volume | PIER Journals

Abstract

An off-grid direction-of-arrival (DOA) estimation method that utilizes a sparse array covariance matrix is proposed. In this method, the array covariance matrix is sparsely represented in the form of a vector and then modified to become an off-grid DOA estimation model according to the first-order Taylor series. By solving for the two sparse vectors in the resulting array covariance matrix, the off-grid DOA estimation can thus be achieved. We present an alternating iterative algorithm that exploits the alternating update of a convex optimization problem and a least-squares problem to solve for these two sparse vectors. Our method also extends the aperture. The effectiveness and efficiency of the proposed method are demonstrated in the simulation results.

1. Krim, H. and M. Viberg, "Two decades of array signal processing research: The parametric approach," IEEE Trans. Signal Process. Mag., Vol. 13, No. 4, 67-94, 1996.
doi:10.1109/79.526899 Google Scholar

2. Schmidt, R., "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., Vol. 34, No. 3, 276-280, 1989.
doi:10.1109/TAP.1986.1143830 Google Scholar

3. Stoica, P. and A. Nehorai, "MUSIC, maximum likelihood, and Cramer-Rao bound," IEEE Trans. Acoust., Lett., Vol. 34, No. 3, 276-280, 1986. Google Scholar

4. Malioutov, D., 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, 2005.
doi:10.1109/TSP.2005.850882 Google Scholar

5. Stoica, P., P. Babu, and J. Li, "SPICE: A sparse covariance-based estimation method for array processing," IEEE Trans. Signal Process., Vol. 59, No. 2, 629-638, 2011.
doi:10.1109/TSP.2010.2090525 Google Scholar

6. Yin, J.-H. and T.-Q. Chen, "Direction-of-arrival estimation using a sparse representation of array covariance vectors," IEEE Trans. Signal Process., Vol. 59, No. 9, 4489-4493, 2011.
doi:10.1109/TSP.2011.2158425 Google Scholar

7. He, Z.-Q., Q.-H. Liu, L.-N. Jin, and S. Ouyang, "Low complexity method for DOA estimation using array covariance matrix sparse representation," Electronics Letters, Vol. 49, No. 3, 228-230, 2013.
doi:10.1049/el.2012.4032 Google Scholar

8. Carlin, M., P. Rocca, G. Oliveri, F. Viani, and A. Massa, "Directions-of-arrival estimation through bayesian compressive sensing strategies," IEEE Trans. Antennas Propag., Vol. 61, No. 7, 3828-3838, 2013.
doi:10.1109/TAP.2013.2256093 Google Scholar

9. Tang, G., B. N. Bhaskar, P. Shah, and B. Recht, "Compressed sensing off the grid," IEEE Trans. Inf. Theory, Vol. 59, No. 11, 7465-7490, 2013.
doi:10.1109/TIT.2013.2277451 Google Scholar

10. Zhu, H., G. Leus, and G. Giannakis, "Sparsity-cognizant total least-squares for perturbed compressive sampling," IEEE Trans. Signal Process., Vol. 59, No. 5, 2002-2016, 2011.
doi:10.1109/TSP.2011.2109956 Google Scholar

11. Zheng, J.-M. and M. Kaveh, "Directions-of-arrival estimation using a sparse spatial spectrum model with uncertainty," IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), 2848-2851, 2011. Google Scholar

12. Tan, Z. and A. Nehorai, "Sparse direction of arrival estimation using co-prime arrays with off-grid targets," IEEE Trans. Signal Process. Lett., Vol. 21, No. 1, 26-29, 2014.
doi:10.1109/LSP.2013.2289740 Google Scholar

13. Tan, Z., P. Yang, and A. Nehorai, "Joint sparse recovery method for compressed sensing with structured dictionary mismatches," IEEE Trans. Signal Process., Vol. 62, No. 19, 4997-5008, 2014.
doi:10.1109/TSP.2014.2343940 Google Scholar

14. Yang, Z., L.-H. Xie, and C.-S. Zhang, "Off-grid direction of arrival estimation using sparse Bayesian inference," IEEE Trans. Signal Process., Vol. 61, No. 1, 38-43, 2013.
doi:10.1109/TSP.2012.2222378 Google Scholar

15. Zhang, Y., Z.-F. Ye, X. Xu, and N. Hu, "Off-grid DOA estimation using array covariance matrix and block-sparse Bayesian learning," Signal Process., Vol. 98, 197-201, 2014.
doi:10.1016/j.sigpro.2013.11.022 Google Scholar

16. Jagannath, R. and K. V. S. Hari, "Block sparse estimator for grid matching in single snapshot DoA estimation," IEEE Trans. Signal Process. Lett., Vol. 20, No. 11, 1038-1041, 2013.
doi:10.1109/LSP.2013.2279124 Google Scholar

17. Yang, Z., C.-S. Zhang, and L.-H. Xie, "Robustly stable signal recovery in compressed sensing with structured matrix perturbation," IEEE Trans. Signal Process., Vol. 60, No. 9, 4658-4671, 2012.
doi:10.1109/TSP.2012.2201152 Google Scholar

18. Donoho, D. L., M. Elad, and V. N. Temlyakov, "Stable recovery of sparse overcomplete representations in the Presence of Noise," IEEE Trans. Inf. Theory, Vol. 52, No. 1, 6-18, 2006.
doi:10.1109/TIT.2005.860430 Google Scholar

19. Tropp, J. A., "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, Vol. 52, No. 3, 1030-1048, 2006.
doi:10.1109/TIT.2005.864420 Google Scholar

Dr. Xiaoyu Luo

Dr. Xiao Chao Fei

Dr. Lu Gan

Dr. Ping Wei