Abstract

Polarization demultiplexing is generally carried out by a multiple-input multiple-output (MIMO) based algorithm in polarization division multiplexing (PDM) coherent systems. However, in some extreme environments, the MIMO algorithm becomes inapplicable due to the ultra-fast rotation of the state of polarization (RSOP) and large polarization mode dispersion (PMD). In addition, the residual chromatic dispersion (RCD) is always present because of the mismatch of the compensated chromatic dispersion and real value induced in the optical fiber channel. According to the literature, the Kalman filter-based polarization demultiplexing algorithms possess very weak RCD tolerance. Faced with this dilemma, in this paper, a new Kalman filter structure is proposed, which can jointly compensate ultra-fast RSOP, large PMD and RCD. This Kalman filter structure enables the equalization of the RSOP in the time domain and compensation for RCD and PMD in the frequency domain. We verified the performance of the proposed Kalman scheme in the 28 Gbaud PDM-QPSK/16 QAM coherent system, with a comparison to constant modulus algorithm/multiple modulus algorithm (CMA/MMA). The simulation results confirm that, compared with CMA/MMA, the proposed Kalman scheme can provide a significant performance enhancement to cope with ultra-fast RSOP (up to 3 Mrad/s) and large PMD (more than 200 ps) with a large tolerance to RCD (over the range of ± 820 ps/nm in PDM-QPSK and ± 500 ps/nm in PDM-16 QAM).

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2018 (2)

2017 (2)

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 1–15 (2017).
[Crossref]

N. J. Muga and A. N. Pinto, “PMD tolerance in Stokes space based polarization de-multiplexing algorithms,” Opt. Quantum Electron. 49(6), 215–228 (2017).
[Crossref]

2016 (2)

2015 (1)

2013 (3)

2011 (1)

2010 (1)

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

2007 (2)

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photonics Technol. Lett. 19(13), 969–971 (2007).
[Crossref]

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

An, V. T.

Z. Chen, V. T. An, S. Chen, T. Anderson, and E. Skafidas, “Low-Complexity Fractionally-Spaced Frequency Domain Equalization with Improved Channel Estimation for Long-Haul Coherent Optical Systems,” in Optical Fiber Communication Conference (Optical Society of America, 2013), paper OW4B-5.

Anderson, T.

Z. Chen, V. T. An, S. Chen, T. Anderson, and E. Skafidas, “Low-Complexity Fractionally-Spaced Frequency Domain Equalization with Improved Channel Estimation for Long-Haul Coherent Optical Systems,” in Optical Fiber Communication Conference (Optical Society of America, 2013), paper OW4B-5.

Andrews, A. P.

G. S. Mohinder and A. P. Andrews, Kalman Filtering: Theory and Practice Using Matlab, Third Edition, (Prentice-Hall, 2008).

Bai, C.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 1–15 (2017).
[Crossref]

Bruns, J.

S. Schwarz, A. Rahim, C. Schaeffer, J. Bruns, and K. Petermann, “Fully adjustable serial-parallel FIR filter for compensation of residual chromatic dispersion,” in 38th European Conference on Optical Communication (ECOC, 2012), paper We.1.A.1.
[Crossref]

Cao, G.

Chen, H.

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

Chen, M.

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

Chen, S.

Z. Chen, V. T. An, S. Chen, T. Anderson, and E. Skafidas, “Low-Complexity Fractionally-Spaced Frequency Domain Equalization with Improved Channel Estimation for Long-Haul Coherent Optical Systems,” in Optical Fiber Communication Conference (Optical Society of America, 2013), paper OW4B-5.

Chen, Z.

Z. Chen, V. T. An, S. Chen, T. Anderson, and E. Skafidas, “Low-Complexity Fractionally-Spaced Frequency Domain Equalization with Improved Channel Estimation for Long-Haul Coherent Optical Systems,” in Optical Fiber Communication Conference (Optical Society of America, 2013), paper OW4B-5.

Ciaramella, E.

Corsini, R.

Cui, N.

