Recently, sparse arrays such as nested array and coprime array have attracted much attention in the field of array signal processing. In this letter, we develop a symmetric coprime array (SCA) whose sensor locations satisfy the nesting property, so it can be used as a dense subarray of nested array. Based on this observation, we propose a new sparse array named coprime nested array, which can achieve the same number of uniform degrees of freedom (uDOFs) as the prototype nested array, while the mutual coupling effect is at the same level as the coprime arrays. Moreover, an improved coprime nested array (ICNA) is proposed by rearranging some sensors in SCA to the right side of the sparse subarray. ICNA possesses more uDOFs than the existing nested arrays with further reduced mutual coupling effect. Numerical simulations verify the effectiveness of the proposed configurations.

Recently, direction of arrival (DOA) estimation for non-circular (NC) sources has attracted great attention in array signal processing since NC signals can provide more information to generate the virtual difference and sum (diff-sum) coarray. In this paper, we propose a generalized vectorized noncircular MUSIC (GVNCM) method, which can solve the underdetermined DOA estimation problem when the difference coarray and the sum coarray are discontinuous. Based on the GVNCM algorithm, an extended transformed nested array strategy is proposed by splitting the dense subarray of transformed nested array (TNA) into several parts and shifting them to the right to reduce the redundant elements between the difference coarray and the sum coarray. Following this strategy, two novel array configurations are developed. The analytical expressions of the new structures and the consecutive range of their diff-sum coarrays are provided. The two proposed arrays can achieve higher degrees of freedom and maximum number of detectable signals compared with TNA. In order to evaluate the underdetermined DOA estimation performance of NC signals, we derive the corresponding expression of Cramér-Rao bound. The effectiveness of the proposed arrays is verified through numerical simulations.

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 $O(R^{2})$ degrees of freedom (DOFs) with only $R$ 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.

Recently, the concept of the difference and sum coarray has attracted increasing interest in the direction of the arrival estimation field because it can generate enhanced degrees of freedom. In this paper, we propose an improved transformed nested array design strategy by relaxing the constraints on the dense subarray of the transformed nested array. Then, three conditions are given for the array design to ensure the continuity of the difference and sum coarray. Based on the strategy, we develop a novel nested configuration named coprime transformed nested array (CTNA) whose dense subarray is a coprime structure, and the closed-form expressions for the sensor positions and the range of consecutive coarray are derived. CTNA can increase the number of degrees of freedom (DOFs) compared to the existing nested arrays, while the mutual coupling effect can be maintained at the same low level as the coprime arrays, which indicates that CTNA has the merits of both nested array and coprime array. Numerical simulations are performed to verify the superiority of the proposed array configuration in terms of the number of DOFs, mutual coupling and direction of arrival (DOA) estimation accuracy.