Skip to main content
SpringerLink
Log in

DOA Estimation of Noncircular Signal Based on Sparse Representation

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In this paper, we propose a novel method employing subspace fitting principle for DOA estimation of noncircular signal based on the sparse representation technology. The proposed method combines the signal information contained in both the covariance and elliptic covariance matrix of the received data matrix. We use the eigenvalue decomposition of the extended covariance to obtain the signal eigenvectors, and represent the steering vector on overcomplete basis subject to sparse constraint in subspace fitting method. After casting multiple dimensional optimization problem of the classical subspace fitting method as a sparse reconstruction problem, we use L1-norm penalty for sparsity, and optimization by the second order cone programming framework to obtain the DOA estimates. The proposed method can be used in arbitrary array configuration. Compared with the existing algorithms, the simulation results show that the proposed method has better performance in low SNR. Compared with L1-SVD, the proposed method also own better resolution probability.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Barabell, A. J. (1983). Improving the resolution performance of eigenstructure-based direction-finding algorithms. ICASSP, 8, 336–339.

  2. Rao, B. D., & Hari, K. V. (1989). Performance analysis of Root-MUSIC. IEEE Transaction on Acoustics, Speech and Signal Processing, 37(12), 1939–1949.

  3. Ren, Q. S., & Willis, A. J. (1997). Fast Root-MUSIC algorithm. IEE Electronics Letters, 33(6), 450–451.

    Article  Google Scholar 

  4. Roy, R., Paulraj, A., & Kailath, T. (1989). ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transaction on Acoustics, Speech and Signal Processing, 37, 984–995.

    Article  Google Scholar 

  5. Shahbazpanahi, S., & Valaee, S. (2001). Distributed source localization using ESPRIT algorithm. IEEE Transaction on Signal Processing, 49, 2169–2178.

    Article  Google Scholar 

  6. Ottersten, B., & Viberg, M. (1991). Sensor array processing based on subspace fitting IEEE Transaction on. Signal Processing, 39(5), 1110–1121.

    MATH  Google Scholar 

  7. Malioutov, D., Cetin, M., & Willsky, A. S. (2005). A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Transaction on Signal Processing, 53(8), 3010–3022.

    Article  MathSciNet  Google Scholar 

  8. Hyder, M. M., & Mahata, K. (2010). Direction-of-arrival estimation using a mixed L2,0 norm approximation. IEEE Transaction on Signal Processing, 58(9), 4646–4655.

    Article  MathSciNet  Google Scholar 

  9. He, Z. Q., Liu, Q. H., Jin, L. N., et al. (2013). Low complexity method for DOA estimation using array covariance matrix sparse representation. Electronics Letters, 49(3), 228–230.

    Article  Google Scholar 

  10. Stoica, P., Babu, P., & Li, J. (2011). SPICE: A sparse covariance-based estimation method for array processing. IEEE Transaction on Signal Processing, 59(2), 629–638.

    Article  MathSciNet  Google Scholar 

  11. Abeida, H., Zhang, Q., Li, J., et al. (2013). Iterative sparse asymptotic minimum variance based approaches for array processing. IEEE Transaction on Signal Processing, 61(4), 933–944.

    Article  Google Scholar 

  12. Gounon, P., Adnet, C., & Galy, J. (1998). Localization angulaire de signaux non circulaires. Traitement du Signal, 15(1), 17–23. 1998.

    MATH  Google Scholar 

  13. Chlarge, P., Wang, Y., & Saillard, J. (2001). A Root-MUSIC algorithm for non circular sources, In IEEE international conference acoustics, speech, and signal processing (pp. 7–11). Salt Lake City, UT.

  14. Chlarge, P., Wang, Y., & Saillard, J. (2001). A non-circular sources direction finding method using polynomial rooting. Signal Processing, 81, 1765–1770.

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Gao, F., Wang, Y., & Nallanathan, A. (2006). Improved MUSIC by exploiting both real and complex sources. Washington, DC: MILCOM.

    Book  Google Scholar 

  17. Zoubir, A., Charge, P., & Wang, Y. (2003). Non circular sources localization with ESPRIT. In Proceedings of European conference on wireless technology (ECWT 2003). Munich, Germany.

  18. Liu, Z., Huang, Z., Zhou, Y., et al. (2012). Direction-of-arrival estimation of noncircular signals via sparse representation. IEEE Transactions on Aerospace and Electronic Systems, 48(3), 2690–2698.

    Article  MathSciNet  Google Scholar 

  19. Wong, K. M., Reilly, J. P., Wu, Q., et al. (1992). Estimation of the directions of arrival of signals in unknown correlated noise. I. The MAP approach and its implementation. IEEE Transaction on Signal Processing, 40(8), 2007–2017.

    Article  MATH  Google Scholar 

  20. Stoica, P., & Sharman, K. C. (1990). Novel eigenanalysis method for direction estimation. IEE Proceedings F (Radar and Signal Processing), 137(1), 19–26.

    Article  MathSciNet  Google Scholar 

  21. Steiglitz, K., & McBride, L. (1965). A technique for identification of linear system. IEEE Transaction on Automatic Control, 10(4), 461–464.

    Article  Google Scholar 

  22. Cadzow, J. A. (1990). Multiple source location-the signal subspace approach. IEEE Transaction on Acoustics, Speech and Signal Processing, 38(7), 1110–1125.

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Grant, M., & Boyd, S. (2010). CVX: MATLAB software for disciplined convex programming. Online available: http://cvxr.com/cvx.

  25. Sturm, J. S. (2010). Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Online available: http://fewcal.kub.nl/strum

  26. Jeffries, D. J., & Farrier, D. R. (1985). Asymptotic results for eigenvector methods. IEE Proceedings F (Communications, Radar and Signal Processing), 132(7), 589–594.

  27. Viberg, M., Ottersten, B., & Kailath, T. (1991). Detection and estimation in sensor arrays using weighted subspace fitting. IEEE Transaction on Signal Processing, 39(11), 2436–2449.

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the National Natural Science Foundation of China under Grant No. 61301155 and 61176025, and the Fundamental Research Funds for the Central Universities Project No. ZYGX2012J003, for which the authors would like to express their thanks. The authors also wish to thank the anonymous reviewers for their helpful and constructive comments and suggestions.

Author information

Authors and Affiliations

  1. School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Xuemin Yang, Guangjun Li & Zhi Zheng

Authors
  1. Xuemin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guangjun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuemin Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Li, G. & Zheng, Z. DOA Estimation of Noncircular Signal Based on Sparse Representation. Wireless Pers Commun 82, 2363–2375 (2015). https://doi.org/10.1007/s11277-015-2352-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-015-2352-z

Keywords

Search

Navigation