Fang, Y.

Faruk, M. S.

Feng, Y.

Foggi, T.

Goldfarb, G.

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photonics Technol. Lett. 19(13), 969–971 (2007).
[Crossref]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Gorshtein, A.

A. Gorshtein and D. Sadot, “Symbol spaced adaptive MIMO equalization for ultrahigh bit rate metro coherent optical links,” IEEE Photonics Technol. Lett. 25(5), 414–417 (2013).
[Crossref]

Herrmann, M.

Howard, M.

Z. Paul and M. Howard, Fundamentals of Kalman Filtering: A Practical Approach, Third Edition, (AIAA, 2009).

Jenau, F.

Kikuchi, K.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Krummrich, P. M.

Lau, A. P.

Li, G.

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photonics Technol. Lett. 19(13), 969–971 (2007).
[Crossref]

Li, L.

Lin, J.

Lu, C.

Magri, R.

Marshall, T. S.

Matarazzo, E.

Meloni, G.

Mohinder, G. S.

G. S. Mohinder and A. P. Andrews, Kalman Filtering: Theory and Practice Using Matlab, Third Edition, (Prentice-Hall, 2008).

Muga, N. J.

N. J. Muga and A. N. Pinto, “PMD tolerance in Stokes space based polarization de-multiplexing algorithms,” Opt. Quantum Electron. 49(6), 215–228 (2017).
[Crossref]

Nebendahl, B.

Nijhof, J.

Paul, Z.

Z. Paul and M. Howard, Fundamentals of Kalman Filtering: A Practical Approach, Third Edition, (AIAA, 2009).

Peracchi, A.

Petermann, K.

S. Schwarz, A. Rahim, C. Schaeffer, J. Bruns, and K. Petermann, “Fully adjustable serial-parallel FIR filter for compensation of residual chromatic dispersion,” in 38th European Conference on Optical Communication (ECOC, 2012), paper We.1.A.1.
[Crossref]

Pinto, A. N.

N. J. Muga and A. N. Pinto, “PMD tolerance in Stokes space based polarization de-multiplexing algorithms,” Opt. Quantum Electron. 49(6), 215–228 (2017).
[Crossref]

Poti, L.

Qiu, C.

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

Rahim, A.

S. Schwarz, A. Rahim, C. Schaeffer, J. Bruns, and K. Petermann, “Fully adjustable serial-parallel FIR filter for compensation of residual chromatic dispersion,” in 38th European Conference on Optical Communication (ECOC, 2012), paper We.1.A.1.
[Crossref]

Ronnenberg, D.

Sadot, D.

A. Gorshtein and D. Sadot, “Symbol spaced adaptive MIMO equalization for ultrahigh bit rate metro coherent optical links,” IEEE Photonics Technol. Lett. 25(5), 414–417 (2013).
[Crossref]

Savory, S. J.

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

Schaeffer, C.

S. Schwarz, A. Rahim, C. Schaeffer, J. Bruns, and K. Petermann, “Fully adjustable serial-parallel FIR filter for compensation of residual chromatic dispersion,” in 38th European Conference on Optical Communication (ECOC, 2012), paper We.1.A.1.
[Crossref]

Schairer, W.

Schwarz, S.

S. Schwarz, A. Rahim, C. Schaeffer, J. Bruns, and K. Petermann, “Fully adjustable serial-parallel FIR filter for compensation of residual chromatic dispersion,” in 38th European Conference on Optical Communication (ECOC, 2012), paper We.1.A.1.
[Crossref]

Shi, Y.

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

Simon, H.

H. Simon, Adaptive filter theory, Fourth Edition (Prentice Hall, 2002).

Skafidas, E.

Z. Chen, V. T. An, S. Chen, T. Anderson, and E. Skafidas, “Low-Complexity Fractionally-Spaced Frequency Domain Equalization with Improved Channel Estimation for Long-Haul Coherent Optical Systems,” in Optical Fiber Communication Conference (Optical Society of America, 2013), paper OW4B-5.

