In this paper, we propose two kinds of improved nested arrays for direction of arrival (DOA) estimation, which are obtained by rearranging physical sensors of the prototype nested array. Specifically, the sum-difference coarrays (SDCAs) of the proposed arrays are constructed by jointly using the temporal and spatial information of the received signal. By systematically analyzing the structures of the proposed two kinds of arrays, we derive the closed-form expressions about their physical sensor positions, SDCAs, consecutive degrees of freedom (DOFs), and maximum physical array apertures, respectively. Compared to the prototype nested array which only considers the difference coarray (DCA), the proposed arrays with SDCAs have a lot more consecutive DOFs. Moreover, all physical sensors of the proposed arrays, except the one at zero point, can be placed at the positions opposite to their original ones, which will not result in a change in the consecutive DOFs. This phenomenon means that the proposed arrays have flexible array configurations with different physical array apertures, which make them more beneficial for practical application. In the end, simulation results demonstrate the superiorities of the proposed arrays in terms of detection performance and estimation accuracy.

In this letter, a novel sparse array consisting of coprime and nested subarrays is designed and a corresponding two-dimensional (2-D) direction of arrival (DOA) estimation method is presented. The proposed array can be decomposed into two sparse planar subarrays, each of which consists of some identical nested linear arrays (NLAs). Especially, the dense subarrays in these NLAs can form the prototype coprime arrays. Then, by vectorizing two covariance matrices, two virtual coprime planar subarrays are available, which have much larger apertures than the physical ones. Subsequently, 2-D spatial smoothing and multiple signal classification are utilized to get two coprime estimations. Combining them, the unique DOA estimation is determined. Theoretical analysis and numerical simulations demonstrate the effectiveness and superiority of the proposed method.

As is well known, the prototype coprime arrays consist of two collinear subarrays, whose physical sensor number is coprime to each other. Moreover, their larger inter-element separations and physical array apertures make them have less mutual coupling than uniform linear arrays. Even so, there is still mutual coupling existing in them, which has an adverse effect on the direction of arrival estimation. To reduce the effects of mutual coupling, several improved coprime configurations based on the concept of difference and sum coarray are proposed in this paper, which can be obtained through three operations. The first one is to shift the prototype coprime array to obtain the translational coprime arrays, which can help to reduce the redundancy between the difference coarray and sum coarray. Secondly, flip one of the subarrays in the translational coprime arrays with zero point as the symmetric center to get the flipped coprime arrays, which can expand the physical array aperture and inter-element separations further. Lastly, move one of the symmetrical placed sensors in the flipped coprime arrays to zero point. Then, the proposed arrays are derived. They have almost the same consecutive DOFs as the prototype coprime array but dramatically reduced mutual coupling due to their larger physical array apertures and inter-element separations, where the virtual arrays are constructed by their respective difference and sum coarray. In the end, numerical simulation results confirm the superiority of proposed arrays.

Nested arrays are considered attractive due to their hole-free performance, and have the ability to resolve $\mathrm{O}\left(N^2\right)$ sources with $\mathrm{O}\left(N\right)$ physical sensors. Inspired by nested arrays, two kinds of three-parallel nested subarrays (TPNAs), which are composed of three parallel sparse linear subarrays with different inter-element spacings, are proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation in this paper. We construct two cross-correlation matrices and combine them as one augmented matrix in the first step. Then, by vectorizing the augmented matrix, a hole-free difference coarray with larger degrees of freedom (DOFs) is achieved. Meanwhile, sparse representation and the total least squares technique are presented to transform the problem of 2-D DOA searching into 1-D searching. Accordingly, we can obtain the paired 2-D angles automatically and improve the 2-D DOA estimation performance. In addition, we derive closed form expressions of sensor positions, as well as number of sensors for different subarrays of two kinds of TPNA to maximize the DOFs. In the end, the simulation results verify the superiority of the proposed TPNAs and 2-D DOA estimation method.

In this letter, we propose a joint processing method of spatial and temporal information from L-shaped sparse array (LSA) for two-dimensional (2-D) direction of arrival (DOA) estimation. In particular, either of the two subarrays in LSA can be any type of linear sparse array. With the proposed method, we can construct a virtual planar sparse array first, whose corresponding 2-D difference coarray owns significantly increased degrees of freedom, which can help to enhance the 2-D DOA estimation performance. Thereafter, subspace-based method with 2-D spatial smoothing can be applied to achieve the automatically paired and unambiguous 2-D DOA estimation. Simulation results verify the superiority of the proposed method.

Recently, many sparse-based direction-of-arrival (DOA) estimation methods for coprime arrays have become popular for their excellent detection performance. However, these methods often suffer from grid mismatch problem due to the discretization of the potential angle space, which will cause DOA estimation performance degradation when the target is off-grid. To this end, we proposed a sparse-based off-grid DOA estimation method for coprime arrays in this paper, which includes two parts: coarse estimation process and fine estimation process. In the coarse estimation process, the grid points closest to the true DOAs, named coarse DOAs, are derived by solving an optimization problem, which is constructed according to the statistical property of the vectorized covariance matrix estimation error. Meanwhile, we eliminate the unknown noise variance effectively through a linear transformation. Due to finite snapshots effect, some undesirable correlation terms between signal and noise vectors exist in the sample covariance matrix. In the fine estimation process, we therefore remove the undesirable correlation terms from the sample covariance matrix first, and then utilize a two-step iterative method to update the grid biases. Combining the coarse DOAs with the grid biases, the final DOAs can be obtained. In the end, simulation results verify the effectiveness of the proposed method.