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Multidimensional Systems and Signal Processing

, Volume 30, Issue 1, pp 465–491 | Cite as

DOA estimation with double L-shaped array based on Hadamard product and joint diagonalization in the presence of sensor gain-phase errors

  • Weiwei HuEmail author
  • Guozheng Xu
Article
  • 83 Downloads

Abstract

A method with double L-shaped array for direction-of-arrival (DOA) estimation in the presence of sensor gain-phase errors is presented. The reason for choosing double L-shaped array is that the shared elements between sub-arrays are the most and rotation invariant property can be applied for this array. The proposed method is introduced as follows. (1) If the number of signal is one, first the gain errors are estimated and removed with the diagonal of the covariance matrix of the array output. Then the array is rotated by an unknown angle and DOA can be estimated with the relationship between signal subspace and steering vector of signal. (2) If signals are more than one, the method for eliminating gain errors is the same with the previous case, and then the phase errors are removed by the Hadamard product of the (cross) covariance matrix and its conjugate. After the errors are eliminated, the DOAs can be estimated by rotation invariant property and orthogonal joint diagonalization for the Hadamard product. This method requires neither calibrated sources nor multidimensional parameter search, and its performance is independent of the phase errors. Simulation results demonstrate the effectiveness of the proposed method.

Keywords

Array signal processing DOA estimation Double L-shaped array Gain-phase errors Hadamard product Joint diagonalization 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their many insightful comments and suggestions, which helped improve the quality and readability of this paper.

References

  1. Blunt, S. D., Chan, T., & Gerlach, K. (2011). Robust DOA estimation: The reiterative superresolution (RISR) algorithm. IEEE Transactions on Aerospace and Electronic Systems, 47(1), 332–346.CrossRefGoogle Scholar
  2. Cao, S., & Ye, Z. (2013). A Hadamard product based method for DOA estimation and gain-phase error calibration. IEEE Trans on Aerospace and Electronic Systems, 49(2), 1224–1233.MathSciNetCrossRefGoogle Scholar
  3. Capon, J. (1969). High-resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE, 57, 1408–1418.CrossRefGoogle Scholar
  4. Cheng, Q. (2000). Asymptotic performance of optimal gain- and-phase estimators of sensor arrays. IEEE Transactions on Signal Processing, 48(12), 3587–3590.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Ferréol, A., Larzabal, P., & Viberg, M. (2010). Statistical analysis of the MUSIC algorithm in the presence of modeling errors, taking into account the resolution probability. IEEE Transactions on Signal Processing, 58(8), 4156–4166.MathSciNetCrossRefzbMATHGoogle Scholar
  6. Friedlander, B., & Weiss, A. J. (1993). Performance of direction-finding systems with sensor gain and phase uncertainties. Circuits, Systems and Signal Processing, 12(1), 3–33.CrossRefzbMATHGoogle Scholar
  7. Godara, L. C. (1997). Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations. Proceedings of the IEEE, 85(8), 1195–1245.CrossRefGoogle Scholar
  8. Krim, J., & Viberg, M. (1996). Two decades of array signal processing research: The parametric approach. IEEE Signal Processing Magazine, 13(3), 67–94.CrossRefGoogle Scholar
  9. Li, J., Stoica, P., & Wang, Z. (2003). On robust Capon beamforming and diagonal loading. IEEE Transactions on Signal Processing, 51(7), 1702–1715.CrossRefGoogle Scholar
  10. Li, Y., et al. (2006). Theoretical analyses of gain and phase uncertainty calibration with optimal implementation for linear equispaced array. IEEE Transactions on Signal Processing, 54(2), 712–723.CrossRefzbMATHGoogle Scholar
  11. Liu, A., et al. (2011). An eigenstructure method for estimating DOA and sensor gain-phase errors. IEEE Transactions on Signal Processing, 59(2), 5944–5956.MathSciNetCrossRefzbMATHGoogle Scholar
  12. Ng, B. P., et al. (2009). A practical simple geometry and gain/phase calibration technique for antenna array processing. IEEE Transactions on Antennas and Propagation, 57(7), 1963–1972.CrossRefGoogle Scholar
  13. Paulraj, A., & Kailath, T. (1985). Direction of arrival estimation by Eigen-structure methods with unknown sensor gain and phase. In Proceedings of IEEE (ICASSP’85) (pp. 640–643).Google Scholar
  14. Roy, R., & Kailath, T. (1989). ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Signal Processing, 37(7), 984–995.CrossRefzbMATHGoogle Scholar
  15. Schmidt, R. O. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3), 276–280.CrossRefGoogle Scholar
  16. Stoica, P., & Sharman, K. C. (1990). Maximum likelihood methods for direction of arrival estimation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(7), 1132–1143.CrossRefzbMATHGoogle Scholar
  17. Stoica, P., Wang, Z., & Li, J. (2005). Extended derivation of MUSIC in presence of steering vector errors. IEEE Transactions on Signal Processing, 53(3), 1209–1211.CrossRefGoogle Scholar
  18. Sylvie, M., Alain, M., & Messaoud, B. (1995). The propagator method for source bearing estimation. Signal Processing, 42(2), 121–138.CrossRefGoogle Scholar
  19. Wang, B. H., Wang, Y. L., & Chen, H. (2003). Array calibration of angularly dependent gain and phase uncertainties with instrumental sensors. In IEEE international symposium on phased array systems and technology (pp. 182–186).Google Scholar
  20. Wang, B. H., Wang, Y. L., Chen, H., et al. (2004). Array calibration of angularly dependent gain and phase uncertainties with carry-on instrumental sensors. Science in China Series F-Information Sciences, 47(6), 777–792.CrossRefGoogle Scholar
  21. Weiss, A. J., & Friedlander, B. (1990). Eigenstructure methods for direction finding with sensor gain and phase uncertainties. Circuits, Systems and Signal Processing, 9(3), 271–300.MathSciNetCrossRefzbMATHGoogle Scholar
  22. Xie, W., Wang, C., Wen, F., et al. (2017a). DOA and gain-phase errors estimation for noncircular sources with central symmetric array. IEEE Sensors Journal, 17(10), 3068–3078.CrossRefGoogle Scholar
  23. Xie, W., Wen, F., Liu, J., & Wan, Q. (2017b). Source association, DOA, and fading coefficients estimation for multipath signals. IEEE Transactions on Signal Processing, 65(11), 2773–2786.MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Posts and TelecommunicationsNanjingPeople’s Republic of China

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