Abstract

We report the use of implicit training-aided channel estimation (ITA-CE) for polarization-division-multiplexed (PDM) single-carrier coherent optical systems. With the concept of ITA-CE, where the training sequence (TS) is arithmetically added onto the information symbols rather than appearing in separate time slots, overhead-free transmission can be achieved with minor optical signal to noise ratio (OSNR) penalty. ITA-CE system enables simple digital pilot-tone based frequency-offset compensation, and inherits the benefits from typical training-aided channel acquisition and data recovery. Furthermore, we address the issue of self-interference to channel estimation (CE) of ITA-CE system in this paper. The data-induced interference can be eliminated by removing the cyclic mean of the transmitted signal, which can accelerate the convergence of the CE and allows smaller power to be allocated to the TS, leading to enhanced system performance. Numerical simulations and experiments for both PDM-QPSK and PDM-16-QAM systems have been conducted to verify the proposed scheme. Comparable performance to the conventional blind equalization system can be achieved when employing the transmitter side pre-distortion approach to the ITA-CE system.

© 2013 OSA

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References

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  1. J.  Yu, X.  Zhou, “Ultra-High-Capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. 48(3), S56–S64 (2010).
    [CrossRef]
  2. K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
    [CrossRef]
  3. S. J.  Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [CrossRef] [PubMed]
  4. C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).
  5. M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
    [CrossRef]
  6. B. Spinnler, S. Calabro, and M. Kuschnerov, “Pilot-assisted channel estimation methods for coherent receivers,” in Proc. Opt. Fiber Commun. Conf. (OFC), paper OM4B.3 (2013).
    [CrossRef]
  7. F. Pittalà, A. Mezghani, F. N. Hauske, Y. Ye, I. T. Monroy, and J. A. Nossek, “Efficient training-based channel estimation for coherent optical communication systems,” in Proceedings of Sig. Process. Photon. Commun. (SPPCOM), paper SpTu3A.4 (2012).
    [CrossRef]
  8. R. Elschner, F. Frey, C. Meuer, J. K. Fischer, S. Alreesh, C. Schmidt-Langhorst, L. Molle, T. Tanimura, and C. Schubert, “Experimental demonstration of a format-flexible single carrier coherent receiver using data-aided digital signal processing,” in Proc. Eur. Conf. Opt. Commun. (ECOC), paper We.1.A.4 (2012).
  9. A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
    [CrossRef]
  10. C. Zhu, A. V. Tran, F. N. Hauske, S. Chen, T. Anderson, and E. Skafidas, “Low-complexity fractionally-spaced frequency domain equalization with improved channel estimation for long-haul coherent optical systems,” in Proc. Opt. Fiber Commun. Conf. (OFC), paper OW4B.5 (2013).
    [CrossRef]
  11. A. G.  Orozco-Lugo, M. M.  Lara, D. C.  McLernon, “Channel estimation using implicit training,” IEEE Trans. Signal Process. 52(1), 240–254 (2004).
    [CrossRef]
  12. C. Zhu, F. Pittalà, M. Finkenbusch, P. Krummrich, F. N. Hauske, A. V. Tran, J. A. Nossek, and T. Anderson, “Overhead-Free Channel Estimation using implicit training for polarization-multiplexed coherent optical systems,” in Proc. Opt. Fiber Commun. Conf. (OFC), paper OW4B.7 (2013).
    [CrossRef]
  13. J. K.  Tugnait, X.  Meng, “On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchonization,” IEEE Trans. Signal Process. 54(2), 752–765 (2006).
    [CrossRef]
  14. S.  Zhang, P. Y.  Kam, C.  Yu, J.  Chen, “Decision-aided carrier phase estimation for coherent optical communications,” J. Lightwave Technol. 28(11), 1597–1607 (2010).
    [CrossRef]
  15. M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
    [CrossRef]

2012

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

2010

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

J.  Yu, X.  Zhou, “Ultra-High-Capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. 48(3), S56–S64 (2010).
[CrossRef]

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

S.  Zhang, P. Y.  Kam, C.  Yu, J.  Chen, “Decision-aided carrier phase estimation for coherent optical communications,” J. Lightwave Technol. 28(11), 1597–1607 (2010).
[CrossRef]

2008

2006

J. K.  Tugnait, X.  Meng, “On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchonization,” IEEE Trans. Signal Process. 54(2), 752–765 (2006).
[CrossRef]

2005

M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
[CrossRef]

2004

A. G.  Orozco-Lugo, M. M.  Lara, D. C.  McLernon, “Channel estimation using implicit training,” IEEE Trans. Signal Process. 52(1), 240–254 (2004).
[CrossRef]

Alameda-Hernandez, E.

