Abstract

We propose and experimentally demonstrate a modulation-format-transparent dual-polarization (DP) transmitter (Tx) in-phase/quadrature (IQ) imbalance estimation scheme based on maximum likelihood independent component analysis (ML-ICA). The proposed scheme can separate Tx IQ imbalance from polarization crosstalk and phase noise and achieve accurate IQ imbalance estimation without training data and the information of modulation format. Firstly, the complex-ML-ICA is used to implement format-transparent polarization de-multiplexing to remove polarization crosstalk; then the real-ML-ICA is employed to estimate inverse IQ mixing matrix and compensate Tx IQ imbalance/phase noise on each polarization channel. Inverse IQ mixing matrix contains the information of phase noise and Tx IQ imbalance; Finally, Tx IQ imbalance is derived from the inverse matrix by analytic method. The impact of Tx IQ imbalance on polarization demultiplexing and carrier phase recovery (CPE) is investigated by numerical simulation from three aspects of Jones space, Stokes space, and Kurtosis. The simulation results demonstrate the proposed scheme has strong robustness to phase noise, quantization noise, and amplified spontaneous emission (ASE) noise. The proposed ML-ICA algorithm is verified experimentally in polarization division multiplexing (PDM) quadrature phase-shift keying (QPSK)/8 quadrature amplitude modulation (QAM)/16QAM/64QAM systems. The experimental results show the scheme can accurately estimate Tx IQ imbalance within wide range in a format transparent manner.

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

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J. Opt. Commun. Netw. 9(9) D42-D50 (2017)

References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

2018 (4)

2017 (3)

2016 (1)

2015 (1)

R. Goścień, K. Walkowiak, and M. Klinkowski, “Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic,” Comput. Netw. 79(14), 148–165 (2015).
[Crossref]

2014 (1)

A. Georgiadis and C. Kalialakis, “Evaluation of error vector magnitude due to combined IQ imbalances and phase noise,” IET Circuits Dev. Syst. 8(6), 421–426 (2014).
[Crossref]

2013 (1)

M. S. Faruk and K. Kikuchi, “Compensation for in-phase/quadrature imbalance in coherent-receiver front end for optical quadrature amplitude modulation,” IEEE Photonics J. 5(2), 7800110 (2013).
[Crossref]

2011 (1)

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (1)

2008 (1)

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

2006 (1)

1988 (1)

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

Adali, T.

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

Alphones, A.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Anderson, J.

Aoudia, F. A.

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

Berder, O.

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

Bramerie, L.

Calhoun, V. D.

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

Correa, N. M.

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

Cui, N.

Da Ros, F.

Da Silva, E.

Demir, A.

Diniz, J.

Erdogan, A. T.

Fan, Y.

J. Liang, Y. Fan, Z. Tao, H. Nakashima, and T. Hoshida, “Transceiver in-phase and quadrature imbalance monitoring by two stage MIMO equalizers,” 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–4. doi:
[Crossref]

Fang, Y.

Faruk, M.

Faruk, M. S.

M. S. Faruk and K. Kikuchi, “Compensation for in-phase/quadrature imbalance in coherent-receiver front end for optical quadrature amplitude modulation,” IEEE Photonics J. 5(2), 7800110 (2013).
[Crossref]

Fatadin, I.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Gautier, M.

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

Gay, M.

Georgiadis, A.

A. Georgiadis and C. Kalialakis, “Evaluation of error vector magnitude due to combined IQ imbalances and phase noise,” IET Circuits Dev. Syst. 8(6), 421–426 (2014).
[Crossref]

Goldfarb, G.

Goscien, R.

R. Goścień, K. Walkowiak, and M. Klinkowski, “Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic,” Comput. Netw. 79(14), 148–165 (2015).
[Crossref]

Guo, C.

Han, J.

Y. Li, M. Li, J. Han, and T. Han, “Investigation of quadrature imbalance compensation algorithm for coherent 6PolSK-QPSK,” Phys. Commun. 25(2), 319–322 (2017).
[Crossref]

Han, T.

