  In this paper, we study the problem of estimating the direction of arrival
(DOA) using a sparsely sampled uniform linear array (ULA). Based on an initial
incomplete ULA measurement, our strategy is to choose a sparse subset of array
elements for measuring the next snapshot. Then, we use a Hankel-structured
matrix completion to interpolate for the missing ULA measurements. Finally, the
source DOAs are estimated using a subspace method such as Prony on the fully
recovered ULA. We theoretically provide a sufficient bound for the number of
required samples (array elements) for perfect recovery. The numerical
comparisons of the proposed method with existing techniques such as atomic-norm
minimization and off-the-grid approaches confirm the superiority of the
proposed method.
