We study the problem of direction of arrival estimation for arbitrary antenna
arrays. We formulate it as a continuous line spectral estimation problem and solve it under
a sparsity prior without any gridding assumptions. Moreover, we incorporate the
array's beampattern in form of the Effective Aperture Distribution Function
(EADF), which allows to use arbitrary (synthetic as well as measured) antenna
arrays. This generalizes known atomic norm based grid-free DOA estimation methods (that
have so far been limited to uniformly spaced arrays) to arbitrary antenna arrays.

In addition, our formulation allows to incorporate compressed sensing in form of
special linear combinations of the antennas' output ports. We provide conditions
for the successful reconstruction of a certain number of targets depending on
the amount of compression and the EADF of the antenna array. Our results are
applicable to measurement matrices from any sub-Gaussian distribution.