Szafraniec, B.

Tang, X.

Wienold, D.

Xi, L.

Xie, S.

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

Xu, H.

Yang, Y.

Yao, Y.

Zhang, W.

Zhang, X.

Zheng, H.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 1–15 (2017).
[Crossref]

Zheng, Z.

Zhong, K.

Zhou, X.

IEEE J Select. Topics Quantum Electron. (1)

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

IEEE Photonics J. (1)

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 1–15 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (3)

M. Chen, Y. Shi, C. Qiu, H. Chen, and S. Xie, “Residual chromatic-dispersion monitoring and dynamic compensation in 40-Gb/s systems,” IEEE Photonics Technol. Lett. 19(15), 1142–1144 (2007).
[Crossref]

A. Gorshtein and D. Sadot, “Symbol spaced adaptive MIMO equalization for ultrahigh bit rate metro coherent optical links,” IEEE Photonics Technol. Lett. 25(5), 414–417 (2013).
[Crossref]

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photonics Technol. Lett. 19(13), 969–971 (2007).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (6)

Opt. Quantum Electron. (1)

N. J. Muga and A. N. Pinto, “PMD tolerance in Stokes space based polarization de-multiplexing algorithms,” Opt. Quantum Electron. 49(6), 215–228 (2017).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Other (8)

J. N. Damask, Polarization Optics in Telecommunications (Springer-Verlag, 2005).

Z. Chen, V. T. An, S. Chen, T. Anderson, and E. Skafidas, “Low-Complexity Fractionally-Spaced Frequency Domain Equalization with Improved Channel Estimation for Long-Haul Coherent Optical Systems,” in Optical Fiber Communication Conference (Optical Society of America, 2013), paper OW4B-5.

M. Kuscherov and M. Herrmann, “Lightning affects coherent optical transmission in aerial fiber,” (Lightwave, 2016), http://www.lightwaveonline.com/articles/2016/03/lightning-affects-coherent-optical-transmission-in-aerial-fiber.html .

H. Simon, Adaptive filter theory, Fourth Edition (Prentice Hall, 2002).

C. Xie, “Polarization and nonlinear impairments in fiber communication systems,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, eds. (Wiley, 2016).

S. Schwarz, A. Rahim, C. Schaeffer, J. Bruns, and K. Petermann, “Fully adjustable serial-parallel FIR filter for compensation of residual chromatic dispersion,” in 38th European Conference on Optical Communication (ECOC, 2012), paper We.1.A.1.
[Crossref]

Z. Paul and M. Howard, Fundamentals of Kalman Filtering: A Practical Approach, Third Edition, (AIAA, 2009).

G. S. Mohinder and A. P. Andrews, Kalman Filtering: Theory and Practice Using Matlab, Third Edition, (Prentice-Hall, 2008).

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Figures (14)

Fig. 1
Fig. 1 (a) Simplification of a generalized combined model of PMD and RSOP; (b) optical transmission model.
Fig. 2
Fig. 2 The proposed polarization effect treatment module.
Fig. 3
Fig. 3 Window-split structure.
Fig. 4
Fig. 4 The flow chart of the proposed Kalman scheme.
Fig. 5
Fig. 5 Simulation platform
Fig. 6
Fig. 6 BER vs. RCD with different window lengths of Kalman filter and different filter lengths of CMA in PDM-QPSK signals. (a) DGD = 50 ps RSOP = 100 krad/s (b) DGD = 100 ps RSOP = 500 krad/s.
Fig. 7
Fig. 7 BER vs. RCD with different window lengths of Kalman filter and different filter lengths of CMA-MMA in PDM-16 QAM signals. (a) DGD = 50 ps RSOP = 100 krad/s (b) DGD = 100 ps RSOP = 500 krad/s.
Fig. 8
Fig. 8 BER vs. RCD with different step sizes of CMA in PDM-QPSK signals. (a) DGD = 50 ps RSOP = 100 krad/s (b) DGD = 100 ps RSOP = 500 krad/s.
Fig. 9
Fig. 9 BER vs. RCD with different step sizes of the CMA-MMA in PDM-16 QAM signals. (a) DGD = 50 ps RSOP = 100 krad/s (b) DGD = 100 ps RSOP = 500 krad/s.
Fig. 10
Fig. 10 Performance evaluation: BER vs. OSNR (a) and (c) in PDM-QPSK, (b) and (d) in PDM-16 QAM.
Fig. 11
Fig. 11 Performance evaluation: (a) and (b) BER vs. RSOP in PDM-QPSK and PDM-16 QAM. (c) and (d) BER vs. RCD in PDM-QPSK and PDM-16 QAM.
Fig. 12
Fig. 12 Performance evaluation of RCD tracking for the proposed Kalman scheme: (a) and (b) RCD tracking error curve in PDM-QPSK and PDM-16 QAM.
Fig. 13
Fig. 13 The window-split structure and the window sliding forward.
Fig. 14
Fig. 14 The signal recovery from the received one to the recovered one.

