Sparse Direction of Arrival Estimation Using Co-Prime Arrays with Off-Grid Targets

Abstract

In this letter, we consider the problem of direction of arrival estimation using sparsity enforced reconstruction methods. Co-prime arrays with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M + N$</tex></formula> sensors are utilized to increase the degrees of the freedom from <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$O(M + N)$</tex></formula> to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$O(MN)$</tex></formula> . The key to the success of sparse-based direction of arrival estimation is that every target must fall on the predefined grid. Off-grid targets can highly jeopardize the reconstruction performance. In this letter, we use joint sparsity reconstruction methods to explore the underlying structure between the sparse signal and the gird mismatch. Two types of sparse reconstruction methods, the greedy method and the convex relaxation method, are considered. By implementing numerical experiments, we demonstrate that our proposed methods can fully utilize the virtual aperture created by co-prime arrays and also outperform the previously proposed MUSIC method with spatial smoothing.