volume | PIER Journals

Abstract

This paper presents an effective weighted-L₁-sparse representation of array covariance vectors (W-L₁-SRACV) algorithm which exploits compressed sensing theory for direction-of-arrival (DOA) estimation of multiple narrow-band sources impinging on the far field of a uniform linear array (ULA). Based on the sparse representation of array covariance vectors, a weighted L₁-norm minimization is applied to the data model, in which the weighted vector can be obtained by taking advantage of the orthogonality between the noise subspace and the signal subspace. By searching the sparsest coe±cients of the array covariance vectors simultaneously, DOAs can be effectively estimated. Compared with the previous works, the proposed method not only has a super-resolution but also improves the robustness in low SNR cases. Furthermore, it can effectively suppresses spurious peaks which will disturb the correct judgment of real signal peak in the signal recovery processing. Simulation results are shown to demonstrate the efficacy of the presented algorithm.

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

2. Bencheikh, M. L. and Y. Wang, "Combined ESPRIT-root music for DOA-DOD estimation in polarimetric bistatic MIMO radar," Progress In Electromagnetics Research Letter, Vol. 22, 109-117, 2011.
doi:10.2528/PIERC11050205

3. Johnson, D. H. and D. E. Dudgeon, Array Signal Processing-concepts and Techniques, Prentice-Hall, Englewood Cliffs, NJ, 1993.

4. 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.

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

6. Liu, F. L., J. K. Wang, C. Y. Sun, and R. Y. Du, "Spatial differencing method for DOA estimation under the coexistence of both uncorrelated and coherent signals," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 4, 2052-2062, 2012.
doi:10.1109/TAP.2012.2186216

7. Anthony, J. W. and G. Motti, "Direction finding using esprit with interpolated arrays," IEEE Transactions on Signal Processing, Vol. 39, No. 6, 1473-1478, 1991.
doi:10.1109/78.136564

8. Viberg, M. and B. Ottersten, "Sensor array processing based on subspace fitting," IEEE Transactions on Signal Processing, Vol. 39, 1110-1120, 1991.
doi:10.1109/78.80966

9. yder, M. and K. Mahata, "An improved smoothed L₀ approximation algorithm for sparse representation," IEEE Transactions on Signal Processing, Vol. 58, 2194-2205, 2010.

10. Gorodnitsky, I. F. and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Transactions on Signal Processing, Vol. 45, No. 3, 600-616, Mar. 1997.
doi:10.1109/78.558475

11. Cotter, S., "Multiple snapshot matching pursuit for direction of arrival (DOA) estimation," Proceedings of the European Signal Processing Conference, 247-251, Poznan, Poland, September 3-7, 2007.

12. Hyder, M. M. and K. Mahata, "Direction-of-arrival estimation using a mixed L_2,0 norm approximation," IEEE Transactions on Signal Processing, Vol. 58, 4646-4655, 2010.
doi:10.1109/TSP.2010.2050477

13. Malioutov, D. M., M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Transactions on Signal Processing, Vol. 53, No. 8, 3010-3022, Aug. 2005.
doi:10.1109/TSP.2005.850882

14. Yin, J. H. and T. Q. Chen, "Direction-of-arrival estimation using a sparse representation of array covariance vectors," IEEE Transactions on Signal Processing, Vol. 59, No. 9, 4489-4493, Sept. 2011.
doi:10.1109/TSP.2011.2158425

15. Donoho, D., "Compressed sensing," IEEE Transactions on Information Theory, Vol. 52, No. 4, 1289-1306, Apr. 2006.
doi:10.1109/TIT.2006.871582

16. Fuchs, J. J., "On the application of the global matched filter to DOA estimation with uniform circular arrays," IEEE Transactions on Signal Processing, Vol. 49, No. 4, 702-709, Apr. 2001.
doi:10.1109/78.912914

17. Candes, 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.
doi:10.1007/s00041-008-9045-x

Dr. Ruiyan Du

Prof. Fulai Liu

Dr. Lu Peng