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Source Enumeration Based on the Singular Vector of Hankel Matrix for Low Signal-to-Noise Ratio

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Abstract

Most existing source enumeration techniques in sensor-based studies have a satisfactory performance in high or middle signal-to-noise ratio (SNR), but lose effectiveness at low SNR. After Hankel matrices with different referenced signals and changeable dimensions are constructed, a source enumeration method is proposed based on the squared Euclidean norm of the product vector of the steering matrix and left singular vectors of Hankel matrix for low SNR. The proposed method employs the blind beamforming technique to estimate the steering matrix and the spatial smoothing scheme to dispose the dimension mismatched problem. Simulations are performed to display the validation for the non-coherent and coherent source signals and better enumeration performance at low SNR, in comparison with the conventional Akaike information criterion and minimum description length methods.

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References

  1. H. Akaike, A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Badeau, B. David, G. Richard, A new perturbation analysis for signal enumeration in rotational invariance techniques. IEEE Trans. Signal Process. 54(2), 450–458 (2006)

    Article  Google Scholar 

  3. F.R. Brcich, A. Zoubir, P. Pelin, Detection of sources using bootstrap techniques. IEEE Trans. Signal Process. 50(2), 206–215 (2002)

    Article  MathSciNet  Google Scholar 

  4. C. Coviello, L. Sibul, Blind source separation and beamforming: algebraic technique analysis. IEEE Trans. Aerosp. Electron. Syst. 40(1), 221–235 (2004)

    Article  Google Scholar 

  5. B. Dahanayake, K. Wong, Detection: a new approach [signals]. in IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5 (1988), pp. 2773–2776

  6. G. Gelli, L. Izzo, Minimum-redundancy linear arrays for cyclostationarity-based source location. IEEE Trans. Signal Process. 45(10), 2605–2608 (1997)

    Article  Google Scholar 

  7. J.F. Gu, P. Wei, H.M. Tai, Detection of the number of sources at low signal-to-noise ratio. IET Signal Process. 1(1), 2–8 (2007)

    Article  Google Scholar 

  8. M. Khan, M. Tufail, Comparative analysis of various matrix pencil methods for direction of arrival estimation. in Proceedings of International Conference on Image Analysis and Signal Processing (IASP), (2010), pp. 496–501

  9. H. Lee, F. Li, An eigenvector technique for detecting the number of emitters in a cluster. IEEE Trans. Signal Process. 42(9), 2380–2388 (1994)

    Article  Google Scholar 

  10. Z. Lu, A. Zoubir, Flexible detection criterion for source enumeration in array processing. IEEE Trans. Signal Process. 61(6), 1303–1314 (2013)

    Article  MathSciNet  Google Scholar 

  11. R. Nadakuditi, J. Silverstein, Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samples. IEEE J. Sel. Top. Signal Process. 4(3), 468–480 (2010)

    Article  Google Scholar 

  12. S. Pillai, B. Kwon, Forward/backward spatial smoothing techniques for coherent signal identication. IEEE Trans. Acoust. Speech Signal Process. 37(1), 8–15 (1989)

    Article  MATH  Google Scholar 

  13. 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  MATH  Google Scholar 

  14. D. Schmidt, E. Makalic, The consistency of MDL for linear regression models with increasing signal-to-noise ratio. IEEE Trans. Signal Process. 60(3), 1508–1510 (2012)

    Article  MathSciNet  Google Scholar 

  15. P. Stoica, M. Jansson, On maximum likelihood estimation in factor analysisan algebraic derivation. Signal Process. 89(6), 1260–1262 (2009)

    Article  MATH  Google Scholar 

  16. A.J. van der Veen, Algebraic methods for deterministic blind beamforming. Proc. IEEE 86(10), 1987–2008 (1998)

    Article  Google Scholar 

  17. M. Viberg, B. Ottersten, T. Kailath, Detection and estimation in sensor arrays using weighted subspace fitting. IEEE Trans. Signal Process. 39(11), 2436–2449 (1991)

    Article  Google Scholar 

  18. M. Wax, I. Ziskind, Detection of signals by information theoretic criteria. IEEE Trans. Acoust. Speech Signal Process. 33(2), 387–392 (1985)

    Article  MathSciNet  Google Scholar 

  19. M. Wax, T. Kailath, Detection of the number of coherent signals by the MDL principle. IEEE Trans. Acoust. Speech Signal Process. 37(8), 1190–1196 (1989)

    Article  Google Scholar 

  20. D. Williams, D. Johnson, Using the sphericity test for source detection with narrowband passive arrays. IEEE Trans. Acoust. Speech Signal Process. 38(11), 2008–2014 (1990)

    Article  Google Scholar 

  21. N. Yilmazer, J. Koh, T.K. Sarkar, Utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival. IEEE Trans. Antennas Propag. 54(1), 175–181 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the Scientific and Technological Scheme of Jilin Province (20130101058JC), the Science and Technology Department of Jilin Province (20150204008GX) and the Education Department of Jilin Province (2014B006).

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Authors and Affiliations

  1. College of Communication Engineering, Jilin University, Changchun, 130012, People’s Republic of China

    Hairong Zhang, Pan Jiang, Guijin Yao & Ling Li

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  1. Hairong Zhang
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  2. Pan Jiang
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  3. Guijin Yao
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  4. Ling Li
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Correspondence to Guijin Yao.

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Zhang, H., Jiang, P., Yao, G. et al. Source Enumeration Based on the Singular Vector of Hankel Matrix for Low Signal-to-Noise Ratio. Circuits Syst Signal Process 36, 1085–1098 (2017). https://doi.org/10.1007/s00034-016-0340-5

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