 6, pp. 998–1008, June 1993.
[CrossRef]

1987

1986

F. M. Gardner, “A BPSK/QPSK timing-error detector for sampled receiver,” IEEE Trans. Commun., vol. com-34, no. 5, pp. 423–429, May 1986.
[CrossRef]

1983

A. J. Viterbi, A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory, vol. IT-29, no. 4, pp. 543–551, July 1983.
[CrossRef]

Alfiad, M. S.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

Bayvel, P.

S. J. Savory, G. Gavioli, R. I. Killry, P. Bayvel, “Transmission of 42.8 Gbit∕s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2007), 2007, paper OYUA1.

Behm, J. D.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

Brown, D. R.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

Casas, R. A.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

Chen, X.

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

Chen, Y.-K.

A. Leven, N. Kaneda, U.-V. Koc, Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett., vol. 19, no. 6, pp. 366–368, Mar. 2007.
[CrossRef]

Cheung, N. K.

Curtis, L.

de Waardt, H.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

Endres, T. J.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

Erup, L.

L. Erup, F. M. Gardner, R. A. Harris, “Interpolation in digital modems—part II: implementation and performance,” IEEE Trans. Commun., vol. 41, no. 6, pp. 998–1008, June 1993.
[CrossRef]

Gardner, F. M.

L. Erup, F. M. Gardner, R. A. Harris, “Interpolation in digital modems—part II: implementation and performance,” IEEE Trans. Commun., vol. 41, no. 6, pp. 998–1008, June 1993.
[CrossRef]

F. M. Gardner, “Interpolation in digital modems—part I: fundamentals,” IEEE Trans. Commun., vol. 41, no. 3, pp. 501–507, Mar. 1993.
[CrossRef]

F. M. Gardner, “A BPSK/QPSK timing-error detector for sampled receiver,” IEEE Trans. Commun., vol. com-34, no. 5, pp. 423–429, May 1986.
[CrossRef]

F. M. Gardner, Phaselock Techniques, 3rd ed. Wiley, 2007.

Gavioli, G.

S. J. Savory, G. Gavioli, R. I. Killry, P. Bayvel, “Transmission of 42.8 Gbit∕s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2007), 2007, paper OYUA1.

Goldfarb, G.

G. Goldfarb, G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett., vol. 19, no. 13, pp. 969–971, July 2007.
[CrossRef]

Gourdon, E.

M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.

Harris, R. A.

L. Erup, F. M. Gardner, R. A. Harris, “Interpolation in digital modems—part II: implementation and performance,” IEEE Trans. Commun., vol. 41, no. 6, pp. 998–1008, June 1993.
[CrossRef]

Hauske, F. N.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.

Hoshida, T.

L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

Johnson, C. R.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

Kaneda, N.

A. Leven, N. Kaneda, U.-V. Koc, Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett., vol. 19, no. 6, pp. 366–368, Mar. 2007.
[CrossRef]

Kazovsky, G. L.

Kikuchi, K.

K. Kikuchi, “Coherent transmission system,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 6, pp. 145–183.

Killry, R. I.

S. J. Savory, G. Gavioli, R. I. Killry, P. Bayvel, “Transmission of 42.8 Gbit∕s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2007), 2007, paper OYUA1.

Koc, U.-V.

A. Leven, N. Kaneda, U.-V. Koc, Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett., vol. 19, no. 6, pp. 366–368, Mar. 2007.
[CrossRef]

Kuschnerov, M.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.

Lank, B.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

Lankl, B.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.

M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.

Leven, A.

A. Leven, N. Kaneda, U.-V. Koc, Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett., vol. 19, no. 6, pp. 366–368, Mar. 2007.
[CrossRef]

Li, G.

G. Goldfarb, G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett., vol. 19, no. 13, pp. 969–971, July 2007.
[CrossRef]

Li, Z.

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

Liu, L.

L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

Meyr, H.

M. Oerder, H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun., vol. 36, no. 5, pp. 605–612, May 1998.
[CrossRef]

Nakashima, H.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

Napoli, A.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

Oda, S.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

Oerder, M.

M. Oerder, H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun., vol. 36, no. 5, pp. 605–612, May 1998.
[CrossRef]

Piyawanno, K.

M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

Rasmussen, J. C.

L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

Savory, S. J.

S. J. Savory, “Digital filter for coherent optical receivers,” Opt. Express, vol. 16, no. 2, pp. 804–817, Jan. 2008.
[CrossRef] [PubMed]

S. J. Savory, G. Gavioli, R. I. Killry, P. Bayvel, “Transmission of 42.8 Gbit∕s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2007), 2007, paper OYUA1.

Schmidt, E.-D.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.

Schniter, P.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE, vol. 86, no. 10, pp. 1927–1950, Oct. 1998.
[CrossRef]

Spinnler, B.

K. Piyawanno, M. Kuschnerov, F. N. Hauske, M. S. Alfiad, B. Spinnler, A. Napoli, H. de Waardt, B. Lank, “Polarization coupled carrier phase estimation for coherent polarization multiplexed QPSK with OOK-neighbours,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2009), 2009, paper OMT6.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, E.-D. Schmidt, B. Lankl, “Joint equalization and timing recovery for coherent fiber optic receivers,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 37–38.

