Wideband DOA Estimation through Projection Matrix Interpolation

This paper presents a method to reduce the complexity of the deterministic maximum likelihood (DML) estimator in the wideband direction-of-arrival (WDOA) problem, which is based on interpolating the array projection matrix in the temporal frequency variable. It is shown that an accurate interpolator like Chebyshev’s is able to produce DML cost functions comprising just a few narrowband-like summands. Actually, the number of such summands is far smaller (roughly by factor ten in the numerical examples) than the corresponding number in the ML cost function that is derived by dividing the spectrum into separate bins. The paper also presents two spinoffs of the interpolation method. The first is a fast procedure to compute one-dimensional search estimators like Multiple Signal Classification (MUSIC), that exploits the close relation between Chebyshev interpolation and the Discrete Cosine Transform (DCT). And the second is a detection-estimation procedure for the DML estimator. The methods in the paper are assessed in several numerical examples.