  The problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation
for the 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 sources 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 sources DOA information in each dimension independently. The
pair-matching of the azimuth and elevation angles is conducted via the
cross-correlation matrix (CCM) of the received signals. An iterative method is
further 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. As a consequence, the DOA estimation with
better accuracy and higher resolution is obtained. The proposed iterative 2-D
DOA estimation method for the L-shaped nested array can resolve more sources
than the number of real elements, 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 the L-shaped nested array.
