volume | PIER Journals

Abstract

In this paper, an improved L1-SVD algorithm based on noise subspace is presented for direction of arrival (DOA) estimation using the reweighted L1 minimization. In the proposed method, the weighted vector is obtained by utilizing the orthogonality between the noise subspace and the subspace spanned by the array manifold matrix. The presented algorithm banishes the nonzero entries whose indices are inside of the row support of the jointly sparse signals by smaller weights and the other entries whose indices are more likely to be outside of the row support of the jointly sparse signals by larger weights. Therefore, the sparsity at the real signal locations can be enhanced by using the presented method. The proposed approach offers a good deal of merits over other DOA techniques. It not only increases the robustness to noise, but also enhances resolution in DOA estimation. Furthermore, it does not require an exact initialization. Simulation results show that the presented algorithm has better performance than the existing algorithms, such as MUSIC, L1-SVD algorithm.

1. Liu, , F. L., J. Wang, C. Y. Sun, and R. Du, , "Robust MVDR beamformer for nulling level control via multi-parametric quadratic programming," Progress In Electromagnetics Research C, Vol. 20, 239-254, 2011.. Google Scholar

2. Yang, , P., F. Yang, and Z. P. Nie, "DOA estimation with sub-array divided technique and interpolated esprit algorithm on a cylindrical conformal array antenna," Progress In Electromagnetics Research, Vol. 103, 201-216, 2010..
doi:10.2528/PIER10011904 Google Scholar

3. Liang, , J., D. Liu, and , "Two L-shaped array-based 2-D DOAs estimation in the presence of mutual coupling," Progress In Electromagnetics Research,, Vol. 112, 273-298, 2011. Google Scholar

4. Zaharis, Z. D. and T. V. Yioultsis, Z. D., T. V. Yioultsis, and , "A novel adaptive beamforming technique applied on linear antenna arrays using adaptive mutated boolean PSO," Progress In Electromagnetics Research , Vol. 117, 165-179, 2011. Google Scholar

5. Liu, , F. L., J. K. Wang, R. Y. Du, L. Peng, and P. P. Chen, "A second-order cone programming approach for robust downlink beamforming with power control in cognitive radio networks ," Progress In Electromagnetics Research M, Vol. 18, 221-231, 2011. Google Scholar

6. Mallipeddi, , R., J. P. Lie, P. N. Suganthan, S. G. Razul, and C. M. S. See, "A differential evolution approach for robust adaptive beamforming based on joint estimation of look direction and array geometry," Progress In Electromagnetics Research, , Vol. 119, 381-394, 2011.
doi:10.2528/PIER11052205 Google Scholar

7. Capon, , J., , "High resolution frequency-wavenumber spectrum analysis ," Proc. IEEE, Vol. 57, No. 8, 1408-1418, Aug. 1969..
doi:10.1109/PROC.1969.7278 Google Scholar

8. Schmidt, , R. O., "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., Vol. 34, No. 3, 276-280, Mar. 1986..
doi:10.1109/TAP.1986.1143830 Google Scholar

9. Bencheikh, , M. L., Y. Wang, and , "Combined esprit-rootmusic for DOA-DOD estimation in polarimetric bistatic MIMO radar," Progress In Electromagnetics Research Letters,, Vol. 22, 109-117, 2011. Google Scholar

10. Sacchi, , M. D., T. J. Ulrych, and C. J. Walker, "Interpolation and extrapolation using a high-resolution discrete fourier transform," IEEE Trans. Signal Process., Vol. 46, No. 1, 31-38, Jan. 1998.
doi:10.1109/78.651165 Google Scholar

11. Jeffs, , B. D., , "Sparse inverse solution methods for signal and image processing applications," Proc. IEEE Int. Conf. Acoust., Speech, Signal Process.,, Vol. 3, 1885-1888, 1998.. Google Scholar

12. Gorodnitsky, , I. F., B. D. Rao, and , "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., Vol. 45, No. 3, 600-616, Mar. 1997. Google Scholar

13. Fuchs, J. J., , "On the application of the global matched flter to DOA estimation with uniform circular arrays," IEEE Trans. Signal Process., Vol. 49, No. 4, 702-709, , Apr. 2001. Google Scholar

14. Rao, , B. D., K. Kreutz-Delgado, and , "An affne scaling methodology for best basis selection," IEEE Trans. Signal Process., Vol. 47, No. 1, 187-200, Jan. 1999. Google Scholar

15. Malioutov, , D. M., M. Cetin, and A. S. Willsky, , "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process., Vol. 53, No. 8, 3010-3022, Aug. 2005. Google Scholar

16. Cands, E. J., M. B. Wakin, and S. P. Boyd, "Enhancing sparsity by reweighted L1 minimization," Journal of Fourier Analysis and Applications, , Vol. 14, No. 5--6, 877-905, Dec. 2008. Google Scholar

17. "Wipf, D. and S. Nagarajan, Iterative reweighted L1 and L2 methods for finding sparse solution," IEEE Journal of Selected Topic in Signal Processing,, Vol. 4, No. 2, 317-329, , Apr. 2010. Google Scholar

18. Needell, , D., "Noisy signal recovery via iterative reweighted L1 minimization," 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, 113-117, 2009. Google Scholar

19. Cands, , E., J. Romberg, and T. Tao, , "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, Vol. 52, No. 2, 489-509, Feb. 2006. Google Scholar

20. Donoho, D. L. and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via L1 minimization," Proc. Natl, Acad. Sci. USA 100, 2197-2202, 2003. Google Scholar

21. Donoho, , D. L., X. Huo, and , "Uncertainty principles and ideal atomic decomposition," IEEE Transactions on Information Theory, Vol. 47, No. 7, 2845-2862, Nov. 2001. Google Scholar

22. Krim, , H., M. Viberg, and , "Two decades of array signal processing research: The parametric approach," IEEE Signal Process. Mag.,, Vol. 13, No. 7, 67-94, Jul. 1996. Google Scholar

Prof. Fulai Liu

Dr. Lu Peng

Dr. Ming Wei

Dr. Pingping Chen

Dr. Shouming Guo