Abstract

Coherent detection in combination with digital signal processing has recently enabled significant progress in the capacity of optical communications systems. This improvement has enabled detection of optimum constellations for optical signals in four dimensions. In this paper, we propose and investigate an algorithm for the blind adaptive equalization of one such modulation format: polarization-switched quaternary phase shift keying (PS-QPSK). The proposed algorithm, which includes both blind initialization and adaptation of the equalizer, is found to be insensitive to the input polarization state and demonstrates highly robust convergence in the presence of PDL, DGD and polarization rotation.

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  1. A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguci, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C – and Extended L-Band Transmission over 240km Using PDM-16-QAM Modulation and Digital Coherent Detection,” Proc. OFC/NFOEC 2010, San Diego, CA, Mar. 21–25, 2009, PDPB7.
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    [CrossRef]
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    [CrossRef]
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  12. 40G Submarine Applications, Ciena Application Note, Ciena Corp, Available: www.ciena.com
  13. Alcatel-Lucent1626Light Manager, Data Sheet release 6.1, Alcatel-Lucent, Available: www.alcatel-lucent.com
  14. P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express 18(11), 11360–11371 (2010).
    [CrossRef] [PubMed]
  15. P. Serena, A. Vannucci, and A. Bononi, “The Performance of Polarization Switched-QPSK (PS-QPSK) in Dispersion Managed WDM Transmissions,” Proc. ECOC 2010, Th.10.E.2, Sept. 2010.
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    [CrossRef]
  17. S. Haykin, Adaptive filter theory, Prentice Hall, 2001.
  18. N. S. Bergano, F. W. Kerfoot, and C. R. Davidsion, “Margin Measurement in Optical Amplifier Systems,” IEEE Photon. Technol. Lett. 5(3), 304–306 (1993).
    [CrossRef]
  19. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for Coherent Single-Carrier Receivers,” J. Lightwave Technol. 27(16), 3614–3622 (2009).
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    [CrossRef]

2010 (5)

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010).
[CrossRef]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express 18(11), 11360–11371 (2010).
[CrossRef] [PubMed]

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

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(1), 45–47 (2010).
[CrossRef]

2009 (4)

2008 (3)

2007 (1)

1993 (1)

N. S. Bergano, F. W. Kerfoot, and C. R. Davidsion, “Margin Measurement in Optical Amplifier Systems,” IEEE Photon. Technol. Lett. 5(3), 304–306 (1993).
[CrossRef]

Agrell, E.

Alfiad, M. S.

Bayvel, P.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

Behrens, C.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

Bergano, N. S.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidsion, “Margin Measurement in Optical Amplifier Systems,” IEEE Photon. Technol. Lett. 5(3), 304–306 (1993).
[CrossRef]

Bosco, G.

Buhl, L. L.

Carena, A.

Chraplyvy, A. R.

Curri, V.

Davidsion, C. R.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidsion, “Margin Measurement in Optical Amplifier Systems,” IEEE Photon. Technol. Lett. 5(3), 304–306 (1993).
[CrossRef]

Doerr, C. R.

Forghieri, F.

Gnauck, A. H.

Hauske, F. N.

Hellerbrand, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

Ip, E.

Kahn, J.

Karlsson, M.

Kerfoot, F. W.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidsion, “Margin Measurement in Optical Amplifier Systems,” IEEE Photon. Technol. Lett. 5(3), 304–306 (1993).
[CrossRef]

Killey, R. I.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

Kuschnerov, M.

Lankl, B.

Li, G.

L. Zhu, X. Li, E. Mateo, and G. Li, “Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009).
[CrossRef]

Li, T.

Li, X.

L. Zhu, X. Li, E. Mateo, and G. Li, “Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009).
[CrossRef]

Magarini, M.

Makovejs, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

Mateo, E.

L. Zhu, X. Li, E. Mateo, and G. Li, “Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009).
[CrossRef]

Millar, D. S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

Napoli, A.

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(1), 45–47 (2010).
[CrossRef]

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(1), 45–47 (2010).
[CrossRef]

Piyawanno, K.

