Bound on the estimation grid size for sparse reconstruction in direction of arrival estimation

A bound for sparse reconstruction involving both the signal-to-noise ratio (SNR) and the estimation grid size is presented. The bound is illustrated for the case of a uniform linear array (ULA). By reducing the number of possible sparse vectors present in the feasible set of a constrained ℓ1-norm minimization problem, ambiguities in the reconstruction of a single source under noise can be reduced. This reduction is achieved by means of a proper selection of the estimation grid, which is naturally linked with the mutual coherence of the sensing matrix. Numerical simulations show the performance of sparse reconstruction with an estimation grid meeting the provided bound demonstrating the effectiveness of the proposed bound.