In this paper, we consider the problem of direction of arrival (DOA) estimation with co-prime arrays via compressed sensing methods. A sparse signal recovery model based on the framework of co-prime array is presented. We propose to use OMP algorithm to efficiently implement the optimization procedure, which have a lower computational cost. The sparse recovery model of DOA estimation obeys the isotropy property and incoherence property. Therefore, by exploiting the RIPless theory in compressed sensing, we develop the upper bound of degrees of freedom (DOF) of the proposed model. The results establish a basic relationship between upper bound of DOF, the number of samplers and the probability of recovery. Numerical examples show the superiority of the proposed method in detection performance and estimation accuracy compared with the existing spatial smoothing MUSIC algorithm using co-prime arrays.
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