Abstract

We propose a training symbols-free polarization demultiplexing method by constructing a cost function (CCF-PDM) for coherent optical PDM-OFDM. This method is applicable for high-speed, wide-bandwidth OFDM signals, different subcarrier modulation formats and long-haul transmission. It shows comparable performance with that of conventional method but without overhead and converges fast. Since the neighboring subcarriers experience similar polarization effects, we set the initial matrix parameters by the neighboring subcarrier to reduce the number of iteration for the gradient algorithm and prevent swapping the data of the two orthogonal polarizations. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960km SSMF respectively. We compare its performance with that of training symbols. We also analyze the convergence speed of this method.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2014 (2)

X. Li, W.-D. Zhong, A. Alphones, and C. Yu, “Channel equalization using independent component analysis in PDM-CO-OFDM,” IEEE Photonics Technol. Lett. 26(5), 497–500 (2014).
[Crossref]

Z. Yu, X. Yi, J. Zhang, D. Zhao, and K. Qiu, “Experimental demonstration of polarization-dependent loss monitoring and compensation in stokes space for coherent optical PDM-OFDM,” J. Lightwave Technol. 32(23), 3926–3931 (2014).

2013 (3)

2011 (4)

2010 (2)

2008 (3)

2007 (1)

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

2006 (1)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

Alphones, A.

X. Li, W.-D. Zhong, A. Alphones, and C. Yu, “Channel equalization using independent component analysis in PDM-CO-OFDM,” IEEE Photonics Technol. Lett. 26(5), 497–500 (2014).
[Crossref]

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

Buchali, F.

Chandrasekhar, S.

Chen, C.

Chen, L.

Chen, X.

Cvijetic, N.

Deng, M.

Dimarcello, F. V.

Doran, N.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Ellis, A. D.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Fini, J. M.

Fishteyn, M.

Fontaine, N. K.

Freude, W.

R. Schmogrow, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “Blind polarization demultiplexing with low computational complexity,” IEEE Photonics Technol. Lett. 25(13), 1230–1233 (2013).
[Crossref]

Giacoumidis, E.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Gnauck, A. H.

Haigh, P. A.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Hu, J.

Jansen, S. L.

Kikuchi, K.

Koos, C.

R. Schmogrow, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “Blind polarization demultiplexing with low computational complexity,” IEEE Photonics Technol. Lett. 25(13), 1230–1233 (2013).
[Crossref]

Le, S. T.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Leuthold, J.

R. Schmogrow, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “Blind polarization demultiplexing with low computational complexity,” IEEE Photonics Technol. Lett. 25(13), 1230–1233 (2013).
[Crossref]

Li, X.

X. Li, W.-D. Zhong, A. Alphones, and C. Yu, “Channel equalization using independent component analysis in PDM-CO-OFDM,” IEEE Photonics Technol. Lett. 26(5), 497–500 (2014).
[Crossref]

Liu, X.

Luo, M.

Mac Suibhne, N.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

McCarthy, M.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Monberg, E. M.

Morita, I.

Pan, Y.

Peckham, D. W.

Plant, D. V.

Qian, D.

Qiu, K.

Schenk, T. C.

Schindler, P. C.

R. Schmogrow, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “Blind polarization demultiplexing with low computational complexity,” IEEE Photonics Technol. Lett. 25(13), 1230–1233 (2013).
[Crossref]

Schmogrow, R.

R. Schmogrow, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “Blind polarization demultiplexing with low computational complexity,” IEEE Photonics Technol. Lett. 25(13), 1230–1233 (2013).
[Crossref]

Scott, R. P.

Shieh, W.

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

Takeda, N.

Tanaka, H.

Tang, Y.

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

Taunay, T. F.

Turitsyn, S. K.

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

Wang, T.

Winzer, P. J.

Yan, M. F.

Yang, Q.

Yi, X.

Yoo, S. J. B.

Yu, C.

