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Mathematical Problems in Engineering
Volume 2015, Article ID 152570, 6 pages
Research Article

Multiple Sparse Measurement Gradient Reconstruction Algorithm for DOA Estimation in Compressed Sensing

Department of Information and Communication Engineering, Harbin Engineering University, 150001 Harbin, China

Received 8 July 2014; Revised 9 November 2014; Accepted 16 March 2015

Academic Editor: Dane Quinn

Copyright © 2015 Weijian Si et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is proposed, in which the DOA estimation problem is cast as the joint sparse reconstruction from multiple measurement vectors (MMV). The proposed method is derived through transforming quadratically constrained linear programming (QCLP) into unconstrained convex optimization which overcomes the drawback that -norm is nondifferentiable when sparse sources are reconstructed by minimizing -norm. The convergence rate and estimation performance of the proposed method can be significantly improved, since the steepest descent step and Barzilai-Borwein step are alternately used as the search step in the unconstrained convex optimization. The proposed method can obtain satisfactory performance especially in these scenarios with low signal to noise ratio (SNR), small number of snapshots, or coherent sources. Simulation results show the superior performance of the proposed method as compared with existing methods.