Skip to main content
SpringerLink
Log in

A Multistage Space–Time Equalizer for Blind Source Separation

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A multistage space–time equalizer (STE) is proposed to blindly separate signals received by an antenna array from different sources simultaneously. Neither the direction of arrival (DOA) nor a training sequence is assumed to be available at the receiver. The only assumption is that the transmitted signals satisfy the constant modulus property, which is valid for many modulation schemes, and can be exploited by the multi-modulus algorithm. Each stage consists of an adaptive beamformer, a DOA estimator and an equalizer. Its function is to jointly combat multi-user interference and the effect of fading channels between sources and the antenna. An adaptive version of the basic structure of generalized sidelobe canceller (GSC), called adaptive GSC, is presented which can track a user and strongly attenuate other users with different DOAs. The possibly time-varying DOA for each user is estimated using the phase shift between the outputs of two subarray beamformers at each stage. The estimated DOAs are used to improve multi-user interference rejection and to compute the input to the next stage. In order to significantly alleviate inter-stage error propagation and provide a fast convergence, a mean-square-error sorting algorithm is proposed which assigns detected sources to different stages according to the reconstruction error. Further, to speed up the convergence, a simple, yet efficient, DOA estimation algorithm is proposed which can provide good initial DOAs for the multistage STE. Simulation results illustrate the performance of the proposed STE and show that it can deal effectively with changing DOAs and time-varying channels.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. A. Antoniou, W.S. Lu, Practical Optimization: Algorithms and Engineering Applications (Springer, Berlin, 2010)

    Google Scholar 

  2. Y. Chen, T. Le-Ngoc, B. Champagne, C. Xu, Recursive least squares constant modulus algorithm for blind adaptive array. IEEE Trans. Signal Process. 52(5), 1452–1456 (2004)

    Article  MathSciNet  Google Scholar 

  3. A.B. Gershman, P. Stoica, MODE with extra-roots (MODEX): a new DOA estimation algorithm with an improved threshold performance, in IEEE International Conference on Acoustics, Speech, and Signal Processing, Proceedings, vol. 5 (1999), pp. 2833–2836

  4. D. Godard, Self-recovering equalization and carrier tracking in two-dimensional data communication systems. IEEE Trans. Commun. 28(11), 1867–1875 (1980)

    Article  Google Scholar 

  5. K. Hayashi, S. Hara, A new spatio-temporal equalization method based on estimated channel response. IEEE Trans. Veh. Technol. 50(5), 1250–1259 (2001)

    Article  Google Scholar 

  6. J. Labat, O. Macchi, C. Laot, Adaptive decision feedback equalization: can you skip the training period? IEEE Trans. Commun. 46(7), 921–930 (1998)

    Article  Google Scholar 

  7. Y. Lee, W.-R. Wu, Equalization with generalized sidelobe cancellation. IEEE Trans. Veh. Technol. 57(5), 2894–2906 (2008)

    Article  MathSciNet  Google Scholar 

  8. M.-L. Leou, C.-C. Yeh, H.-J. Li, A novel hybrid of adaptive array and equalizer for mobile communications. IEEE Trans. Veh. Technol. 49(1), 1–10 (2000)

    Article  Google Scholar 

  9. J.-W. Liang, J.-T. Chen, A.J. Paulraj, A two-stage hybrid approach for CCI/ISI reduction with space–time processing. Commun. Lett. IEEE 1(6), 163–165 (1997)

    Article  Google Scholar 

  10. A. Mathur, A.V. Keerthi, J.J. Shyok, A variable step-size CM array algorithm for fast fading channels. IEEE Trans. Signal Process. 45(4), 1083–1087 (1997)

    Article  Google Scholar 

  11. I. Moazzen, P. Agathoklis, An approach for joint blind space–time equalization and DOA estimation, in IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2183–2186, 19–23 May 2013

  12. J. Palicot, A. Goupil, Performance analysis of the weighted decision feedback equalizer. Signal Process. 88(2), 284–295 (2008)

    Article  MATH  Google Scholar 

  13. A.J. Paulraj, B.C. Ng, Space–time modems for wireless personal communications. IEEE Pers. Commun. 5(1), 36–48 (1998)

    Article  Google Scholar 

  14. J. Prokis, M. Salehi, Digital Communications, 5th edn. (McGrew-Hill, New York, 2008)

    Google Scholar 

  15. R. Roy, T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984–995 (1989)

    Article  Google Scholar 

  16. T.K. Sarkar, O. Pereira, Using the matrix pencil method to estimate the parameters of a sum of complex exponentials. Antennas Propag. Mag. IEEE 37(1), 48–55 (1995)

    Article  Google Scholar 

  17. R. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276–280 (1986)

    Article  Google Scholar 

  18. J.J. Shynk, R.P. Gooch, The constant modulus array for cochannel signal copy and direction finding. IEEE Trans. Signal Process. 44(3), 652–660 (1996)

    Article  Google Scholar 

  19. J.J. Shynk, A.V. Keerthi, A. Mathur, Steady-state analysis of the multistage constant modulus array. IEEE Trans. Signal Process. 44(4), 948–962 (1996)

    Article  Google Scholar 

  20. P. Stoica, K. Sharman, Maximum likelihood methods for direction-of-arrival estimation. IEEE Trans. Acoust. Speech Signal Process. 38(7), 1132–1143 (1990)

    Article  MATH  Google Scholar 

  21. L. Tao, H.K. Kwan, A novel approach to fast DOA estimation of multiple spatial narrowband signals, in The 45th Midwest Symposium on Circuits and Systems, MWSCAS-2002, vol. 1, pp. I.431–I.434, 4–7 Aug 2002

  22. H.L. Van Trees, Optimum Array Processing (Detection, Estimation, and Modulation Theory, Part IV) (Wiley, London, 2002)

    Google Scholar 

  23. V. Venkataraman, J.J. Shynk, A multistage hybrid constant modulus array with constrained adaptation for correlated sources. IEEE Trans. Signal Process. 55(6), 2509–2519 (2007)

    Article  MathSciNet  Google Scholar 

  24. N. Wang, P. Agathoklis, A. Antoniou, A new DOA estimation technique based on subarray beamforming. IEEE Trans. Signal Process. 54(9), 3279–3290 (2006)

    Article  Google Scholar 

  25. Y. Xiang, N. Gu, K.L. Wong, Adaptive blind source separation using constant modulus criterion and signal mutual information, in IEEE International Conference on Industrial Technology, pp. 1371–1375, 14–17 Dec 2005

  26. J. Yang, J.-J. Werner, G.A. Dumont, The multimodulus blind equalization and its generalized algorithms. IEEE J. Sel. Areas Commun. 20(5), 997–1015 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their detailed comments and suggestions. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Author information

Authors and Affiliations

  1. Department of ECE, University of Victoria, Victoria, BC, Canada

    Iman Moazzen & Panajotis Agathoklis

Authors
  1. Iman Moazzen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Panajotis Agathoklis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iman Moazzen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moazzen, I., Agathoklis, P. A Multistage Space–Time Equalizer for Blind Source Separation. Circuits Syst Signal Process 35, 185–209 (2016). https://doi.org/10.1007/s00034-015-0042-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0042-4

Keywords

Search

Navigation