Abstract

We propose a joint multi-polarization-effect tracking and equalization method based on two extended Kalman filters, which can cope with state of polarization (SOP) tracing, polarization demultiplexing, equalization for polarization dependent loss (PDL) and polarization mode dispersion (PMD) in PDM-M-QAM coherent optical communication system. The mathematical model of the proposed method is given and analyzed in detail. Through simulation, the proposed method is proved to be very effective in a 28 Gbaud/s PDM-16QAM system. With the proposed method, SOP tracing speed is up to 110 Mrad/s for azimuth angle and 1200 krad/s for phase angle, respectively, and PDL and PMD can be equalized simultaneously in the values of 10 dB and more than half of the symbol period.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Joint equalization scheme of ultra-fast RSOP and large PMD compensation in presence of residual chromatic dispersion

Wei Yi, Zibo Zheng, Nan Cui, Xiaoguang Zhang, Liyuan Qiu, Nannan Zhang, Lixia Xi, Wenbo Zhang, and Xianfeng Tang
Opt. Express 27(15) 21896-21913 (2019)

Window-split structured frequency domain Kalman equalization scheme for large PMD and ultra-fast RSOP in an optical coherent PDM-QPSK system

Zibo Zheng, Nan Cui, Hengying Xu, Xiaoguang Zhang, Wenbo Zhang, Lixia Xi, Yuanyuan Fang, and Liangchuan Li
Opt. Express 26(6) 7211-7226 (2018)

Two-parameter-SOP and three-parameter-RSOP fiber channels: problem and solution for polarization demultiplexing using Stokes space

Nan Cui, Xiaoguang Zhang, Zibo Zheng, Hengying Xu, Wenbo Zhang, Xianfeng Tang, Lixia Xi, Yuanyuan Fang, and Liangchuan Li
Opt. Express 26(16) 21170-21183 (2018)

References

  • View by:
  • |
  • |
  • |

  1. P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2004), paper FI3.
  2. K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express 19(10), 9868–9880 (2011).
    [Crossref] [PubMed]
  3. H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in 34th European Conference on Optical Communication, (2008).
    [Crossref]
  4. X. Zhou, J. Yu, and P. D. Magill, “Cascaded two-modulus algorithm for blind polarization de-multiplexing of 114-Gb/s PDM-8QAM optical signals,” in Optical Fiber Communication Conference and National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWG3.
    [Crossref]
  5. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
  6. B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31(4), 648–663 (2013).
    [Crossref]
  7. Z. Yu, X. Yi, J. Zhang, M. Deng, H. Zhang, and K. Qiu, “Modified constant modulus algorithm with polarization demultiplexing in Stokes space in optical coherent receiver,” J. Lightwave Technol. 31(19), 3203–3209 (2013).
    [Crossref]
  8. T. Marshall, B. Szafraniec, and B. Nebendahl, “Kalman filter carrier and polarization-state tracking,” Opt. Lett. 35(13), 2203–2205 (2010).
    [Crossref] [PubMed]
  9. B. Szafraniec, T. Marshall, and D. M. Baney, “Kalman filtering for optical impairment estimation and compensation,” in Advanced Photonics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper SpT4D.1.
  10. Y. Yang, G. Cao, K. Zhong, X. Zhou, Y. Yao, A. P. T. Lau, and C. Lu, “Fast polarization-state tracking scheme based on radius-directed linear Kalman filter,” Opt. Express 23(15), 19673–19680 (2015).
    [Crossref] [PubMed]
  11. N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Lightwave Technol. 32(19), 3290–3298 (2014).
    [Crossref]
  12. N. J. Muga and A. N. Pinto, “Digital PDL compensation in 3D Stokes space,” J. Lightwave Technol. 31(13), 2122–2130 (2013).
    [Crossref]
  13. S. S. Haykin, Adaptive Filter Theory, Fourth Edition (Pearson Education India, 2008).
  14. R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
    [Crossref]
  15. C. Poole and D. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
    [Crossref]
  16. R. L. Eubank, A Kalman Filter Primer (Chapman and Hall, 2006).

2015 (1)

2014 (1)

2013 (3)

2011 (1)

2010 (2)

2001 (1)

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

1994 (1)

C. Poole and D. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
[Crossref]

Cao, G.

Deng, M.

Ebrahimi, P.

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

Favin, D.

C. Poole and D. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
[Crossref]

Ibragimov, E.

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

Khosravani, R.

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

Kikuchi, K.

Kuzmin, K.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in 34th European Conference on Optical Communication, (2008).
[Crossref]

Lau, A. P. T.

Lima, I. T.

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

Louchet, H.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in 34th European Conference on Optical Communication, (2008).
[Crossref]

Lu, C.

Marshall, T.

Marshall, T. S.

Menyuk, C. R.

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

Muga, N. J.

Nebendahl, B.

Pinto, A. N.

Poole, C.

C. Poole and D. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
[Crossref]

Qiu, K.

Richter, A.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in 34th European Conference on Optical Communication, (2008).
[Crossref]

Szafraniec, B.

Willner, A. E.

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

Yang, Y.

Yao, Y.

