A Novel Coprime Nested Array With Enhanced DOFs and Reduced Mutual Coupling for DOA Estimation of Noncircular Sources

Recently, many sparse array configurations have been designed for direction of arrival (DOA) estimation of noncircular sources due to their capability of constructing high-performance difference-sum coarray. Nested array, coprime array, along with their improved structures are the most commonly used array configurations. Nested arrays could provide <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(R^{2})$</tex-math></inline-formula> degrees of freedom (DOFs) with only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> sensors, but suffer from severe mutual coupling effect owing to closely arranged elements. Coprime arrays generally offer a lower number of DOFs than nested arrays, but are more robust to mutual coupling effect due to sparser array structure. Unfortunately, existing sparse arrays cannot possess the benefits of nested arrays and coprime arrays at the same time within the framework of difference-sum coarray. To compensate for the above shortcoming, we first analyze the nesting property for difference coarray, and generalize the nesting property to difference-sum coarray, allowing nearly half of the sensors to be removed from dense subarray. Then, a new nested configuration called thinned coprime nested array (TCNA) is proposed, whose dense subarray is a coprime structure that satisfies the aforementioned nesting property. TCNA can generate a comparable number of DOFs to nested arrays due to the nesting property between two subarrays. Meanwhile, the mutual coupling effect is greatly reduced since its dense subarray is replaced with a coprime structure, which limits the number of sensor pairs with small spacing. Therefore, TCNA is able to combine the advantages of both nested array and coprime array. Finally, simulations verify the superiority of TCNA with respect to DOF ratio, coupling leakage, and DOA estimation accuracy.