Y. Li, M. Li, J. Han, and T. Han, “Investigation of quadrature imbalance compensation algorithm for coherent 6PolSK-QPSK,” Phys. Commun. 25(2), 319–322 (2017).
[Crossref]

Hoffmann, S.

Hoshida, T.

J. Liang, Y. Fan, Z. Tao, H. Nakashima, and T. Hoshida, “Transceiver in-phase and quadrature imbalance monitoring by two stage MIMO equalizers,” 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–4. doi:
[Crossref]

Ives, D.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Joindot, M.

Jones, R.

Kalialakis, C.

A. Georgiadis and C. Kalialakis, “Evaluation of error vector magnitude due to combined IQ imbalances and phase noise,” IET Circuits Dev. Syst. 8(6), 421–426 (2014).
[Crossref]

Kikuchi, K.

M. S. Faruk and K. Kikuchi, “Compensation for in-phase/quadrature imbalance in coherent-receiver front end for optical quadrature amplitude modulation,” IEEE Photonics J. 5(2), 7800110 (2013).
[Crossref]

Klinkowski, M.

R. Goścień, K. Walkowiak, and M. Klinkowski, “Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic,” Comput. Netw. 79(14), 148–165 (2015).
[Crossref]

Lau, A. P. T.

Li, G.

X. Xie, F. Yaman, X. Zhou, and G. Li, “Polarization demultiplexing by independent component analysis,” J. Lightwave Technol. 22(11), 805–807 (2010).

G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14(18), 8043–8053 (2006).
[Crossref] [PubMed]

Li, H.

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

Li, L.

Li, M.

Y. Li, M. Li, J. Han, and T. Han, “Investigation of quadrature imbalance compensation algorithm for coherent 6PolSK-QPSK,” Phys. Commun. 25(2), 319–322 (2017).
[Crossref]

Li, X.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Li, Y.

Y. Li, M. Li, J. Han, and T. Han, “Investigation of quadrature imbalance compensation algorithm for coherent 6PolSK-QPSK,” Phys. Commun. 25(2), 319–322 (2017).
[Crossref]

Liang, J.

J. Liang, Y. Fan, Z. Tao, H. Nakashima, and T. Hoshida, “Transceiver in-phase and quadrature imbalance monitoring by two stage MIMO equalizers,” 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–4. doi:
[Crossref]

Lu, C.

Luo, M.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Marshall, T.

Meyr, H.

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

Nakashima, H.

J. Liang, Y. Fan, Z. Tao, H. Nakashima, and T. Hoshida, “Transceiver in-phase and quadrature imbalance monitoring by two stage MIMO equalizers,” 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–4. doi:
[Crossref]

Nebendahl, B.

Nguyen, T. H.

T. H. Nguyen, P. Scalart, M. Gay, L. Bramerie, O. Sentieys, J. C. Simon, C. Peucheret, and M. Joindot, “Blind adaptive transmitter IQ imbalance compensation in m-QAM optical coherent systems,” J. Opt. Commun. Netw. 9(9), D42–D50 (2017).
[Crossref]

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

Nguyen-Ti, T.

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

Noé, R.

Oerder, M.

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

Oktem, T. M.

Peucheret, C.

Pfau, T.

Qiu, Y.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Rodriguez, P. A.

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

Savory, S.

Savory, S. J.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Scalart, P.

T. H. Nguyen, P. Scalart, M. Gay, L. Bramerie, O. Sentieys, J. C. Simon, C. Peucheret, and M. Joindot, “Blind adaptive transmitter IQ imbalance compensation in m-QAM optical coherent systems,” J. Opt. Commun. Netw. 9(9), D42–D50 (2017).
[Crossref]

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

Sentieys, O.

Silva, E. P.

Simon, J. C.

Szafraniec, B.

Tang, X.

Tao, Z.

J. Liang, Y. Fan, Z. Tao, H. Nakashima, and T. Hoshida, “Transceiver in-phase and quadrature imbalance monitoring by two stage MIMO equalizers,” 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–4. doi:
[Crossref]

Walkowiak, K.

