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Noncircularity restoral for multi-antenna blind beamforming

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Abstract

Blind beamforming for extracting noncircular signals without the prior knowledge about the objective steering vector is considered. Three second-order blind techniques via NonCircularity REstoral (NCRE) are proposed to recover a dominant noncircular signal from circular interferences plus sensor noise with arbitrary and unknown correlation structure. These schemes are labeled as NCRE1, NCRE2, and NCRE3, respectively. For the high-rank environments where a number of rectilinear/circular interfering signals are present a Mixed-Order BEamspace (MOBE) technique, using simultaneously the second- and fourth-order cumulants, is developed. The performance of these proposed methods is studied based on numerical simulations. NCRE1 is computationally simple but performs well only in the case of very weak interferences and moderate noise, NCRE3 can provide good performance in the presence of medium or weak interferences, while NCRE2 is very suitable for adverse signal environments. NCRE2 outperforms NCRE1 and NCRE3 in terms of convergence rate, over a wide range of signal to interference plus noise ratio values. It is demonstrated that all the three NCRE methods are better than the traditional sample matrix inversion technique in the presence of look direction mismatch. They are also more attractive than the high-order cumulant method when non-Gaussian circular interferences are encountered. The MOBE method is shown to be competent for handling rectilinear/circular interfering signals, with respect to the attainable output signal to interference plus noise ratio.

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References

  • Abeida H., Delmas P. J. (2006) MUSIC-like estimation of direction of arrival for noncircular sources. IEEE Transactions on Signal Processing 54(7): 2678–2690

    Article  Google Scholar 

  • Abeida H., Delmas P. J. (2008) Statistical performance of MUSIC-like algorithms in resolving noncircular sources. IEEE Transactions on Signal Processing 56(9): 4317–4329

    Article  Google Scholar 

  • Agee B. G., Schell S. V., Gardner W. A. (1990) Spectral self-coherence restoral: A new approach to blind adaptive signal extraction using antenna arrays. Proceedings of the IEEE 78(4): 753–767

    Article  Google Scholar 

  • Albera L., Ferréol A., Chevalier P., Comon P. (2005) ICAR: A tool for blind source separation using fourth-order statistics only. IEEE Transactions on Signal Processing 53(10): 3633–3643

    Article  MathSciNet  Google Scholar 

  • Bell K. L., Ephraim Y., Van Trees H. L. (2000) A Bayesian approach to robust adaptive beamforming. IEEE Transactions on Signal Processing 48(2): 386–398

    Article  Google Scholar 

  • Belouchrani A., Abed-Meraim K., Cardoso J.-F., Moulines E. (1997) A blind source separation technique using second-order statistics. IEEE Transactions on Signal Processing 45(2): 434–444

    Article  Google Scholar 

  • Cardoso J.-F., Souloumiac A. (1993) Blind beamforming for non-Gaussian signals. Proceedings of IEE-f 140(6): 362–370

    Google Scholar 

  • Chargé J., Wang Y., Saillard J. (2001) A non-circular sources direction finding method using polynomial rooting. Signal Processing 81(8): 1765–1770

    Article  MATH  Google Scholar 

  • Chevalier P., Blin A. (2007) Widely linear MVDR beamformers for the rejection of an unknown signal corrupted by noncircular interferences. IEEE Transactions on Signal Processing 55(11): 5323–5336

    Article  MathSciNet  Google Scholar 

  • De Lathauwer, L., & De Moor, B. (2002). On the blind separation of non-circular sources. In Proceedings of the 11th European signal processing conference (EUSIPCO’02) (pp. 99–102). Toulouse, France.

  • Delmas J. P. (2004) Asymptotically minimum variance second-order estimation for noncircular signals with application to DOA estimation. IEEE Transactions on Signal Processing 52(5): 1235–1241

    Article  MathSciNet  Google Scholar 

  • Delmas J. P., Abeida H. (2004) Stochastic Cramer-Rao bound for noncircular signals with application to DOA estimation. IEEE Transactions on Signal Processing 52(11): 3192–3199

    Article  MathSciNet  Google Scholar 

  • Dögan M.C., Mendel J. M. (1994) Cumulant-based blind optimum beamforming. IEEE Transactions on Aerospace and Electronic Systems 30(3): 722–741

    Article  Google Scholar 

  • Du K.-L., Swamy M. N. S. (2008) A class of adaptive cyclostationary beamforming algorithms. Circuits, Systems and Signal Processing 27(1): 35–63

    Article  MATH  Google Scholar 

  • Fabrizio G. A., Gray D. A., Turley M. D. (2004) Experimental evaluation of adaptive beamforming methods and interference models for high frequency over-the-horizon radar systems. Multidimensional Systems and Signal Processing 14(1–3): 241–263

    Google Scholar 

  • Friedlander B., Porat B. (1989) Performance analysis of a null-steering algorithm based on direction-of-arrival estimation. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(4): 461–466

    Article  MathSciNet  Google Scholar 

  • Galy, J., & Adnet, C. (2000). Blind separation of non-circular sources. In Proceedings of the 10th IEEE workshop on statistical signal and array processing (pp. 315–318).