X. Li, W.-D. Zhong, A. Alphones, and C. Yu, “Channel equalization using independent component analysis in PDM-CO-OFDM,” IEEE Photonics Technol. Lett. 26(5), 497–500 (2014).
[Crossref]

Yu, Z.

Zhang, H.

Zhang, J.

Zhao, D.

Zhong, W.-D.

X. Li, W.-D. Zhong, A. Alphones, and C. Yu, “Channel equalization using independent component analysis in PDM-CO-OFDM,” IEEE Photonics Technol. Lett. 26(5), 497–500 (2014).
[Crossref]

Zhu, B.

Zhuge, Q.

Electron. Lett. (1)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (3)

X. Li, W.-D. Zhong, A. Alphones, and C. Yu, “Channel equalization using independent component analysis in PDM-CO-OFDM,” IEEE Photonics Technol. Lett. 26(5), 497–500 (2014).
[Crossref]

R. Schmogrow, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “Blind polarization demultiplexing with low computational complexity,” IEEE Photonics Technol. Lett. 25(13), 1230–1233 (2013).
[Crossref]

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

J. Lightwave Technol. (6)

J. Opt. Netw. (1)

Opt. Express (5)

Other (4)

X. Chen, J. He, D. Che, and W. Shieh, “Demonstration of software-defined multiband OFDM with low-complexity phase noise compensation,” in Proc. OFC 2014, paper Tu2G.3.
[Crossref]

S. T. Le, M. McCarthy, N. Mac Suibhne, P. A. Haigh, E. Giacoumidis, N. Doran, A. D. Ellis, and S. K. Turitsyn, “Decision-directed-free blind phase noise estimation for CO-OFDM,” in Proceedings of the OFC2015, paper W1E.5.
[Crossref]

T. Bo, L. Huang, and C. K. Chan, “Image processing based common phase estimation for coherent optical orthogonal frequency division multiplexing system,” in Proc. OFC 2015, paper W1E.8.
[Crossref]

H. Kogelnik, at al. “Polarization-mode dispersion,” in Optical Fiber Telecommunications IV B, I. Kaminow, T. Li, (Elsevier Science, 2002) 725–861.

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Figures (4)

Fig. 1
Fig. 1 Cost function J(α,ϕ) for one OFDM subcarrier with 4QAM modulation (a) three-dimensional view and (b) two-dimensional view; Constellations of received PDM-OFDM signals (c) before and (d) after CCF-PDM, and (e) after PDL compensation, phase noise compensation and channel compensation, respectively.
Fig. 2
Fig. 2 Experimental setup. PBS/C: Polarization beam splitter/combiner; ECL: External cavity laser; SW: switch; OTF: optical tunable filter.
Fig. 3
Fig. 3 (a) BER results of 66.7-Gb/s PDM-OFDM with 4QAMsubcarrier modulation using CCF-PDM and TSs respectively; (b) and (c) Constellations after transmission over 5440km with 4QAM subcarrier modulation using CCF-PDM vs. OSNR 18.42dB; (d) BER results of 133.3-Gb/s PDM-OFDM with 16QAM subcarrier modulation using CCF-PDM and TSs respectively; (e) and (f) Constellations after transmission over 960km with 16QAM subcarrier modulation using CCF-PDM vs. OSNR 26.75dB.
Fig. 4
Fig. 4 (a) Speed of convergence of CCF-PDM of 4QAM subcarrier modulation. (b) Number of iteration for the gradient algorithm to find the correct matrix parameters of one subcarrier.

Equations (4)

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s ki r =exp(j φ i )exp(j Φ k ) M k s ki t + n ki .
( s ki,x t' s ki,y t' )=( a * (k) b(k) b * (k) a(k) )( s ki,x r s ki,y r )=( cosα e jϕ sinα e jϕ sinα cosα )( s ki,x r s ki,y r ).
J(α,ϕ)= | s k,x t' | + | s k,y t' | = 1 I i=1 I [ | s ki,x t' |+| s ki,y t' | ] .
J= J α e α + J ϕ e ϕ .

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