R. Goścień, K. Walkowiak, and M. Klinkowski, “Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic,” Comput. Netw. 79(14), 148–165 (2015).
[Crossref]

Wang, Q.

Xi, L.

Xie, X.

X. Xie, F. Yaman, X. Zhou, and G. Li, “Polarization demultiplexing by independent component analysis,” J. Lightwave Technol. 22(11), 805–807 (2010).

Xu, H.

Yaman, F.

X. Xie, F. Yaman, X. Zhou, and G. Li, “Polarization demultiplexing by independent component analysis,” J. Lightwave Technol. 22(11), 805–807 (2010).

Yang, Q.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Yang, Y.

Yao, Y.

Yu, C.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Yue, Y.

Zhang, Q.

Zhang, W.

Zhang, X.

Zheng, Z.

Zhong, W.

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Zhou, X.

Q. Zhang, Y. Yang, C. Guo, X. Zhou, Y. Yao, A. P. T. Lau, and C. Lu, “Algorithms for blind separation and estimation of transmitter and receiver IQ Imbalances,” J. Lightwave Technol. 37(10), 2201–2208 (2019).
[Crossref]

X. Xie, F. Yaman, X. Zhou, and G. Li, “Polarization demultiplexing by independent component analysis,” J. Lightwave Technol. 22(11), 805–807 (2010).

Zibar, D.

Comput. Netw. (1)

R. Goścień, K. Walkowiak, and M. Klinkowski, “Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic,” Comput. Netw. 79(14), 148–165 (2015).
[Crossref]

IEEE Photonics J. (1)

M. S. Faruk and K. Kikuchi, “Compensation for in-phase/quadrature imbalance in coherent-receiver front end for optical quadrature amplitude modulation,” IEEE Photonics J. 5(2), 7800110 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

H. Li, N. M. Correa, P. A. Rodriguez, V. D. Calhoun, and T. Adali, “Application of independent component analysis with adaptive density model to complex-valued fMRI data,” IEEE Trans. Biomed. Eng. 58(10), 2794–2803 (2011).
[Crossref] [PubMed]

IEEE Trans. Commun. (1)

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

IET Circuits Dev. Syst. (1)

A. Georgiadis and C. Kalialakis, “Evaluation of error vector magnitude due to combined IQ imbalances and phase noise,” IET Circuits Dev. Syst. 8(6), 421–426 (2014).
[Crossref]

J. Lightwave Technol. (7)

J. Opt. Commun. Netw. (1)

Opt. Commun. (1)

X. Li, M. Luo, Y. Qiu, A. Alphones, W. Zhong, C. Yu, and Q. Yang, “Independent component analysis based digital signal processing in coherent optical fiber communication systems,” Opt. Commun. 409, 13–22 (2018).
[Crossref]

Opt. Express (4)

Phys. Commun. (1)

Y. Li, M. Li, J. Han, and T. Han, “Investigation of quadrature imbalance compensation algorithm for coherent 6PolSK-QPSK,” Phys. Commun. 25(2), 319–322 (2017).
[Crossref]

Other (4)

J. Liang, Y. Fan, Z. Tao, H. Nakashima, and T. Hoshida, “Transceiver in-phase and quadrature imbalance monitoring by two stage MIMO equalizers,” 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–4. doi:
[Crossref]

C. R. S. Fludger and T. Kupfer, “Transmitter impairment mitigation and monitoring for high baud-rate, high order modulation systems,” in Proceedings of European Conference on Optical Communication (VDE, 2016), pp. Tu. 2. A. 2.

T. Nguyen-Ti, M. Gautier, P. Scalart, O. Berder, T. H. Nguyen, and F. A. Aoudia, “Blind I/Q imbalance compensation for m-QAM optical coherent systems based on pseudo-rotation,” in proceedings of Global Communications Conference (IEEE, 2016), pp.1–6.
[Crossref]

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).

