Abstract

We propose a training symbol based channel estimation (TS-EST) algorithm that estimates the 2 × 2 Jones channel matrix. The estimated matrix entries are then used as the initial center taps of the 2 × 2 butterfly equalizer. Employing very few training symbols for TS-EST, ultrafast polarization tracking is achieved and tap update can be initially pursued using the decision-directed least mean squares (DD-LMS) algorithm to mitigate residual intersymbol interference (ISI). We experimentally verify the proposed TS-EST algorithm for 112 Gbps PDM-QPSK and 224 Gbps PDM-16QAM systems using 10 and 40 training symbols for TS-EST, respectively. Steady-state and transient bit error rates (BERs) achieved using the TS-EST algorithm are compared to those obtained using the constant modulus algorithm (CMA) and the training symbol least mean squares (TS-LMS) algorithm and results show that the proposed TS-EST algorithm provides the same steady-state BER with a superior convergence speed. Also, the tolerance of the proposed TS-EST algorithm to laser phase noise and fiber nonlinearity is experimentally verified. Finally, we show by simulation that the superior tracking speed of the TS-EST algorithm allows not only for initial polarization tracking but also for tracking fast polarization transients if four training symbols are periodically sent during steady-state operation with an overhead as low as 0.57%.

© 2012 OSA

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References

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    [CrossRef]
  13. 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,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2009), paper OMT2.
  14. G. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley & Sons, 2005), Chap. 3.
  15. M. Morsy-Osman, M. Chagnon, Q. Zhuge, X. Xu, M. E. Mousa-Pasandi, Z. A. El-Sahn, and D. V. Plant, “Training symbol based channel estimation for ultrafast polarization demultiplexing in coherent single-carrier transmission systems with M-QAM constellations,” in Proceedings of European Conference and Exhibition on Optical Communication 2012, paper Mo.1A.4.
  16. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol.27(7), 901–914 (2009).
    [CrossRef]
  17. P. Ciblat and M. Ghogho, “Blind NLLS carrier frequency-offset estimation for QAM, PSK, and PAM modulations: performance at low SNR,” IEEE Trans. Commun.54(10), 1725–1730 (2006).
    [CrossRef]
  18. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16(20), 15718–15727 (2008).
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  19. Q. Zhuge, X. Xu, Z. A. El-Sahn, M. E. Mousa-Pasandi, M. Morsy-Osman, M. Chagnon, M. Qiu, and D. V. Plant, “Experimental investigation of the equalization-enhanced phase noise in long haul 56 Gbaud DP-QPSK systems,” Opt. Express20(13), 13841–13846 (2012).
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  21. L. Nelson, “Polarization effects in coherent systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1A.4.
  22. L. Nelson, M. Birk, S. L. Woodward, and P. Magill, “Field measurements of polarization transients on a long-haul terrestrial link,” in Proceedings of IEEE Photonics Conference 2011, paper ThT5.

2012

2011

2010

E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol.28(4), 502–519 (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]

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (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

2008

2006

P. Ciblat and M. Ghogho, “Blind NLLS carrier frequency-offset estimation for QAM, PSK, and PAM modulations: performance at low SNR,” IEEE Trans. Commun.54(10), 1725–1730 (2006).
[CrossRef]

2004

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

Barros, D. J.

Beckett, D.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

Berthold, J.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

Boertjes, D.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

Buhl, L. L.

Chagnon, M.

Chandrasekhar, S.

Chen, X.

Ciblat, P.

P. Ciblat and M. Ghogho, “Blind NLLS carrier frequency-offset estimation for QAM, PSK, and PAM modulations: performance at low SNR,” IEEE Trans. Commun.54(10), 1725–1730 (2006).
[CrossRef]

Dimarcello, F. V.

Doerr, C. R.

El-Sahn, Z. A.

Fatadin, I.

Fini, J. M.

Fishteyn, M.

Ghogho, M.

P. Ciblat and M. Ghogho, “Blind NLLS carrier frequency-offset estimation for QAM, PSK, and PAM modulations: performance at low SNR,” IEEE Trans. Commun.54(10), 1725–1730 (2006).
[CrossRef]

Gnauck, A. H.

Ho, K. P.

Ip, E.

Ives, D.

Kahn, J. M.