M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
[CrossRef]

Alfiad, M. S.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Anderson, T.

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

Beckett, D.

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Berthold, J.

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Boertjes, D.

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Chen, J.

Chen, S.

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

Chouayakh, M.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

de Man, E.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Do, C. C.

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

Du, L. B.

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

Ghogho, M.

M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
[CrossRef]

Hewitt, D.

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

Kainzmaier, P.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Kam, P. Y.

Kuschnerov, M.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Lankl, B.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Laperle, C.

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Lara, M. M.

A. G.  Orozco-Lugo, M. M.  Lara, D. C.  McLernon, “Channel estimation using implicit training,” IEEE Trans. Signal Process. 52(1), 240–254 (2004).
[CrossRef]

Lowery, A. J.

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

Mclernon, D.

M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
[CrossRef]

McLernon, D. C.

A. G.  Orozco-Lugo, M. M.  Lara, D. C.  McLernon, “Channel estimation using implicit training,” IEEE Trans. Signal Process. 52(1), 240–254 (2004).
[CrossRef]

Meng, X.

J. K.  Tugnait, X.  Meng, “On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchonization,” IEEE Trans. Signal Process. 54(2), 752–765 (2006).
[CrossRef]

Napoli, A.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Orozco-Lugo, A. G.

A. G.  Orozco-Lugo, M. M.  Lara, D. C.  McLernon, “Channel estimation using implicit training,” IEEE Trans. Signal Process. 52(1), 240–254 (2004).
[CrossRef]

Piyawanno, K.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Roberts, K.

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Savory, S. J.

Skafidas, E.

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

Spinnler, B.

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

Swami, A.

M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
[CrossRef]

Tran, A. V.

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

Tugnait, J. K.

J. K.  Tugnait, X.  Meng, “On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchonization,” IEEE Trans. Signal Process. 54(2), 752–765 (2006).
[CrossRef]

Yu, C.

Yu, J.

J.  Yu, X.  Zhou, “Ultra-High-Capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. 48(3), S56–S64 (2010).
[CrossRef]

Zhang, S.

Zhou, X.

J.  Yu, X.  Zhou, “Ultra-High-Capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. 48(3), S56–S64 (2010).
[CrossRef]

Zhu, C.

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

IEEE Commun. Mag.

J.  Yu, X.  Zhou, “Ultra-High-Capacity DWDM transmission system for 100G and beyond,” IEEE Commun. Mag. 48(3), S56–S64 (2010).
[CrossRef]

K.  Roberts, D.  Beckett, D.  Boertjes, J.  Berthold, C.  Laperle, “100G and beyond with digital coherent signal processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

IEEE Photon. J.

C.  Zhu, A. V.  Tran, S.  Chen, L. B.  Du, T.  Anderson, A. J.  Lowery, E.  Skafidas, “Frequency-domain blind equalization for long-haul coherent pol-mux 16-QAM system with CD prediction and dual-mode adaptive algorithm,” IEEE Photon. J. 4(5), 1654–1661 (2012).

M.  Kuschnerov, M.  Chouayakh, K.  Piyawanno, B.  Spinnler, E.  de Man, P.  Kainzmaier, M. S.  Alfiad, A.  Napoli, B.  Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2(3), 387–403 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

A. V.  Tran, C.  Zhu, C. C.  Do, S.  Chen, T.  Anderson, D.  Hewitt, E.  Skafidas, “8×40-Gb/s optical coherent pol-mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012).
[CrossRef]

IEEE Signal Process. Lett.

