Abstract

We experimentally investigate the singularity problem in DP-QPSK 112-Gb/s receivers using the CMA. Three algorithms are compared: Constrained, Two-Stage, and Multi-User. Although these algorithms have been individually evaluated, they have not been compared by extensive experiments. The transmission setup emulates amplifier noise; first-order PMD; and chromatic dispersion. It is shown that all algorithms effectively mitigate singularities. However, under certain conditions, the Multi-User and the Constrained algorithms – both used for system startup – outperformed the Two-Stage, which does not distinguish between system operation and startup. In light of its effectiveness and low computational complexity, we recommend the Constrained algorithm.

© 2011 OSA

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  1. L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).
  2. S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” OptoElectron. and Commun. Conf. Tech. Digest(2010).
  3. C. Xie and S. Chandrasekhar, “Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver,” OSA/OFC/NFOEC pp. 1–3 (2010).
  4. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Quantum Electron. 16, 2120–2126 (2010).
  5. J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
    [CrossRef]
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    [CrossRef]
  7. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  8. C. B. Papadias and A. Paulraj, “A space-time constant modulus algorithm for SDMA systems,” Vehicular Tech. Conf. 1, 86–90 (1996).
  9. A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
    [CrossRef]
  10. T. Benedict and T. Soong, “The joint estimation of signal and noise from the sum envelope,” IEEE Trans. Inform. Theory 13, 447–454 (1967).
    [CrossRef]

2010 (2)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Quantum Electron. 16, 2120–2126 (2010).

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

1998 (1)

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

1996 (1)

C. B. Papadias and A. Paulraj, “A space-time constant modulus algorithm for SDMA systems,” Vehicular Tech. Conf. 1, 86–90 (1996).

1967 (1)

T. Benedict and T. Soong, “The joint estimation of signal and noise from the sum envelope,” IEEE Trans. Inform. Theory 13, 447–454 (1967).
[CrossRef]

1941 (1)

Behm, J.

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Benedict, T.

T. Benedict and T. Soong, “The joint estimation of signal and noise from the sum envelope,” IEEE Trans. Inform. Theory 13, 447–454 (1967).
[CrossRef]

Brown, D.

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Casas, R.

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Chandrasekhar, S.

C. Xie and S. Chandrasekhar, “Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver,” OSA/OFC/NFOEC pp. 1–3 (2010).

Endres, T.

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Faruk, S.

S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” OptoElectron. and Commun. Conf. Tech. Digest(2010).

Hoshida, T.

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

Johnson, J.

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Jones, R. C.

Kikuchi, K.

K. Kikuchi, “Polarization-demultiplexing algorithm in the digital coherent receiver,” IEEE/LEOS Summer Topical Meetings pp. 101–102 (2008).
[CrossRef]

S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” OptoElectron. and Commun. Conf. Tech. Digest(2010).

Liu, L.

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

Mori, Y.

S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” OptoElectron. and Commun. Conf. Tech. Digest(2010).

Oda, S.

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

Papadias, C. B.

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

C. B. Papadias and A. Paulraj, “A space-time constant modulus algorithm for SDMA systems,” Vehicular Tech. Conf. 1, 86–90 (1996).

Paulraj, A.

C. B. Papadias and A. Paulraj, “A space-time constant modulus algorithm for SDMA systems,” Vehicular Tech. Conf. 1, 86–90 (1996).

Petrou, C. S.

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

R.,

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Raptis, L.

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

Rasmussen, J. C.

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

Roudas, I.

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

Savory, S. J.

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Quantum Electron. 16, 2120–2126 (2010).

Schniter, P.

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Soong, T.

T. Benedict and T. Soong, “The joint estimation of signal and noise from the sum envelope,” IEEE Trans. Inform. Theory 13, 447–454 (1967).
[CrossRef]

Tao, Z.

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

Vgenis, A.

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

Xie, C.

C. Xie and S. Chandrasekhar, “Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver,” OSA/OFC/NFOEC pp. 1–3 (2010).

Yan, W.

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

Zhang, C.

S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” OptoElectron. and Commun. Conf. Tech. Digest(2010).

IEEE J. Quantum Electron. (1)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Quantum Electron. 16, 2120–2126 (2010).

IEEE Photon. Technol. Lett. (1)

A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22, 45–47 (2010).
[CrossRef]

IEEE Trans. Inform. Theory (1)

T. Benedict and T. Soong, “The joint estimation of signal and noise from the sum envelope,” IEEE Trans. Inform. Theory 13, 447–454 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

J. Johnson, R., P. Schniter, T. Endres, J. Behm, D. Brown, and R. Casas, “Blind equalization using the constant modulus criterion: a review,” Proc. IEEE 86, 1927–1950 (1998).
[CrossRef]

Vehicular Tech. Conf. (1)

C. B. Papadias and A. Paulraj, “A space-time constant modulus algorithm for SDMA systems,” Vehicular Tech. Conf. 1, 86–90 (1996).

Other (4)

K. Kikuchi, “Polarization-demultiplexing algorithm in the digital coherent receiver,” IEEE/LEOS Summer Topical Meetings pp. 101–102 (2008).
[CrossRef]

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OSA/OFC/NFOEC(2009).

S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” OptoElectron. and Commun. Conf. Tech. Digest(2010).

C. Xie and S. Chandrasekhar, “Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver,” OSA/OFC/NFOEC pp. 1–3 (2010).

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Figures (7)

Fig. 1
Fig. 1

MU-CMA Implementation.

Fig. 2
Fig. 2

Experimental analysis diagram.

Fig. 3
Fig. 3

Reference curves.

Fig. 4
Fig. 4

Estimated SNR in the presence of amplifier noise only (OSNR=17 dB).

Fig. 5
Fig. 5

Estimated SNR in the presence of amplifier noise (OSNR=18 dB) and residual chromatic dispersion (CD=50 ps).

Fig. 6
Fig. 6

Estimated SNR in the presence of amplifier noise (OSNR=18 dB) and first-order PMD (DGD=20 ps).

Fig. 7
Fig. 7

Singularities in the presence of CD and PMD (over 1,000 sequences).

Tables (4)

Tables Icon

Table 1 Number of Singularities Observed in 1,000 Sequences Versus CEV Length for the MU-CMA, at OSNR=17 dB

Tables Icon

Table 2 Number of Convergence Failures Observed in 1,000 Sequences Versus CEV Length for the MU-CMA, at OSNR=17 dB

Tables Icon

Table 3 Convergence Failures in 1,000 Sequences

Tables Icon

Table 4 Number of Singularities Observed in 1,000 Sequences, at OSNR=17 dB

Equations (5)

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

T ( j ω ) = [ U ( j ω ) V ( j ω ) V * ( j ω ) U * ( j ω ) ] F T [ u ( t ) v ( t ) v * ( t ) u * ( t ) ] .
J ( F ) = E [ l = 1 2 { ( | y l | 2 1 ) 2 } ] .
J M U C M A ( F ) = J C M A ( F ) + 2 i = 1 2 δ = δ 1 δ 2 | r i j ( δ ) | 2 , i + j = 3 ,
F [ k + 1 ] = F [ k ] μ [ Δ 1 [ k ] Δ 2 [ k ] ] ,
Δ l [ k ] = 4 ( | y l [ k ] | 2 1 ) y l [ k ] X * [ k ] + δ = δ 1 δ 2 r l i ( δ ) y i [ k δ ] X * [ k ] ; l = 1 , 2 ; l + i = 3 .

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