Abstract

We propose and experimentally demonstrate two independent component analysis (ICA) based channel equalizers (CEs) for 6 × 6 MIMO-OFDM transmission over few-mode fiber. Compared with the conventional channel equalizer based on training symbols (TSs-CE), the proposed two ICA-based channel equalizers (ICA-CE-I and ICA-CE-II) can achieve comparable performances, while requiring much less training symbols. Consequently, the overheads for channel equalization can be substantially reduced from 13.7% to 0.4% and 2.6%, respectively. Meanwhile, we also experimentally investigate the convergence speed of the proposed ICA-based CEs.

© 2016 Optical Society of America

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References

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  1. D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.
  2. D. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
    [Crossref]
  3. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011).
    [Crossref] [PubMed]
  4. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
    [Crossref]
  5. R. G. van Uden, C. M. Okonkwo, H. Chen, H. de Waardt, and A. M. Koonen, “Time domain multiplexed spatial division multiplexing receiver,” Opt. Express 22(10), 12668–12677 (2014).
    [Crossref] [PubMed]
  6. A. Al Amin, A. Li, S. Chen, X. Chen, G. Gao, and W. Shieh, “Dual-LP11 mode 4x4 MIMO-OFDM transmission over a two-mode fiber,” Opt. Express 19(17), 16672–16679 (2011).
    [Crossref] [PubMed]
  7. X. Chen, J. Ye, Y. Xiao, A. Li, J. He, Q. Hu, and W. Shieh, “Equalization of two-mode fiber based MIMO signals with larger receiver sets,” Opt. Express 20(26), B413–B418 (2012).
    [Crossref] [PubMed]
  8. X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
    [Crossref]
  9. X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
    [Crossref]
  10. X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-division-multiplexed CO-OFDM in long-haul fiber transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
    [Crossref]
  11. Q. Hu, X. Chen, A. Li, and W. Shieh, “High-dimensional Stokes-space analysis for monitoring fast change of mode dispersion in few-mode fibers,” Optical Fiber Communication Conference (OFC), 2014, W3D.3.
    [Crossref]
  12. S. Cao, P. Y. Kam, and C. Yu, “Decision-aided, pilot-aided, decision-feedback phase estimation for coherent optical OFDM systems,” IEEE Photonics Technol. Lett. 24(22), 2067–2069 (2012).
    [Crossref]
  13. H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Trans. Wirel. Commun. 24(5), 822–839 (2003).
    [Crossref]
  14. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007).
    [Crossref]
  15. T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
    [Crossref]
  16. X. Chen, J. He, D. Che, and W. Shieh, “Hybrid Modulated Multiband Coherent Optical OFDM for Low-Complexity Phase Noise Compensation,” J. Lightwave Technol. 33(1), 126–132 (2015).
    [Crossref]
  17. S.-I. Amari and J.-F. Cardoso, “Blind source separation: Semi-parametrical statistical approach,” IEEE Trans. Signal Process. 45(11), 2692–2700 (1997).
    [Crossref]

2015 (1)

2014 (1)

2013 (1)

D. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

2012 (3)

2011 (2)

2009 (1)

2008 (1)

T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
[Crossref]

2007 (2)

W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007).
[Crossref]

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

2003 (1)

H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Trans. Wirel. Commun. 24(5), 822–839 (2003).
[Crossref]

1997 (1)

S.-I. Amari and J.-F. Cardoso, “Blind source separation: Semi-parametrical statistical approach,” IEEE Trans. Signal Process. 45(11), 2692–2700 (1997).
[Crossref]

Adali, T.

T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
[Crossref]

Al Amin, A.

Alphones, A.

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Amari, S.-I.

S.-I. Amari and J.-F. Cardoso, “Blind source separation: Semi-parametrical statistical approach,” IEEE Trans. Signal Process. 45(11), 2692–2700 (1997).
[Crossref]

Bhargava, V. K.

H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Trans. Wirel. Commun. 24(5), 822–839 (2003).
[Crossref]

Bolle, C.

Bolle, C. A.

Buchali, F.

Burrows, E. C.

Cao, S.

S. Cao, P. Y. Kam, and C. Yu, “Decision-aided, pilot-aided, decision-feedback phase estimation for coherent optical OFDM systems,” IEEE Photonics Technol. Lett. 24(22), 2067–2069 (2012).
[Crossref]

Cardoso, J. F.

