Direction of arrival estimation using co-prime arrays: A super resolution viewpoint

We consider the problem of direction of arrival (DOA) estimation using a recently proposed structure of nonuniform linear arrays, referred to as co-prime arrays. By exploiting the second order statistical information of the received signals, co-prime arrays exhibit O(MN) degrees of freedom with only M+N sensors. A sparsity-based recovery algorithm is proposed to fully utilize these degrees of freedom. The suggested method is based on the developing theory of super resolution, which considers a continuous range of possible sources instead of discretizing this range onto a grid. With this approach, off-grid effects inherent in traditional sparse recovery can be neglected, thus improving the accuracy of DOA estimation. We show that in the noiseless case it is theoretically possible to detect up to MN/2 sources with only 2M+N sensors. The noise statistics of co-prime arrays are also analyzed to demonstrate the robustness of the proposed optimization scheme. A source number detection method is presented based on the spectrum reconstructed from the sparse method. By extensive numerical examples, we show the superiority of the suggested algorithm in terms of DOA estimation accuracy, degrees of freedom, and resolution ability over previous techniques, such as MUSIC with spatial smoothing and discrete sparse recovery.