M.  Ghogho, D.  Mclernon, E.  Alameda-Hernandez, A.  Swami, “Channel estimation and symbol detection for block transmission using data-dependent superimposed training,” IEEE Signal Process. Lett. 12(3), 226–229 (2005).
[CrossRef]

IEEE Trans. Signal Process.

J. K.  Tugnait, X.  Meng, “On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchonization,” IEEE Trans. Signal Process. 54(2), 752–765 (2006).
[CrossRef]

A. G.  Orozco-Lugo, M. M.  Lara, D. C.  McLernon, “Channel estimation using implicit training,” IEEE Trans. Signal Process. 52(1), 240–254 (2004).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

C. Zhu, F. Pittalà, M. Finkenbusch, P. Krummrich, F. N. Hauske, A. V. Tran, J. A. Nossek, and T. Anderson, “Overhead-Free Channel Estimation using implicit training for polarization-multiplexed coherent optical systems,” in Proc. Opt. Fiber Commun. Conf. (OFC), paper OW4B.7 (2013).
[CrossRef]

C. Zhu, A. V. Tran, F. N. Hauske, S. Chen, T. Anderson, and E. Skafidas, “Low-complexity fractionally-spaced frequency domain equalization with improved channel estimation for long-haul coherent optical systems,” in Proc. Opt. Fiber Commun. Conf. (OFC), paper OW4B.5 (2013).
[CrossRef]

B. Spinnler, S. Calabro, and M. Kuschnerov, “Pilot-assisted channel estimation methods for coherent receivers,” in Proc. Opt. Fiber Commun. Conf. (OFC), paper OM4B.3 (2013).
[CrossRef]

F. Pittalà, A. Mezghani, F. N. Hauske, Y. Ye, I. T. Monroy, and J. A. Nossek, “Efficient training-based channel estimation for coherent optical communication systems,” in Proceedings of Sig. Process. Photon. Commun. (SPPCOM), paper SpTu3A.4 (2012).
[CrossRef]

R. Elschner, F. Frey, C. Meuer, J. K. Fischer, S. Alreesh, C. Schmidt-Langhorst, L. Molle, T. Tanimura, and C. Schubert, “Experimental demonstration of a format-flexible single carrier coherent receiver using data-aided digital signal processing,” in Proc. Eur. Conf. Opt. Commun. (ECOC), paper We.1.A.4 (2012).

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Figures (9)

Fig. 1
Fig. 1

Transmitter’s DSP block diagram for: (a) ITA-CE system and (b) TA-CE system.

Fig. 2
Fig. 2

Receiver’s DSP structure for ITA-CE system.

Fig. 3
Fig. 3

Simulation results for frequency offset estimation (the true and estimated FO value is in log scale, with negative FO value calculated as -log10(|FO|) and 0 means no frequency offset).

Fig. 4
Fig. 4

Simulation results for PDM-16-QAM system with different OSNR and DTR values.

Fig. 5
Fig. 5

(a) Applying pre-distortion at the transmitter, (b) Recovering equalized signal from pre-distortion at the receiver.

Fig. 6
Fig. 6

Amplitude of DFT of transmitted data and TS.

Fig. 7
Fig. 7

PDM coherent optical long-haul experimental setup for ITA-CE system.

Fig. 8
Fig. 8

Channel estimation convergence performance comparison for different ITA-CE systems in 10-Gbaud PDM-QPSK transmission.

Fig. 9
Fig. 9

Equalization performance for different equalization systems: (a) QPSK and (b) 16-QAM.

Equations (8)

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

s k (n)= d k (n)+t(n), n=0,1,...,N1
TS(n)= 1 M k=1 M R k (n) =H(n)T(n)+ 1 M k=1 M ( H k (n) D k (n)+ N k (n))
Y k (n)= R k (n)H'(n)T(n)
T subg (nQ)=QT(n), T subg (n)=0 otherwise
D subg (nQ)=0
d k ' = d k m, k=1,2,...,Q
m(n)= 1 Q k=0 Q1 d k (n) , n=0,1,...,P1
d subg ' = d subg 1 Q ( 1 Q I P ) d subg

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