Doa estimation using a sparse linear model based on eigenvectors


To reduce high computational cost of existing Direction-Of-Arrival (DOA) estimation techniques within a sparse representation framework, a novel method with low computational complexity is proposed. Firstly, a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built. Then based on the FOCal Underdetermined System Solver (FOCUSS) algorithm, a sparse solution finding algorithm to solve the model is developed. Compared with other state-of-the-art methods using a sparse representation, our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources. However, our method has lower computational complexity and performs better in low Signal-to-Noise Ratio (SNR). Lastly, the performance of the proposed method is illustrated by computer simulations.

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  1. [1]

    H. Krim and M. Viberg. Two decades of array signal processing research: The parametric approach. IEEE Signal Processing Magazine, 13(1996)4, 67–94.

    Article  Google Scholar 

  2. [2]

    D. Malioutov, M. Çetin, and A. Willsky. A Sparse Signal Reconstruction Perspective for DOA estimation with Sensor Arrays. IEEE Transactions on Signal Processing, 53(2005)8, 3010–3022.

    MathSciNet  Article  Google Scholar 

  3. [3]

    G. Karabulut, T. Kurt, and A. Yongaçoĝlu. Estimation of directions of arrival by matching pursuit (EDAMP). EURASIP Journal of Wireless Communications and Networking, 2005(2005)2, 197–205.

    MATH  Google Scholar 

  4. [4]

    S. Cotter, B. Rao, K. Engan, et al. Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Transactions on Signal Processing, 53(2005)7, 2477–2488.

    MathSciNet  Article  Google Scholar 

  5. [5]

    D. Model and M. Zibulevsky. Signal reconstruction in sensor arrays using sparse representations. Elsevier Signal Processing, 86(2006)1, 624–638.

    MATH  Google Scholar 

  6. [6]

    X. Guo, Q. Wan, C. Chang, et al. DOA estimation using a sparse representation framework to achieve superresolution. Multidimensional Systems and Signal Processing, 21(2010)4, 391–402.

    MathSciNet  MATH  Article  Google Scholar 

  7. [7]

    M. Hyder and K. Mahata. Direction-of-arrival estimation using a mixed l 2,0 norm approximation. IEEE Transactions on Signal Processing, 58(2010)9, 4646–4655.

    MathSciNet  Article  Google Scholar 

  8. [8]

    I. Gorodnitsky and B. Rao. Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Transactions on Signal Processing, 45(1997)3, 600–616.

    Article  Google Scholar 

  9. [9]

    A. Cadzow, S. Kim, and C. Shiue. General direction-of-arrival estimation: a signal subspace approach. IEEE Transactions on Aerospace and Electronic Systems, 25(1989)1, 31–47.

    MathSciNet  Article  Google Scholar 

  10. [10]

    A. Bruckstein, D. Donoho, and M. Elad. From sparse solution of system of equations to sparse modeling of signals and image. SIAM Review, 51(2009)1, 34–81.

    MathSciNet  MATH  Article  Google Scholar 

  11. [11]

    J. Tropp and S. Wright. Computational methods for sparse solution of linear inverse problem. Proceedings of the IEEE, 98(2010)6, 948–958.

    Article  Google Scholar 

  12. [12]

    D. Needell and J. Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26 (2009)3, 301–321.

    MathSciNet  MATH  Article  Google Scholar 

  13. [13]

    S. Chen, D. Donoho, and M. Saunders. Atomic decomposition by basis pursuit. SIAM Review, 20(2001) 1, 33–61.

    MathSciNet  Google Scholar 

  14. [14]

    R. Chartrand. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Processing Letters, 14(2007)10, 707–710.

    Article  Google Scholar 

  15. [15]

    C. Austin, R. Moses, J. Ash, et al. On the relation between sparse reconstruction and parameter estimation with model order selection. IEEE Journal of Selected Topics in Signal Processing, 4(2010)3, 560–570.

    Article  Google Scholar 

  16. [16]

    R. Giryes, M. Elad, and Y. Eldar. The projected GSURE for automatic parameter tuning in iterative shrinkage methods. Applied and Computational Harmonic Analysis, 30(2011)3, 407–422.

    MathSciNet  MATH  Article  Google Scholar 

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Author information



Corresponding author

Correspondence to Libin Wang.

Additional information

Supported by the National Natural Science Foundation of China (No. 60502040) and the Innovation Foundation for Outstanding Postgraduates in the Electronic Engineering Institute of PLA (No. 2009YB005).

Communication author: Wang Libin, 1984, male, Ph. D. candidate.

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Wang, L., Cui, C. & Li, P. Doa estimation using a sparse linear model based on eigenvectors. J. Electron.(China) 28, 496–502 (2011).

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Key words

  • Direction-Of-Arrival (DOA) estimation
  • Sparse linear model
  • Eigen-value decomposition
  • Sparse solution finding

CLC index

  • TN911.23