Tables (1)

Tables Icon

Table 1 Computational complexity comparison

Equations (22)

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

( cos α 2 e j δ 2 sin α 2 e j δ 2 sin α 2 cos α 2 )( e jωΔτ/2 0 0 e jωΔτ/2 )( cos α 1 e j δ 1 sin α 1 e j δ 1 sin α 1 cos α 1 ).
q( t )= F 1 { U e j β 2 ω 2 2 z F{ Ms( t ) e j( Δωt+θ ) } }+η.
M eq =[ e jξ cosκ e jη sinκ e jη sinκ e jξ cosκ ].
U eq (ω)=cos( ωΔτ 2 )I j( τ σ ) Δτ sin( ωΔτ 2 ).
G( z,ω )=exp( j D λ 2 ω 2 4πc z ).
g eq ( ω )=exp( j ρ λ 2 ω 2 4πc ).
x k = ( τ 1 , τ 2 , τ 3 ,κ,ξ,η,ρ ) T .
h( x k )=[ i=1 m ( u x,k u x,k * r i 2 ) i=1 m ( u y,k u y,k * r i 2 ) ].
d k =[ 0 0 ] h k ( x ^ k| k1 ).
x k =f( x k1 )+ w k1 .
z k =h( x k )+ v k .
x ^ 0 =E( x 0 ), P 0 =E[( x 0 x ^ 0 ) ( x 0 x ^ 0 ) T ].
x ^ k|k1 = F k1 x ^ k1 , P k|k1 = P k1 + Q k1 .
d k = z k h k ( x ^ k|k1 ) K k = P k|k1 H k T [ H k P k|k1 H k T + R k ] 1 .
x ^ k = x ^ k|k1 + K k d k P k = (I K k H k ) P k|k1 .
x k = ( τ 1 T s , τ 2 T s , τ 3 T s , κ 2π , ξ 2π , η 2π , ρ ρ 0 ) T .
q t =[ q i q i+1 q i+ L w 1 ].
g eq ( ω )= A 0 , U eq ( ω )=( A 1 A 2 A 3 A 4 ), M eq =( A 5 A 6 A 7 A 8 ).
d k =[ 0 0 ] h k ( x ^ k| k1 ), h k ( x ^ k )=[ ( u x,k u x,k 1 ) ( u y,k u y,k 1 ) ].
H τ 1 ,k = [ u x ( u x τ 1 ) + u x * ( u x τ 1 ) u y ( u y τ 1 ) + u y * ( u y τ 1 ) ] k .
u x τ 1 = A 5 q Ugt x τ 1 + A 6 q Ugt y τ 1 , u y τ 1 = A 7 q Ugt x τ 1 + A 8 q Ugt y τ 1 .
q Ugt x τ 1 =ifft( A 1 τ 1 A 0 q f x + A 2 τ 1 A 0 q f y ), q Ugt y τ 1 =ifft( A 3 τ 1 A 0 q f x + A 4 τ 1 A 0 q f y ).

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