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Off-Grid Direction-of-Arrival Estimation Based on Steering Vector Approximation

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Abstract

In this paper, a novel off-grid direction-of-arrival (DOA) estimation algorithm is proposed based on steering vector approximation. The conventional multiple signal classification (MUSIC) technique estimates the DOA with a uniformly discretized grid by assuming that the true DOAs lie on the grids. In practice, this assumption is rarely satisfied. In order to improve the estimation accuracy, a dense sampling grid is required for the MUSIC technique. Besides the higher computational complexity, it is still not guaranteed that the dense sampling grids will cover the true DOAs. In order to address the off-grid problem with a lower computational complexity, we use the Taylor series expansion to approximate the steering vectors. We first construct a two-dimensional spectrum searching method to simultaneously estimate the nearest on-grid DOA and the corresponding off-grid error. To further improve the estimation accuracy, we then solve an optimization problem to obtain the accurate DOA estimation, which is formulated by the fact that the signal and noise subspaces are orthogonal to each other. Simulation results demonstrate the effectiveness of the proposed off-grid DOA estimation algorithm.

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References

  1. J. Capon, High-solution frequency-wavenumber spectrum analysis. Proc. IEEE 57, 1408–1418 (1969)

    Article  Google Scholar 

  2. Y. Chi, L.L. Scharf, A. Pezeshki, A.R. Calderbank, Sensitivity to basis mismatch in compressed sensing. IEEE Trans. Signal Process. 59, 2182–2195 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. D.L. Donoho, Compressive sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006)

    Article  MATH  Google Scholar 

  4. N.R. Goodman, Statistical analysis based on a certain multivariate complex gaussian distribution. Ann. Math. Stat. 34, 152–177 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. Gu, A. Leshem, Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation. IEEE Trans. Signal Process. 60, 3881–3885 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. Gu, N.A. Goodman, S. Hong, Y. Li, Robust adaptive beamforming based on interference covariance matrix sparse reconstruction. Signal Process. 96, 375–381 (2014)

    Article  Google Scholar 

  7. Y. Gu, N.A. Goodman, Information-theoretic compressive sensing kernel optimization and Bayesian Cramer–Rao bound for time delay estimation. IEEE Trans. Signal Process. 65, 4525–4537 (2017)

    Article  MathSciNet  Google Scholar 

  8. L. Huang, H.C. So, Source enumeration via MDL criterion based on linear shrinkage estimation of noise subspace covariance matrix. IEEE Trans. Signal Process. 61, 4806–4821 (2013)

    Article  Google Scholar 

  9. A. Leshem, A.-J. van der Veen, Radio-astronomical imaging in the presence of strong radio interference. IEEE Trans. Inf. Theory 53, 1730–1747 (2000)

    Article  MATH  Google Scholar 

  10. F. Li, H. Liu, R.J. Vaccaro, Performance analysis for DOA estimation algorithms: unification, simplification, and observations. IEEE Trans. Aerosp. Electron. Syst. 29, 1170–1184 (1993)

    Article  Google Scholar 

  11. D. Malioutov, M. Çetin, A.S. Willsky, A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. 63, 3010–3022 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Pal, P.P. Vaidyanathan, A grid-less approach to underdetermined direction of arrival estimation via low rank matrix denoising. IEEE Signal Process. Lett. 21, 737–741 (2014)

    Article  Google Scholar 

  13. B.D. Rao, K.V.S. Hari, Performance analysis of root-MUSIC. IEEE Trans. Acoust. Speech Signal Process. 37, 1939–1949 (1989)

    Article  Google Scholar 

  14. R. Roy, A. Paulraj, T. Kailath, ESPRIT-A subspace rotation approach to estimation of parameters of Cisoids in noise. IEEE Trans. Acoust. Speech Signal Process. 34, 1340–1342 (1986)

    Article  Google Scholar 

  15. R.O. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 37, 276–280 (1986)

    Article  Google Scholar 

  16. P. Stoica, A. Nehorai, Performance study of conditional and unconditional direction-of-arrival estimation. IEEE Trans. Acoust. Speech Signal Process. 38, 1783–1795 (1990)

    Article  MATH  Google Scholar 

  17. H.L. Van Trees, Detection, Estimation and Modulation Theory, Part IV: Optimum Array Processing (Wiley, Hoboken, 2002)

    Google Scholar 

  18. S.A. Vorobyov, A.B. Gershman, Z.Q. Luo, Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem. IEEE Trans. Signal Process. 51, 313–324 (2003)

    Article  Google Scholar 

  19. S.A. Vorobyov, A. Gershman, K.M. Wong, Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays. IEEE Trans. Signal Process. 53, 34–43 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. B. Wang, Y.D. Zhang, W. Wang, Robust DOA estimation in the presence of miscalibrated sensors. IEEE Signal Process Lett. 24, 1073–1077 (2017)

    Article  Google Scholar 

  21. B. Wang, W. Wang, Y. Gu, S. Lei, Underdetermined DOA estimation of quasi-stationary signals using a partly-calibrated array. Sensors 17, 1–14 (2017)

    Article  Google Scholar 

  22. G. Wang, J. Xin, N. Zheng, A. Sano, Computationally efficient subspace-based method for two-dimensional direction estimation with L-shaped array. IEEE Trans. Signal Process. 59, 3197–3212 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. G. Wang, J. Xin, J. Wang, N. Zheng, A. Sano, Subspace-based two-dimensional direction estimation and tracking of multiple targets. IEEE Trans. Aerosp. Electron. Syst. 51, 1386–1402 (2015)

    Article  Google Scholar 

  24. X. Wu, W. Zhu, J. Yan, A fast gridless covariance matrix reconstruction method for one- and two-dimensional direction-of-arrival estimation. IEEE Sens. J. 17, 4916–4927 (2017)

    Article  Google Scholar 

  25. X. Wu, W. Zhu, J. Yan, Z. Zhang, Two sparse-based methods for off-grid direction-of-arrival estimation. Signal Process. 142, 87–95 (2018)

    Article  Google Scholar 

  26. Z. Yang, L. Xie, C. Zhang, Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans. Signal Process. 61, 38–43 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. C. Zhou, Y. Gu, Y.D. Zhang, Z. Shi, T. Jin, X. Wu, Compressive sensing-based coprime array direction-of-arrival estimation. IET Commun. 11, 1719–1724 (2017)

    Article  Google Scholar 

  28. I. Ziskind, M. Wax, Maximum likelihood localization of multiple sources by alternate projection. IEEE Trans. Acoust. Speech Signal Process. 36, 1553–1560 (1988)

    Article  MATH  Google Scholar 

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Acknowledgements

The work of W. Wang is supported by the National Natural Science Foundation (61571148) and Fundamental Research for the Central University (HEUCFG201823 and HEUCFP201836).

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Authors and Affiliations

  1. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Ben Wang & Wei Wang

  2. Department of Electrical and Computer Engineering, Temple University, Philadelphia, PA, 19122, USA

    Yujie Gu

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  1. Ben Wang
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  2. Yujie Gu
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  3. Wei Wang
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Correspondence to Wei Wang.

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Wang, B., Gu, Y. & Wang, W. Off-Grid Direction-of-Arrival Estimation Based on Steering Vector Approximation. Circuits Syst Signal Process 38, 1287–1300 (2019). https://doi.org/10.1007/s00034-018-0914-5

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  • DOI: https://doi.org/10.1007/s00034-018-0914-5

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