T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
[Crossref]

Cardoso, J.-F.

S.-I. Amari and J.-F. Cardoso, “Blind source separation: Semi-parametrical statistical approach,” IEEE Trans. Signal Process. 45(11), 2692–2700 (1997).
[Crossref]

Che, D.

Chen, H.

Chen, S.

Chen, X.

de Waardt, H.

Esmaeelpour, M.

Essiambre, R. J.

Essiambre, R.-J.

Fini, J. M.

D. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Gao, G.

Gnauck, A. H.

He, J.

Hu, J.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Hu, Q.

X. Chen, J. Ye, Y. Xiao, A. Li, J. He, Q. Hu, and W. Shieh, “Equalization of two-mode fiber based MIMO signals with larger receiver sets,” Opt. Express 20(26), B413–B418 (2012).
[Crossref] [PubMed]

Q. Hu, X. Chen, A. Li, and W. Shieh, “High-dimensional Stokes-space analysis for monitoring fast change of mode dispersion in few-mode fibers,” Optical Fiber Communication Conference (OFC), 2014, W3D.3.
[Crossref]

Hu, R.

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Huang, M. F.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Huang, Y. K.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Ip, E.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Kam, P. Y.

S. Cao, P. Y. Kam, and C. Yu, “Decision-aided, pilot-aided, decision-feedback phase estimation for coherent optical OFDM systems,” IEEE Photonics Technol. Lett. 24(22), 2067–2069 (2012).
[Crossref]

Koonen, A. M.

Letaief, K. B.

H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Trans. Wirel. Commun. 24(5), 822–839 (2003).
[Crossref]

Li, A.

Li, H.

T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
[Crossref]

Li, X.

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Lingle, R.

Liu, X.

Luo, M.

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

McCurdy, A.

McCurdy, A. H.

Minn, H.

H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Trans. Wirel. Commun. 24(5), 822–839 (2003).
[Crossref]

Mumtaz, S.

Nelson, L. E.

D. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Novey, M.

T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
[Crossref]

Okonkwo, C. M.

Peckham, D. W.

Qian, D.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Randel, S.

Richardson, D.

D. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Ryf, R.

Shao, Y.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Shieh, W.

X. Chen, J. He, D. Che, and W. Shieh, “Hybrid Modulated Multiband Coherent Optical OFDM for Low-Complexity Phase Noise Compensation,” J. Lightwave Technol. 33(1), 126–132 (2015).
[Crossref]

X. Chen, J. Ye, Y. Xiao, A. Li, J. He, Q. Hu, and W. Shieh, “Equalization of two-mode fiber based MIMO signals with larger receiver sets,” Opt. Express 20(26), B413–B418 (2012).
[Crossref] [PubMed]

A. Al Amin, A. Li, S. Chen, X. Chen, G. Gao, and W. Shieh, “Dual-LP11 mode 4x4 MIMO-OFDM transmission over a two-mode fiber,” Opt. Express 19(17), 16672–16679 (2011).
[Crossref] [PubMed]

W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007).
[Crossref]

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

Q. Hu, X. Chen, A. Li, and W. Shieh, “High-dimensional Stokes-space analysis for monitoring fast change of mode dispersion in few-mode fibers,” Optical Fiber Communication Conference (OFC), 2014, W3D.3.
[Crossref]

Sierra, A.

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]

W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007).
[Crossref]

Tkach, R. W.

van Uden, R. G.

Wang, T.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

Winzer, P. J.

Xiao, Y.

Yang, Q.

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Ye, J.

Yi, X.

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, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007).
[Crossref]

Yu, C.

S. Cao, P. Y. Kam, and C. Yu, “Decision-aided, pilot-aided, decision-feedback phase estimation for coherent optical OFDM systems,” IEEE Photonics Technol. Lett. 24(22), 2067–2069 (2012).
[Crossref]

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Zhong, W. D.

