Tensor-Based 2D DOA Estimation for L-Shaped Nested Array

Among various sensor array configurations, the L-shaped nested array offers improved performance for 2-D direction-of-arrival (DOA) estimation through co-array processing. However, conventional methods overlook the multidimensional signal structure and fail to eliminate the cross term generated from the correlated co-array signal and noise components. It leads to a significant degradation in DOA estimation performance. To deal with this problem, an iterative 2-D DOA estimation algorithm based on tensor modeling is proposed. It is capable of eliminating the cross term. Specifically, the co-array signals of virtual subarrays in orthogonal directions are derived and concatenated to construct a higher order tensor, whose factor matrices have the Vandermonde structure and preserve the interconnected azimuth and elevation information. A computationally efficient tensor decomposition method is then developed to independently estimate the azimuth and elevation angles, which are effectively paired using the spatial cross-correlation matrix. Furthermore, after investigating the cross term effect, a two-step iterative algorithm is proposed to sequentially estimate and remove the cross term based on the initial estimates obtained from the high-order tensor decomposition. Consequently, the 2-D DOA estimation with enhanced estimation accuracy, resolution, and moderate computational complexity is achieved for the L-shaped nested array. Simulation results demonstrate the superiority of the proposed algorithm over competing methods.