Two-Dimensional DOA Estimation for L-shaped Nested Array via Tensor Modeling

The problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation for L-shaped nested array is considered. Typically, the multi-dimensional structure of the received signal in co-array domain is ignored in the problem considered. Moreover, the cross term generated by the correlated signal and noise components degrades the 2-D DOA estimation performance seriously. To tackle these issues, an iterative 2-D DOA estimation approach based on tensor modeling is proposed. To develop such approach, a higher-order tensor is constructed, whose factor matrices contain the target azimuth and elevation information. By exploiting the Vandermonde structure of the factor matrix, a computationally efficient tensor decomposition method is then developed to estimate the targets DOA information in each dimension independently. Then, an eigenvalue-based approach that exploits a natural coupling of the 2-D spatial parameters is proposed to pair the azimuth and elevation angles. Finally, an iterative method is designed to improve the DOA estimation performance. Specifically, the cross term is estimated and removed in the next step of such iterative procedure on the basis of the DOA estimates originated from the tensor decomposition in the previous step. Consequently, the DOA estimation with better accuracy and higher resolution is obtained. The proposed iterative 2-D DOA estimation method for L-shaped nested array can resolve more targets than the number of real elements, even when the azimuth or elevation angles are identical, which is superior to conventional approaches. Simulation results validate the performance improvement of the proposed 2-D DOA estimation method as compared to existing state-of-the-art DOA estimation techniques for L-shaped nested array.