Abstract

Simultaneous polarization and phase noise tracking and compensation is proposed based on an unscented Kalman filter (UKF). We experimentally demonstrate the tracking under noise-loading and after 800-km single-mode fiber transmission with 20-Gbaud QPSK and 16-QAM signals. These experiments show that the proposed UKF outperforms both conventional blind tracing algorithms and a previously proposed extended Kalman filter, at the cost of higher complexity. Additionally, we propose and test modified Kalman filter algorithms to reduce computational complexity.

© 2016 Optical Society of America

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    [Crossref] [PubMed]
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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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    [Crossref]
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    [Crossref]
  12. H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Proceedings of European Conference and Exhibition on Optical Communication (2008), pp. 57–58.
    [Crossref]
  13. C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
    [Crossref]
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2015 (2)

2013 (1)

2012 (1)

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

2011 (2)

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

D. S. Millar and S. J. Savory, “Blind adaptive equalization of polarization-switched QPSK modulation,” Opt. Express 19(9), 8533–8538 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

1977 (1)

Agrell, E.

Alvarado, A.

Anderson, T.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

Bayvel, P.

Berry, H. G.

Borel, P. I.

Cao, G.

Carlson, K.

Chen, J.

Chen, S.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

Ciblat, P.

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. of European Conference and Exhibition on Optical Communication (2009), pp. 1–2.

Du, L. B.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

Forzati, M.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Friberg, A. T.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Gabrielse, G.

Isaac, R.

Islam, A. H. M. R.

R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in Proc. of International Conference on Electrical and Computer Engineering (2006), pp. 408–411.
[Crossref]

Jacobsen, G.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Jaouen, Y.

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. of European Conference and Exhibition on Optical Communication (2009), pp. 1–2.

Kam, P. Y.

Kuzmin, K.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Proceedings of European Conference and Exhibition on Optical Communication (2008), pp. 57–58.
[Crossref]

Lau, A. P. T.

Lavery, D.

Li, J.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Livingston, A. E.

Louchet, H.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Proceedings of European Conference and Exhibition on Optical Communication (2008), pp. 57–58.
[Crossref]

Lowery, A. J.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

Lu, C.

Magill, P.

Maher, R.

Marshall, T.

Mårtensson, J.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Millar, D. S.

Mussolin, M.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Nebendahl, B.

Nelson, L. E.

Peckham, D. W.

Popov, S.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Rahman, M. S.

R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in Proc. of International Conference on Electrical and Computer Engineering (2006), pp. 408–411.
[Crossref]

Richter, A.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Proceedings of European Conference and Exhibition on Optical Communication (2008), pp. 57–58.
[Crossref]

Savory, S. J.

Selmi, M.

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. of European Conference and Exhibition on Optical Communication (2009), pp. 1–2.

Shafik, R. A.

R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in Proc. of International Conference on Electrical and Computer Engineering (2006), pp. 408–411.
[Crossref]

Skafidas, E.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

Szafraniec, B.

Taylor, M. G.

Tran, A. V.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

van der Merwe, R.

E. A. Wan and R. van der Merwe, “The unscented Kalman filter for nonlinear estimation”, in Proc. IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium Conference (2000), (2000), pp. 153–158.
[Crossref]

Wan, E. A.

E. A. Wan and R. van der Merwe, “The unscented Kalman filter for nonlinear estimation”, in Proc. IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium Conference (2000), (2000), pp. 153–158.
[Crossref]

Wang, K.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Xu, T.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Yang, Y.

Yao, Y.

Yu, C.

Zhang, S.

Zhang, Y.

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Zhong, K.

Zhou, X.

Zhu, B.

Zhu, C.

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

Appl. Opt. (1)

IEEE Photonics J. (1)

C. Zhu, A. V. Tran, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photonics J. 4(5), 1653–1661 (2012).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Commun. (1)

T. Xu, G. Jacobsen, S. Popov, M. Forzati, J. Mårtensson, M. Mussolin, J. Li, K. Wang, Y. Zhang, and A. T. Friberg, “Frequency-domain chromatic dispersion equalization using overlap-add methods in coherent optical system,” J. Opt. Commun. 32(2), 131–135 (2011).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (9)

E. A. Wan and R. van der Merwe, “The unscented Kalman filter for nonlinear estimation”, in Proc. IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium Conference (2000), (2000), pp. 153–158.
[Crossref]

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. of European Conference and Exhibition on Optical Communication (2009), pp. 1–2.

OIF-Tech-Options-400G–01.0 – Technology Options for 400G Implementation (July 2015) (White paper). Available: http://www.oiforum.com/wp-content/uploads/OIF-Tech-Options-400G-01.0.pdf .

