  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 searchfree
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 represented with
a trigonometric polynomial using a truncated Fourier series. A linear rule of
thumb is derived for selecting the minimum number of Fourier coefficients
required for accurate polynomial representation, 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 searchfree 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.