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Figures (11)

Fig. 1
Fig. 1 The diagram of DP-Tx.
Fig. 2
Fig. 2 Received QPSK signals in Jones space. QPSK Constellation (a) without IQ imbalance; (b) QPSK Constellation with 30-degree IQ phase imbalance; (c) QPSK Constellation with 3 dB IQ phase imbalance.
Fig. 3
Fig. 3 Received QPSK signals in Stokes space. QPSK constellation (a) without IQ imbalance; (b) with 30-degree IQ phase imbalance; (c) with 45-degree IQ phase imbalance; (d) with 3 dB IQ amplitude imbalance; (e) with 6 dB IQ amplitude imbalance. Blue dot is constellation point; red plane is the least square plane; green line is the normal vector of the least squares plane.
Fig. 4
Fig. 4 Kurtosis of received signal (a) under polarization crosstalk and IQ amplitude imbalance (b) under polarization crosstalk and IQ phase imbalance.
Fig. 5
Fig. 5 Kurtosis of received signals (a) under phase difference and IQ amplitude imbalance (b) under phase difference and IQ phase imbalance.
Fig. 6
Fig. 6 The diagram of ML-ICA based DP-Tx IQ imbalance estimation algorithm.
Fig. 7
Fig. 7 Signal evolution process. (a) The introduction of signal impairment; (b) The compensation of signal impairment.
Fig. 8
Fig. 8 The diagram of simulation system of 28 Gbaud PDM-16QAM coherent optical communication system.
Fig. 9
Fig. 9 The tolerance of the proposed scheme on phase noise, quantization noise, and ASE noise.
Fig. 10
Fig. 10 The diagram of experimental system of 28 Gbaud PDM-QPSK/8QAM/16QAM/64QAM coherent optical communication system.
Fig. 11
Fig. 11 Tx IQ imbalance estimation error of ML-ICA in PDM-QPSK/8QAM/16QAM/64QAM system.

Tables (1)

Tables Icon

Table 1 ML-ICA under different IQ imbalances on each polarization.

Equations (17)

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

[ e( E out ) m( E out ) ]M[ S I S Q ]=[ 1 gsin(θ) 0 gcos(θ) ][ S I S Q ]
J=[ cosκ e jξ sinκ e jη sinκ e jη cosκ e jξ ]
D=[ cosφ sinφ sinφ cosφ ]
[ S 0 S 1 S 2 S 3 ]= 1 2 [ E x E x H + E y E y H E x E x H E y E y H E x H E y + E x E y H i E x H E y +i E x E y H ]
Z out,k = W k Z in,k
W k+1 = W k +μ(I+φ( Z out,k ) Z out,k H ) W k
φ( Z out,k )=lnp( Z out,k )/ Z out,k =p'( Z out,k )/p( Z out,k )
lnp + ( Z out,k )= α 1 2ln(cosh( Z out,k ))
ln p - ( Z out,k )= α 2 ( Z out,k 2 /2ln(cosh( Z out,k )))
Z in =[ X in Y in ], Z out =[ X out Y out ], W=H=[ H XX H YX H YY H YY ]
Z in =[ I in,X/Y Q in,X/Y ], Z out =[ I out,X/Y Q out,X/Y ], W= B X/Y =[ B II,X/Y B IQ,X/Y B QI,X/Y B QQ,X/Y ]
[ I out Q out ]αB P 1 P N M[ I ideal Q ideal ]
αB P 1 P N M=α[ B II B IQ B QI B QQ ][ cos(ψ) sin(ψ) sin(ψ) cos(ψ) ][ 1 gsin(θ) 0 gcos(θ) ]=I
ψ=arctan( B QI / B QQ )
α=1/( B II cos(ψ)+ B IQ sin(ψ))
θ=arctan(( B II sin(ψ)+ B IQ cos(ψ))/( B II cos(ψ)+ B IQ sin(ψ)))
g=1/(αsin(θ)( B QI cos(ψ)+ B QQ sin(ψ))+αcos(θ)( B QI sin(ψ)+ B QQ cos(ψ)))

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