  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.