Poggiolini, P.

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(1), 45–47 (2010).
[CrossRef]

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(1), 45–47 (2010).
[CrossRef]

Savory, S. J.

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[CrossRef] [PubMed]

Spinnler, B.

Tkach, R. W.

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(1), 45–47 (2010).
[CrossRef]

Winzer, P. J.

Zhu, L.

L. Zhu, X. Li, E. Mateo, and G. Li, “Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009).
[CrossRef]

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

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of Fiber Nonlinearity using a Digital Coherent Receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010).
[CrossRef]

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

L. Zhu, X. Li, E. Mateo, and G. Li, “Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009).
[CrossRef]

N. S. Bergano, F. W. Kerfoot, and C. R. Davidsion, “Margin Measurement in Optical Amplifier Systems,” IEEE Photon. Technol. Lett. 5(3), 304–306 (1993).
[CrossRef]

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(1), 45–47 (2010).
[CrossRef]

J. Lightwave Technol. (6)

Opt. Express (3)

Other (6)

A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguci, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C – and Extended L-Band Transmission over 240km Using PDM-16-QAM Modulation and Digital Coherent Detection,” Proc. OFC/NFOEC 2010, San Diego, CA, Mar. 21–25, 2009, PDPB7.

P. Serena, A. Vannucci, and A. Bononi, “The Performance of Polarization Switched-QPSK (PS-QPSK) in Dispersion Managed WDM Transmissions,” Proc. ECOC 2010, Th.10.E.2, Sept. 2010.

S. Haykin, Adaptive filter theory, Prentice Hall, 2001.

H. Bülow, “Polarization QAM Modulation (POL-QAM) for Coherent Detection Schemes,” Proc. OFC/NFOEC 2009, San Diego, CA, Mar. 22–26, 2009, OWG2.

40G Submarine Applications, Ciena Application Note, Ciena Corp, Available: www.ciena.com

Alcatel-Lucent1626Light Manager, Data Sheet release 6.1, Alcatel-Lucent, Available: www.alcatel-lucent.com

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Figures (2)

Fig. 1
Fig. 1

Constellation diagrams showing two orthogonal linear polarizations of a PS-QPSK signal with bit mapping inset. Red triangles denote a symbol which has been transmitted on the x polarization, while blue circles denote a symbol transmitted on the y polarization.

Fig. 2
Fig. 2

(a). Performance of the PS-CMA with PS-QPSK modulation in the presence of PDL. Mean Q-factor penalty in dB is plotted against the applied PDL in dB. 2(b) Performance of the PS-CMA with PS-QPSK modulation in the presence of polarization rotation. Q-factor penalty in dB is plotted against the polarization rotation frequency, where τs is the symbol period.

Equations (8)

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

if | x o u t | > | y o u t | R x = 1 ; R y = 0 , else R x = 0 ; R y = 1 , end e x = R x - | x o u t | 2 ; e y = R y - | y o u t | 2 .
h x x = h x x + μ e x x i n x o u t * ; h x y = h x y + μ e x y i n x o u t * , h y x = h y x + μ e y x i n y o u t * ; h y y = h y y + μ e y y i n y o u t * ,
x o u t = h x x H x i n + h x y H y i n , y o u t = h y x H x i n + h y y H y i n ,
J = ( e j ψ cos ( θ ) e j ϕ sin ( θ ) e j ϕ sin ( θ ) e j ψ cos ( θ ) ) .
( h x x h x y h y x h y y ) = ( cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ) .
( x o u t y o u t ) = ( cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ) ( x i n y i n )
θ = arg min θ ε 2 , where : ε 2 = | x o u t | 2 | y o u t | 2 ,
ε 2 = a { 1 - cos ( 4 θ ) } + b sin ( 4 θ ) + c { 3 + cos ( 4 θ ) } , where: a = 1 8 | x i n | 4 + | y i n | 4  -  4 | Re ( x i n * y i n ) | 4 , b = 1 2 ( | y i n | 2 | x i n | 2 ) Re ( x i n * y i n ) , c = 1 4 | x i n | 2 | y i n | 2 .

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