R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in Proc. of International Conference on Electrical and Computer Engineering (2006), pp. 408–411.
[Crossref]

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Proceedings of European Conference and Exhibition on Optical Communication (2008), pp. 57–58.
[Crossref]

J. Jokhakar, B. Corcoran, C. Zhu, and A. J. Lowery, “Unscented Kalman filters for polarization state tracking and phase noise mitigation,” in Proc. of Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.4.
[Crossref]

S. Kay, Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory (Wiley, 1993).

D. Chang, F. Yu, Z. Xiao, N. Stojanovic, F. N. Hauske, Y. Cai, C. Xie, L. Li, X. Xu, and Q. Xiong, “LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission,” in Proc. of Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW1H.4.
[Crossref]

R. Driggers, Encyclopedia of Optical Engineering, Volume 2, (Marcel Dekker Inc. 2003).

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Figures (8)

Fig. 1
Fig. 1

Block representation of extended Kalman filter (EKF) and unscented Kalman filter (UKF).

Fig. 2
Fig. 2

Experimental setup for a) back-to-back configuration and b) 800-km transmission link configuration; CMZM: complex Mach-Zehnder modulator, BPF: band pass filter, VOA: variable optical attenuator, ECL: external cavity laser, EDFA: erbium doped fiber amplifier.

Fig. 3
Fig. 3

Digital signal processing flow for a) CMA + VVPE/MMA + ML b) Kalman filters under test.

Fig. 4
Fig. 4

Q-value vs. OSNR in back-to-back configuration for 20 Gbaud QPSK and 20 Gbaud 16-QAM respectively.

Fig. 5
Fig. 5

Q-value vs. launch power (dBm) in 800 km link configuration for 20 Gbaud QPSK and 16-QAM respectively.

Fig. 6
Fig. 6

Q (dB) vs linewidth (kHz) for 8 dB OSNR, QPSK; 20 dB OSNR, QPSK; 15 dB OSNR, 16 QAM and 20 dB OSNR, 16 QAM respectively.

Fig. 7
Fig. 7

Q (dB) vs. PMD (ps) for 8 dB OSNR, QPSK; 20 dB OSNR, QPSK; 15 dB OSNR, 16 QAM and 20 dB OSNR, 16 QAM respectively.

Fig. 8
Fig. 8

Poincare sphere showing different polarizations with Stokes parameter and equivalent [a, b, c, d] parameters in the form {(S1, S2, S3);(a, b, c, d)}.

Tables (1)

Tables Icon

Table 1 Number of complex multiplications per symbol detection required by the algorithms.

Equations (22)

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

Z= e jθ ( a+jb c+jd c+jd ajb )( T x T y )+N
Q BER =20 log 10 ( 2(M1) 3 ×erf c 1 ( BER× log 2 M ( 1 1 M ) ) )
J= e jθ [ Z x    j Z x      Z y j Z y j( a+jb ) Z x +j( c+jd ) Z y ) Z y j Z y Z x j Z x j( c+jd ) Z x +j( ajb ) Z y ]
J=[ e jθ Z x e jθ Z y j( e jθ a ˜ Z x + e jθ c ˜ Z y ) e jθ Z y * e jθ Z x * j( e jθ c ˜ Z x * e jθ a ˜ Z y * ) ]
S 0 = [0,0,...0] 1×L T
P 0 = [0] L×L
A= I L×L
S i =A S i1
P i =A P i1 A T +Q
t ik = e j{ ( S i ) k (5)} [ { ( S i ) k (1)}+j{ ( S i ) k (2)} { ( S i ) k (3)}+j{ ( S i ) k (4)} { ( S i ) k (3)}+j{ ( S i ) k (4)} { ( S i ) k (1)}j{ ( S i ) k (2)} ][ Z x Z y ]
t ^ í = k=0 2L ω k (m) t ik
P tt = k=0 2L ω k (c) ( t ik t ^ i ) ( t ik t ^ i ) * +R P tt = k=0 2L ω k (c) ( t ik t ^ i ) ( t ik t ^ i ) * +R
P ts = k=0 2L ω k (c) ( ( S i ) k ( S i ) f ) ( t ik t ^ i ) *
ω 0 (m) =λ/(L+λ)
ω 0 (c) ={λ/(L+λ)}+(1 α 2 +β)
S i = ( S i ) f + G i [ t ^ i decision( t ^ i )]
P i = P i G i P tt G i *
M=[ e jη/2 cos 2 ϑ+ e jη/2 sin 2 ϑ ( e jη/2 e jη/2 ) e jϕ cosϑsinϑ ( e jη/2 e jη/2 ) e jϕ cosϑsinϑ e jη/2 cos 2 ϑ+ e jη/2 sin 2 ϑ ]
M=[ a+jb c+jd c+jd ajb ]
Now, X n =    a n +j b n = a n1 2 + b n1 2 + (Δa) 2 + (Δb) 2 +j(2aΔa+2bΔb)
X n = X n1 ( 1+ (Δa) 2 + (Δb) 2 +j(2aΔa+2bΔb) X n1 2 ) ( from ( 7 ) )
ΔX= X n1 ( 1+ (Δa) 2 + (Δb) 2 +j(2aΔa+2bΔb) X n1 2 1 )

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