Skip to main content
SpringerLink
Log in

Novel methods of DOA estimation based on compressed sensing

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

Making use of the sparsity of targets, three novel direction of arrival (DOA) models based on compressed sensing (CS) theory are proposed. Covariance matrix CS, interpolated array CS and beam space CS carry out compressive sampling on covariance matrix, interpolated array and beam space, respectively. High-resolution DOA estimations are obtained through reconstruction of sparse signal by convex optimization problem resolution. The proposed methods are conceptually different from subspace-based methods and provide high resolution using a uniform linear array without restricting requirements on the spatial and temporal stationary and correlation properties of the sources and the noise. Results of both simulated data and measured data show that these methods are superior to conventional DOA methods in angular estimation performance.

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

Similar content being viewed by others

References

  • Baraniuk, R. (2007). A lecture on compressive sensing. IEEE Signal Processing Magazine, 24(4), 118–121.

    Article  Google Scholar 

  • Bilik, I. (2011). Spatial compressive sensing for direction-of-arrival estimation of multiple sources using dynamic sensor arrays. IEEE Transactions on Aerospace and Electronic Systems, 47(3), 1754–1769.

    Article  MathSciNet  Google Scholar 

  • Candas, E. J., & WaKin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.

    Article  Google Scholar 

  • Candes, E. J., & Tao, T. (2006). Near-optimal signal recovery from random projections: Universal encoding strategies. IEEE Transactions on Information Theory, 52(12), 5406–5425.

    Article  MathSciNet  Google Scholar 

  • Chen, S. S., Donoho, D. L., & Saunders, M. A. (2001). Atomic decomposition by basis pursuit. SIAM Review, 43(1), 129–159.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Dmitry, M. M., Mujdat, C., & Alan, S. W. (2005). A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Transactions on Signal Processing, 53(8), 3010–3022.

    Article  MathSciNet  Google Scholar 

  • Donoho, D. L., & Tsaig, Y. (2006). Extensions of compressed sensing. Signal Processing, 86(3), 533–548.

    Article  MATH  Google Scholar 

  • Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.

    Article  MATH  MathSciNet  Google Scholar 

  • Figueiredo, M. A. T., Nowak, R. D., & Wright, S. J. (2007). Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 1(4), 586–598.

    Article  Google Scholar 

  • Gurbuz, A. C., Mcclellan, J. H., & Cevher, V. (2008). A compressive beamforming method. In Proceedings of the international conference on acoustics, speech and signal processing, ICASSP March (pp. 2617–2620).

  • Gurbuz, A. C., Cevher, V., & Mcclellan, J. H. (2012). Bearing estimation via spatial sparsity using compressive sensing. IEEE Transactions on Aerospace and Electronic Systems, 48(2), 1358–1369.

    Article  Google Scholar 

  • Huang, J., & Zhang, T. (2010). The benefit of group sparsity. The Annals of Statistics, 38(4), 1978–2004.

    Article  MATH  MathSciNet  Google Scholar 

  • Kim, S. J., Koh, K., Lustig, M., et al. (2007). A method for large-scale regularized least-squares. IEEE Journal of Selected Topics in Signal Processing, 4(1), 606–617.

    Article  Google Scholar 

  • Kim, J. K., Lee, O. K., & Ye, J. C. (2012). Compressive MUSIC: A missing link between compressive sensing and array signal processing. IEEE Transactions on Information Theory, 58(1), 278–301.

    Article  MathSciNet  Google Scholar 

  • Li, J. (1992). Improved angular resolution for spatial smoothing techniques. IEEE Transactions on Signal Processing, 40(12), 3078–3081.

    Article  Google Scholar 

  • Liu, Z., Ruan, X., & He, J. (2013). Efficient 2-D DOA estimation for coherent sources with a sparse acoustic vector-sensor array. Multidimensional Systems and Signal Processing, 24(1), 105–120.

    Article  MATH  MathSciNet  Google Scholar 

  • Mallat, S., & Zhang, Z. (1993). Matching pursuit with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(12), 3397–3415.

    Article  MATH  Google Scholar 

  • Pillai, S. U., & Kwon, B. H. (1989). Forward/backward spatial smoothing techniques for coherent signal identification. IEEE Transactions on Acoustics, Speech, Signal Processing, 37(1), 8–15.

    Article  MATH  Google Scholar 

  • Roy, R., Paulraj, A., & Kailath, T. (1986). ESPRIT-A subspace rotation approach to estimation of parameters of Cisoids in noise. IEEE Transactions on Acoustics, Speech and Signal Processing, 34(5), 1340–1342.

    Article  Google Scholar 

  • Schmidt, R. O. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 24(3), 276–280.

    Article  Google Scholar 

  • Stoica, P., & Nehorai, A. (1990). Performance study of conditional and unconditional direction-of-arrival estimation. IEEE Transactions on Signal Process, 38(10), 1783–1795.

    Article  MATH  Google Scholar 

  • Stoica, P., Ottersten, B., Viberg, M., et al. (1996). Maximum likelihood array processing for stochastic coherent sources. IEEE Transactions on Signal Processing, 44(1), 96–105.

    Article  Google Scholar 

  • Tropp, J. A., & Gilbert, A. C. (2007). Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 53(12), 4655–4666.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, Y., Leus, G., & Pandharipande, A. (2009). Direction estimation using compressive sampling array processing. In Proceedings of the 15th IEEE workshop on statistical, signal processing, (pp. 626–629).

  • Xu, X., Wei, X. H., & Ye, Z. F. (2012). DOA estimation based on sparse signal recovery utilizing weighted l1-norm penalty. IEEE Signal Processing Letters, 19(3), 155–158.

    Article  Google Scholar 

  • Yu, Y., & Poor, H. V. (2010). MIMO Radar using compressive sampling. IEEE Journal of Selected Topics in Signal Processing, 4(1), 146–163.

    Article  Google Scholar 

  • Zhao, G. H., Chen, B. X., & Dong, M. (2008). A new DOA estimator based on alternating projection and its application in VHF radar (in Chinese). Journal of Electronic and Information Technology, 30(1), 224–227.

    Article  Google Scholar 

  • Zheng, Z., Li, G. J., & Fast, D. O. A. (2013). Estimation of incoherently distributed sources by novel propagator. Multidimensional Systems and Signal Processing, 24(3), 573–581.

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation of China (61001209, 61101244), the Fundamental research Funds for the Central Universities (K5051202038) and Program for Changjiang Scholars and Innovative Research Team in University (IRT0954).

Author information

Authors and Affiliations

  1. National Key Lab of Radar Signal Processing, Xidian University, Xi’an, Shaanxi, 710071, China

    Wei Zhu & Bai-Xiao Chen

Authors
  1. Wei Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bai-Xiao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Zhu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, W., Chen, BX. Novel methods of DOA estimation based on compressed sensing. Multidim Syst Sign Process 26, 113–123 (2015). https://doi.org/10.1007/s11045-013-0239-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-013-0239-2

Keywords

Search

Navigation