Laperle, C.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

Lau, A. P.

Li, G.

Liu, X.

Magarini, M.

Monberg, E. M.

Morsy-Osman, M.

Mousa-Pasandi, M. E.

Pan, Y.

Plant, D. V.

Qiu, M.

Roberts, K.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

Savory, S. J.

Shieh, W.

Taunay, T. F.

Taylor, M. G.

M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol.27(7), 901–914 (2009).
[CrossRef]

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

Winzer, P. J.

Xu, X.

Yan, M. F.

Zhu, B.

Zhuge, Q.

Adv. Opt. Photon.

IEEE Commun. Mag.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag.48(7), 62–69 (2010).
[CrossRef]

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

IEEE Trans. Commun.

P. Ciblat and M. Ghogho, “Blind NLLS carrier frequency-offset estimation for QAM, PSK, and PAM modulations: performance at low SNR,” IEEE Trans. Commun.54(10), 1725–1730 (2006).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

L. Nelson, “Polarization effects in coherent systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1A.4.

L. Nelson, M. Birk, S. L. Woodward, and P. Magill, “Field measurements of polarization transients on a long-haul terrestrial link,” in Proceedings of IEEE Photonics Conference 2011, paper ThT5.

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,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2009), paper OMT2.

G. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley & Sons, 2005), Chap. 3.

M. Morsy-Osman, M. Chagnon, Q. Zhuge, X. Xu, M. E. Mousa-Pasandi, Z. A. El-Sahn, and D. V. Plant, “Training symbol based channel estimation for ultrafast polarization demultiplexing in coherent single-carrier transmission systems with M-QAM constellations,” in Proceedings of European Conference and Exhibition on Optical Communication 2012, paper Mo.1A.4.

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Figures (5)

Fig. 1
Fig. 1

(a) Experimental setup (PBS: Polarization Beam Splitter, PBC: Polarization Beam Combiner, VOA: Variable Optical Attenuator, SW: Optical Switch, ODL: Optical Delay Line, PC: Polarization Controller), (b) Training symbols and framing synchronization header.

Fig. 2
Fig. 2

(a) Steady-state BER versus distance for all algorithms for both PDM-QPSK and PDM-16QAM, (b) Constellations after 320 km transmission for both PDM-QPSK and PDM-16QAM obtained by merely applying the inverse Jones matrix obtained by TS-EST, (c) Constellations of the same case in (d) after the butterfly filter updated using DD-LMS and carrier recovery using DD-PLL.

Fig. 3
Fig. 3

Transient BER for all algorithms for (a) PDM-QPSK, (b) PDM-16QAM.

Fig. 4
Fig. 4

BER for the TS-EST algorithm for PDM-QPSK in both high phase noise and high launch power scenarios for: (a) steady-state, (b) transient cases.

Fig. 5
Fig. 5

(a) Periodic training symbols for SOP tracking, (b) Steady-state BER versus SOP angular frequency for different algorithms for 14 Gbaud PDM-16QAM, (c) Steady-state BER versus SOP angular frequency for different algorithms for 28 Gbaud PDM-16QAM.

Equations (10)

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

R=[ a b b * a * ]
a= e jδ cosθ, b= e jφ sinθ
S rx [n]= e jψ[n] R S tx [n]= e jψ[n] [ a s tx x [n]+b s tx y [n] b * s tx x [n]+ a * s tx y [n] ]
ψ[ n ]=2πΔfT+ ψ pn [n]
T rx [k]=c e j( ξ+ψ[k] ) [ a+b b * + a * ] , T rx [k+1]=c e j( ξ+ψ[k+1] ) [ ab b * a * ]
| a | 0.5( 1+ 1 N Re{ i=0 N/2 1 ( T rx x [2i] T rx x * [2i+1]... T rx y [2i] T rx y * [2i+1] ) } )
| b | 1 | a | 2
arg{ a }+arg{ b }=arg{ i=0 N/21 ( T rx x [2i] T rx y * [2i+1]+... T rx y * [2i] T rx y [2i+1] ) }
R 1 =[ | a | | b | e j(arg{ a }+arg{ b }) | b | e j(arg{ a }+arg{ b }) | a | ]
R=[ cosωt sinωt sinωt cosωt ]

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