M. Kuschnerov, F. N. Hauske, E. Gourdon, K. Piyawanno, B. Lankl, B. Spinnler, “Digital timing recovery for coherent fiber optic systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC 2008), 2008, paper JThA63.

Tanimura, T.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.

Tao, Z.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.

Viterbi, A. J.

A. J. Viterbi, A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory, vol. IT-29, no. 4, pp. 543–551, July 1983.
[CrossRef]

Viterbi, A. M.

A. J. Viterbi, A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory, vol. IT-29, no. 4, pp. 543–551, July 1983.
[CrossRef]

Young, W. C.

Yuki, M.

T. Tanimura, T. Hoshida, S. Oda, H. Nakashima, M. Yuki, Z. Tao, L. Liu, J. C. Rasmussen, “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 35–36.

Zhang, H.

L. Liu, Z. Tao, H. Zhang, T. Tanimura, T. Hoshida, J. C. Rasmussen, “Controlled adaptive equalization for dual-polarization coherent receivers with simple clock recovery,” in European Conf. on Optical Communication (ECOC 2008), 2008, vol. 1, pp. 43–44.

Zhang, Z.

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

Zhou, W.

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

Zhou, X.

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

Zhu, H.

Z. Li, X. Chen, W. Zhou, H. Zhu, X. Zhou, Z. Zhang, “Wide-range and fast-convergence frequency offset estimator by BER-aiding for optical coherent receivers,” Proc. SPIE, vol. 7632, pp. 194–196, 2009.

Appl. Opt.

IEEE Photon. Technol. Lett.

A. Leven, N. Kaneda, U.-V. Koc, Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett., vol. 19, no. 6, pp. 366–368, Mar. 2007.
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Figures (11)

Fig. 1
Fig. 1

All-digital timing recovery loop. NCO, number-controlled oscillator; T s , sampling intervals of ADC; T i , synchronized sampling intervals ( T i = Symbol   Period n , n C ; in our paper, n equals 2); m k , base-point index; μ, fractional interval.

Fig. 2
Fig. 2

Sample relation: X [ ( n 1 ) 1 2 ] and X ( n 1 ) , are the output samples of the interpolator, where X indicates one of I or Q.

Fig. 3
Fig. 3

NCO relation.

Fig. 4
Fig. 4

S-curves of the Gardner timing error detector.

Fig. 5
Fig. 5

Block diagram of the timing recovery and equalizer. (a) The timing recovery and equalizer are independent of each other, (b) the joint scheme of timing recovery and the equalizer.

Fig. 6
Fig. 6

Transmission system model: (a) transmitter, (b) receiver, and (c) Matlab processing

Fig. 7
Fig. 7

B L versus the number of symbols required to achieve a timing recovery locking condition at OSNR = 16.5 dB and different SCO without CD and PMD.

Fig. 8
Fig. 8

B L versus LF_MSE under the conditions of OSNR = 16.5 dB and different SCO without CD and PMD.

Fig. 9
Fig. 9

Output constellation diagrams of the equalizer for X-polarization (a) with the independent scheme and (c) with the joint scheme. A portion of the fractional interval for X-polarization (b) with the independent scheme and (d) with the joint scheme.

Fig. 10
Fig. 10

BER versus CD with the joint scheme and the independent scheme under different OSNR conditions.

Fig. 11
Fig. 11

Joint scheme of timing recovery and the equalizer. (a) A constellation diagram of equalizer output for X-polarization. (b) A portion of the fractional interval for X-polarization.

Tables (1)

Tables Icon

Table 1 B L Versus ARSCO

Equations (12)

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X ( k T i ) = x [ ( m k 2 ) T s ] × ( 1 6 μ k 3 + 1 6 μ k ) + x [ ( m k 1 ) T s ] × ( 1 2 μ k 3 + 1 2 μ k 2 μ k ) + x [ ( m k ) T s ] × ( 1 2 μ k 3 μ k 2 + 1 2 μ k + 1 ) + x [ ( m k + 1 ) T s ] × ( 1 6 μ k 3 + 1 2 μ k 2 + 1 3 μ k ) ,
e ( n ) = I ( n 1 2 ) [ I ( n ) I ( n 1 ) ] + Q ( n 1 2 ) [ Q ( n ) Q ( n 1 ) ] ,
LF P ( n ) = k 1 e ( n ) ,
LF I ( n ) = k 2 e ( n ) + LF I ( n 1 ) ,
W ( n ) = LF p ( n ) + LF I ( n ) .
NCO ( n ) = [ NCO ( n 1 ) W ( n 1 ) ] mod 1 ,
μ k T s NCO ( n ) = ( 1 μ k ) T s NCO ( n ) W ( n ) ,
μ k = NCO ( n ) W ( n ) NCO ( n ) + NCO ( n ) = NCO ( n ) w ( n ) .
w n = 8 B L ζ 1 + 4 ζ 2 ,
k 2 = w n 2 k d ,
k 1 = 2 ζ k d k 2 ,
N = 2 × [ | D | λ 2 z 2 c T 2 ] + 1 ,