  • Gao F.-F., Nallanathan A., Wang Y. (2008) Improved MUSIC under the coexistence of both circular and noncircular sources. IEEE Transactions on Signal Processing 56(7): 3033–3038

    Article  MathSciNet  Google Scholar 

  • Gönen E., Mendel J. M. (1997) Applications of cumulants to array processing—Part III: Blind beamforming for coherent signals. IEEE Transactions on Signal Processing 45(9): 2252–2264

    Article  Google Scholar 

  • Gooch, R., Lundell, J. (1986). The CM array: An adaptive beamformer for constant-modulus signals. In Proceedings of the IEEE international conference on acoustics, speech, signal processing (ICASSP) (pp. 2523–2526). Tokyo, Japan.

  • Lee J.-H., Lee Y.-T. (1999) Robust adaptive array beamforming for cyclostationary signals under cycle frequency error. IEEE Transactions on Antennas and Propagation 47(2): 233–241

    Article  Google Scholar 

  • Li J., Stoica P. (2006) Robust adaptive beamforming. Wiley, New York

    Google Scholar 

  • Li J., Stoica P., Wang Z. (2003) On robust capon beamforming and diagonal loading. IEEE Transactions on Signal Processing 51(7): 1702–1715

    Article  Google Scholar 

  • Lorenz G. R., Boyd P. S. (2005) Robust minimum variance beamforming. IEEE Transactions on Signal Processing 53(5): 1684–1696

    Article  MathSciNet  Google Scholar 

  • Porat B., Friedlander B. (1991) Direction finding algorithms based on higher order statistics. IEEE Transactions on Signal Processing 39(9): 2016–2024

    Article  MATH  Google Scholar 

  • Roy R., Kailath T. (1989) ESPRIT—Estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(7): 984–995

    Article  Google Scholar 

  • Schmidt R. O. (1986) Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation 34(3): 276–280

    Article  Google Scholar 

  • Shahbazpanahi S., Gershman A. B., Luo Z.-Q, Wong K. M. (2003) Robust adaptive beamforming for general-rank signal models. IEEE Transactions on Signal Processing 51(9): 2257–2269

    Article  Google Scholar 

  • Tong, L., Soon, V. C., Huang, Y.-F., & Liu, R. (1990). AMUSE: A new blind identification algorithm. In Proceedings of the IEEE international symposium on circuits and systems (Vol. 3, pp. 1784–1787).

  • Tong L., Liu R., Soon V. C., Huang Y.-F. (1991) Indeterminacy and identifiability of blind identification. IEEE Transactions on Circuits and Systems 38(5): 499–509

    Article  MATH  Google Scholar 

  • Treichler J. R., Larimore M. G. (1985) New processing techniques based on constant modulus adaptive algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing 33(4): 420–431

    Article  Google Scholar 

  • van der Veen A. J. (1998) Algebraic methods for deterministic blind beamforming. Proceedings of the IEEE 86(10): 1987–2008

    Article  Google Scholar 

  • van der Veen A. J., Paulraj A. (1996) An analytical constant modulus algorithm. IEEE Transactions on Signal Processing 44(5): 1136–1155

    Article  Google Scholar 

  • Van Veen B.D., Buckley K.M. (1988) Beamforming: A versatile approach to spatial filtering. IEEE Acoustics, Speech, Signal Processing Magazine, 5(2): 4–24

    Google Scholar 

  • Vorobyov S. A., Gershman A. B., Luo Z. Q. (2003) Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem. IEEE Transactions on Signal Processing 51(2): 313–324

    Article  Google Scholar 

  • Wu Q., Wong K. M. (1996) Blind adaptive beamforming for cyclostationary signals. IEEE Transactions on Signal Processing 44(11): 2757–2767

    Article  Google Scholar 

  • Xu Y.-G., Liu Z.-W. (2007) Closed-form multiple invariance ESPRIT. Multidimensional Systems and Signal Processing 18(1): 47–54

    Article  MATH  Google Scholar 

  • Xu Y.-G., Liu Z.-W. (2008) Noncircularity-exploitation in direction estimation of noncircular signals with an acoustic vector-sensor. Digital Signal Processing 18(5): 777–796

    Article  Google Scholar 

  • Xu Y.-G., Liu Z.-W. (2008) Adaptive array utilising multimode antennas for correlated non-circular arrivals. Electronics Letters 44(22): 1285–1286

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Electronic Engineering, Beijing Institute of Technology, 100081, Beijing, People’s Republic of China

    Yougen Xu & Zhiwen Liu

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  1. Yougen Xu
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  2. Zhiwen Liu
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Correspondence to Yougen Xu.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant 60602037, 60672084, 60736006.

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Xu, Y., Liu, Z. Noncircularity restoral for multi-antenna blind beamforming. Multidim Syst Sign Process 21, 133–160 (2010). https://doi.org/10.1007/s11045-009-0093-4

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  • DOI: https://doi.org/10.1007/s11045-009-0093-4

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