  We study the problem of noisy sparse array interpolation, where a large
virtual array is synthetically generated by interpolating missing sensors using
matrix completion techniques that promote low rank. The current understanding
is quite limited regarding the effect of the (sparse) array geometry on the
angle estimation error (post interpolation) of these methods. In this paper, we
make advances towards solidifying this understanding by revealing the role of
the physical beampattern of the sparse array on the performance of low rank
matrix completion techniques. When the beampattern is analytically tractable
(such as for uniform linear arrays and nested arrays), our analysis provides
concrete and interpretable bounds on the scaling of the angular error as a
function of the number of sensors, and demonstrates the effectiveness of nested
arrays in presence of noise and a single temporal snapshot.