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Electron. Lett. (1)

W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007).
[Crossref]

IEEE Photonics Technol. Lett. (2)

S. Cao, P. Y. Kam, and C. Yu, “Decision-aided, pilot-aided, decision-feedback phase estimation for coherent optical OFDM systems,” IEEE Photonics Technol. Lett. 24(22), 2067–2069 (2012).
[Crossref]

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

IEEE Trans. Signal Process. (2)

T. Adali, H. Li, M. Novey, and J. F. Cardoso, “Complex ICA using nonlinear functions,” IEEE Trans. Signal Process. 56(9), 4536–4544 (2008).
[Crossref]

S.-I. Amari and J.-F. Cardoso, “Blind source separation: Semi-parametrical statistical approach,” IEEE Trans. Signal Process. 45(11), 2692–2700 (1997).
[Crossref]

IEEE Trans. Wirel. Commun. (1)

H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Trans. Wirel. Commun. 24(5), 822–839 (2003).
[Crossref]

J. Lightwave Technol. (3)

Nat. Photonics (1)

D. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Opt. Express (4)

Other (3)

X. Li, W. D. Zhong, A. Alphones, C. Yu, M. Luo, R. Hu, and Q. Yang, “Experimental demonstration of independent component analysis based channel equalization in multiband coherent optical PDM-OFDM,” European Conference on Optical Communication (ECOC), 2015, P.3.1.
[Crossref]

Q. Hu, X. Chen, A. Li, and W. Shieh, “High-dimensional Stokes-space analysis for monitoring fast change of mode dispersion in few-mode fibers,” Optical Fiber Communication Conference (OFC), 2014, W3D.3.
[Crossref]

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370× 294-Gb/s) PDM-128QAM-OFDM transmission over 3× 55-km SSMF using pilot-based phase noise mitigation,” Optical Fiber Communication Conference (OFC), 2011, p. PDPB5.

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Figures (7)

Fig. 1
Fig. 1 Schematic DSP flow of (a) ICA-CE-I and (b) ICA-CE-II. DeMux: De-multiplexing. Mid.: middle. Sub.: sub-band. PN: phase noise. Esti.: estimation. Comp.: compensation. Freq.: frequency. Sync.: synchronization.
Fig. 2
Fig. 2 Experimental setup for the FMF transmission of MB-PDM-CO-OFDM signals. Inset: (i) optical spectrum of the generated multiband signal; (ii) electrical spectrum of received multiband signal. AWG: arbitrary waveform generator, ECL: external cavity laser, MZM: Mach-Zehnder modulator, PBS: polarization beam splitter, PBC: polarization beam combiner, ICR: integrated coherent receiver, OSC: oscilloscope, PL: photonics lantern, OC: optical coupler.
Fig. 3
Fig. 3 Design of OFDM symbols for (a) conventional TSs-CE, (b) ICA-CE-I and (c) ICA-CE-II.
Fig. 4
Fig. 4 BER versus OSNR of TSs-CE, ICA-CE-I and ICA-CE-II for (a) 4-QAM and (b) 16-QAM formats. Constellations for ICA-CE-I and ICA-CE-II with 4-QAM format at OSNR of 17.1 dB; Constellations for ICA-CE-I and ICA-CE-II with 16-QAM format at OSNR of 23.8 dB.
Fig. 5
Fig. 5 BER performances of TSs-CE, ICA-CE-I and ICA-CE-II in all modes for (a) 4-QAM at OSNR of 17.1 dB and (b) 16-QAM at OSNR of 23.8 dB.
Fig. 6
Fig. 6 AI as an indicator to evaluate the performance of ICA-CE-I and ICA-CE-II, under the condition of various modulation formats.
Fig. 7
Fig. 7 Convergence performances of (a) ICA-CE-I and (b) ICA-CE-II with 4-QAM; (c) ICA-CE-I and (d) ICA-CE-II with 16-QAM. The OSNR is 15.7 dB and 25.2 dB for 4-QAM and 16-QAM format, respectively.

Equations (4)

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Y k i = H k i X k i exp(j φ k )+ N k i
X ^ k i = [ H ˜ k i ] 1 Y k i exp(j φ ˜ k ) = H ^ k i Y k i exp(j φ ˜ k )
H ^ ^ k i (m)= H ^ ^ k i (m1)+μ{ I 6×6 tanh[ H ^ ^ k i (m1) Y i ]× [ H ^ ^ k i (m1) Y i ] }× H ^ ^ k i (m1)
AI= 1 2×6×(61) [ i=1 N ( j=1 N | p ij | max k | p ik | 1 ) + j=1 N ( i=1 N | p ij | max k | p kj | 1 ) ]

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