Single Snapshot Super-Resolution DOA Estimation for Arbitrary Array Geometries
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We address the problem of search-free direction of arrival (DOA) estimation for sensor arrays of arbitrary geometry under the challenging conditions of a single snapshot and coherent sources. We extend a method of search-free super-resolution beamforming, originally applicable only for uniform linear arrays, to arrays of arbitrary geometry. The infinite dimensional primal atomic norm minimization problem in continuous angle domain is converted to a dual problem. By exploiting periodicity, the dual function is then approximated with a trigonometric polynomial using a truncated Fourier series, which is estimated via the discrete Fourier transform (DFT). A linear rule of thumb is derived for selecting the minimum number of DFT points required for accurate polynomial approximation, based on the distance of the farthest sensor from a reference point. The dual problem is then expressed as a semidefinite program and solved efficiently. Finally, the search-free DOA estimates are obtained through polynomial rooting, and source amplitudes are recovered through least squares. Simulations using circular and random planar arrays show perfect DOA estimation in noise-free cases.
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