Yi, X.

Yu, Z.

Zhang, H.

Zhang, J.

Zhong, K.

Zhou, X.

IEEE Photonics Technol. Lett. (1)

R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, “Time and frequency domain characteristics of polarization-mode dispersion emulators,” IEEE Photonics Technol. Lett. 13(2), 127–129 (2001).
[Crossref]

J. Lightwave Technol. (5)

Opt. Express (3)

Opt. Lett. (1)

Other (6)

B. Szafraniec, T. Marshall, and D. M. Baney, “Kalman filtering for optical impairment estimation and compensation,” in Advanced Photonics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper SpT4D.1.

P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2004), paper FI3.

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in 34th European Conference on Optical Communication, (2008).
[Crossref]

X. Zhou, J. Yu, and P. D. Magill, “Cascaded two-modulus algorithm for blind polarization de-multiplexing of 114-Gb/s PDM-8QAM optical signals,” in Optical Fiber Communication Conference and National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWG3.
[Crossref]

S. S. Haykin, Adaptive Filter Theory, Fourth Edition (Pearson Education India, 2008).

R. L. Eubank, A Kalman Filter Primer (Chapman and Hall, 2006).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 The model of optical transmission.
Fig. 2
Fig. 2 The configuration model of receiver including the proposed polarization effect treatment module.
Fig. 3
Fig. 3 Numerical simulation system framework with two extended Kalman filters.
Fig. 4
Fig. 4 BER as the functions of (a) OSNR, (b) angular frequency of azimuth angle α, (c) angular frequency of phase angle φ, (d) PDL, and (e) PMD, respectively. (b)-(e) are at OSNR of 23 dB.
Fig. 5
Fig. 5 BER as the functions of (a)α, (b)φ, (c) PDL and (d) PMD, respectively, at OSNR equals to 23 dB.
Fig. 6
Fig. 6 (a) Convergence procedure ofα and φ at OSNR of 22dB, DGD of 14 ps and PDL of 4 dB. (b) the detail of (a) marked with the circle.

Tables (1)

Tables Icon

Table 1 Complexity Comparison between CMA-MMA-BPS and Kalman Method for Each Symbol

Equations (27)

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

q( t )=K 1 { M e 1 2 j D ω ω 2 { Rx( t ) e j( Δωt+θ ) } }+η,
R=ΑΦ=[ cosα sinα sinα cosα ][ e j φ 2 0 0 e j φ 2 ],
M=cos( ωτ )I+ sin( ωτ ) τ N,
N=[ j τ 1 j τ 2 + τ 3 j τ 2 τ 3 j τ 1 ],
τ= τ 1 2 + τ 2 2 + τ 3 2 .
y( t )= 1 { MZ( ω ) } = 1 { cos( ωτ )Z( ω )+ sin( ωτ ) τ NZ( ω ) } = 1 2 [ z( t+τ )+z( tτ ) ]j N 2τ [ z( t+τ )z( tτ ) ],
z( t )= 1 { M 1 Y( ω ) }= 1 2 [ y( t+τ )+y( tτ ) ]+j N 2τ [ y( t+τ )y( tτ ) ]
K= R 1 1 [ 1+ρ 0 0 1ρ ] R 1 ,
R 1 =[ cosβ sinβ sinβ cosβ ],
Γ( dB )=10 log 10 1ρ 1+ρ .
Φx( t ) e j( Δωt+θ ) + η = Α 1 1 { M 1 { K 1 q( t ) } } = 1 2τ Α 1 ( τI+jN ) K 1 [ q( t+τ )q( tτ ) ].
Φ k x k e j( kΔω T s + θ k ) + η k = 1 2r T s Α k 1 ( r T s I+jN ) K k 1 [ ( q k+r q kr ) ].
ρ= x k 2 + y k 2 + z k 2 ,
β= 1 2 arctan( y k x k ).
h k =( u k u k r 1 2 )( u k u k r 2 2 )( u k u k r 3 2 ),
h k =[ ( u x,k u x,k r 1 2 )( u x,k u x,k r 2 2 )( u x,k u x,k r 3 2 ) ( u y,k u y,k r 1 2 )( u y,k u y,k r 2 2 )( u y,k u y,k r 3 2 ) ],
s k = [ α k , τ 1,k , τ 2,k , τ 3,k ] T .
δ( s k )=[ 0 0 ]h( s k ).
H ij,k = h i,k s j,k , i=1,2 and j=1,2,3,4.
K k = P k H ( s ^ k ) [ H( s ^ k ) P k H ( s ^ k )+ Q 2 ] 1 ,
s ^ k = s ^ k + K k δ( s ^ k ),
s ^ k+1 = s ^ k ,
P k = P k K k H( s ^ k ) P k ,
P k+1 = P k + Q 1 ,
s k = [ φ k , θ k ] T ,
h QPSK,k =[ Re { u QPSK,x,k } 2 Im { u QPSK,x,k } 2 Re { u QPSK,y,k } 2 Im { u QPSK,y,k } 2 ],
δ k ( s k )=[ 0 0 ] h QPSK ( s k ).

Metrics