Grid-Free Direction-of-Arrival Estimation with Compressed Sensing and Arbitrary Antenna Arrays

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.