A Quadratic Sparse Reconstruction Algorithm for DOA Estimation Based on L-shaped Coprime Array

An L-shaped coprime phased array has the minimum redundancy of antenna elements, but the high sparsity makes the two-dimensional (2-D) direction of arrival (DOA) estimation very difficult when carrying on a data reconstruction. In this paper, a quadratic reconstruction algorithm based on convex optimization is proposed to restore the whole covariance matrix of an L-shaped coprime array and thus the 2-D DOA estimation can be obtained. First, two virtual uniform linear arrays (ULAs) with the same aperture of the real arrays were extended on X and Y axis, respectively. The properties of Hermite positive definite and Toeplitz structure were used for the first sparse reconstruction to restore the covariance matrix of the two extended ULAs. Then, with the sparse mutual covariance data between the two linear arrays, a secondary sparse reconstruction based on convex optimization was conducted to get the full covariance matrix of the extended L-shaped uniform array according to its positive definite Hermite property. Finally, based on the whole recovered covariance matrix, the 2-D DOA estimates were obtained. By means of the commercial CVX computing platform, the effectiveness and accuracy of the algorithm are verified. The simulation results demonstrate that the accuracy of DOA estimates produced by the proposed method is better than that of the comparison algorithms especially in the low signal-to-noise ratio interval.