Abstract

We propose and experimentally demonstrate a fast polarization tracking scheme based on radius-directed linear Kalman filter. It has the advantages of fast convergence and is inherently insensitive to phase noise and frequency offset effects. The scheme is experimentally compared to conventional polarization tracking methods on the polarization rotation angular frequency. The results show that better tracking capability with more than one order of magnitude improvement is obtained in the cases of polarization multiplexed QPSK and 16QAM signals. The influences of the filter tuning parameters on tracking performance are also investigated in detail.

© 2015 Optical Society of America

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References

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  1. P. M. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, 2004 OSA Technical Digest Series (Optical Society of America, 2004), paper FI3.
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2014 (2)

2013 (1)

2011 (1)

2010 (2)

2009 (1)

2008 (1)

Agrell, E.

Andrekson, P. A.

Bishop, G.

G. Welch and G. Bishop, “An introduction to the Kalman filter,” in Proceedings of the Siggraph Course, Los Angeles (2001).

Fatadin, I.

Inoue, T.

Ives, D.

Johannisson, P.

Karlsson, M.

Marshall, T.

Marshall, T. S.

Muga, N. J.

Namiki, S.

Nebendahl, B.

Pinto, A. N.

Savory, S. J.

Sjödin, M.

Szafraniec, B.

Tan, A. S.

Welch, G.

G. Welch and G. Bishop, “An introduction to the Kalman filter,” in Proceedings of the Siggraph Course, Los Angeles (2001).

Wymeersch, H.

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (1)

Opt. Express (3)

Opt. Lett. (1)

Other (6)

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Frequency Offset Estimation Using Kalman Filter in Coherent Optical Phase-Shift Keying Systems,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (Optical Society of America, 2010), paper CThDD4.
[Crossref]

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

V. B. Ribeiro, J. C. Oliveira, J. C. Diniz, E. Rosa, R. Silva, E. P. Silva, L. H. Carvalho, and A. C. Bordonalli, “Enhanced Digital Polarization Demultiplexation via CMA Step Size Adaptation for PM-QPSK Coherent Receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW3H.4.
[Crossref]

L. Pakala and B. Schmauss, “Joint compensation of phase and amplitude noise using extended Kalman filter in coherent QAM systems,” in European Conference on Optical Communication (IEEE, 2014), paper Tu.1.3.2.
[Crossref]

G. Cao, Y. Yang, K. Zhong, X. Zhou, Y. Yao, A. P. T. Lau, and C. Lu, “Fast Polarization-State Tracking Based on Radius-Directed Linear Kalman Filter,” in Optical Fiber Communication Conference, 2015 OSA Technical Digest Series (Optical Society of America, 2015), paper Th4F.2.
[Crossref]

G. Welch and G. Bishop, “An introduction to the Kalman filter,” in Proceedings of the Siggraph Course, Los Angeles (2001).

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Figures (7)

Fig. 1
Fig. 1 Kalman process and the computation of ∆U(k).
Fig. 2
Fig. 2 Experimental setup and digital signal processing modules of a 112 Gb/s PDM-QPSK/PDM-16QAM coherent optical communication system.
Fig. 3
Fig. 3 The constellation graphs after RD-LKF and the estimated {a b c d} with Q = 1e-3 (a, b), Q = 1e-5 (c, d), Q = 1e-7 (e, f).
Fig. 4
Fig. 4 (a) BER vs. OSNR (dB/0.1nm) under different Q for 3Mrad/s polarization rotation; (b) The BER as a function of polarization rotation frequency under different Q.
Fig. 5
Fig. 5 The estimated parameters a, b, c and d for (a) PDM QPSK and (b) PDM 16QAM.
Fig. 6
Fig. 6 Q-factor performance versus polarization rotation angular frequency for (a) QPSK and (b) 16QAM.
Fig. 7
Fig. 7 The scheme of two stage RD-LKF.

Equations (16)

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Z(t)=αJ(t)X(t) e j(Δωt) e jθ(t) +ξ(t),
X(t) e j(Δωt) e jθ(t) +ξ'(t)= (αJ(t)) 1 Z(t)=[ a(t)+jb(t) c(t)+jd(t) c(t)+jd(t) a(t)jb(t) ][ Z x (t) Z y (t) ],
H(k)=[ Z x (k) j Z x (k) Z y (k) j Z y (k) Z y (k) -j Z y (k) - Z x (k) j Z x (k) ],
S(k)= [a(k) b(k) c(k) d(k)] T ,
U(k)=H(k)S(k)+v(k),
S( k )=S( k1 )+w( k ).
S (k)=S(k1)
P (k)=P(k1)+Q
K(k)= P (k) H T (k) (H(k) P (k) H T (k)+R) 1
ΔU(k)= U c (k)U(k)= U c (k)H(k) S (k)
S(k)= S (k)+K(k)ΔU(k)
P(k)= P (k)K(k)H(k) P (k)
U c ( k )= [ r x · U x ( k ) | U x ( k ) |   r y · U y ( k ) | U y ( k ) | ] T ,
H DME (k)=[ H(k) H(k) ]
U DME (k)=[ U(k) U(k) ]= H DME (k) S (k)
Δ U DME (k)=[ Δ U QPSK (k) Δ U 16QAM (k) ]=[ U c (k) QPSK U c (k) 16QAM ] U DME (k)

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