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Nowadays, sparse arrays have been a hotspot for research in the direction of arrival (DOA). In order to achieve a big value for degrees of freedom (DOFs) using spatial smoothing methods, researchers try to use multiple uniform linear arrays (ULAs) to construct sparse arrays. But, with the number of subarrays increasing, the complexity also increases. Hence, in this paper, a design method, named as the cross-coarray consecutive-connected (4C) criterion, and the sparse array using Q ULAs (SA-UQ) are proposed. We first analyze the virtual sensor distribution of SA-U2 and extend the conclusions to SA-UQ, which is the 4C criterion. Then, we give an algorithm to solve the displacement between subarrays under the given Q ULAs. At last, we consider a special case, SA-U3. Through the analysis of DOFs, SA-UQ can find underdetermined signals. Moreover, SA-U3 can obtain DOFs close to other sparse arrays using three ULAs. The simulation experiments prove the performance of SA-UQ. [ABSTRACT FROM AUTHOR]

Sparse arrays with O(N) $\mathcal{O}(N)$ sensors can offer ON2 $\mathcal{O}\left({N}^{2}\right)$ number of degrees of freedom by exploiting the difference co‐array that can be obtained from the second‐order statistics of received signals. In this article, a novel sparse array with seven subarrays (SA‐7S) by carefully assembling the subarrays is proposed, and the resulting SA‐7S can generate a hole‐free uniform difference co‐array. The sensor locations of the SA‐7S array are uniquely determined by a closed‐form expression and the number of achievable degrees of freedom is analytically presented as well. Theoretical analysis shows that the SA‐7S can provide a higher number of degrees of freedom than most sparse linear arrays. Simulations are performed to validate the advantage of the proposed array in terms of uDOFs, mutual coupling and direction of arrival estimation performance. [ABSTRACT FROM AUTHOR]

In this letter, a dilating and embedding scheme for constructing sparse multiple‐input and multiple‐output radar arrays is addressed, which seeks to increase the uniform degrees of freedom (uDOFs) and reduce the mutual coupling effects for a given number of transmitters and receivers (Tx/Rx). According to this scheme, a dilated maximum inter‐element spacing constraint (MISC) array with an embedded thinned coprime array in the collocated MIMO radar for DOA estimation is proposed. Theoretical analysis shows that the proposed array can provide higher uDOFs and is robust in a scenario with heavy levels of mutual coupling. Numerical simulations are conducted to validate its aforementioned advantages in line with the design scheme.In this letter, a dilating and embedding scheme for constructing sparse multiple‐input and multiple‐output (MIMO) radar is addressed, which seeks to increase the uniform degrees of freedom and reduce the mutual coupling effect for a given number of transmitters and receivers (Tx/Rx). According to this principle, a dilated maximum inter‐element spacing constraint array with an embedded thinned coprime array in collocated MIMO radar for DOA estimation is proposed. [ABSTRACT FROM AUTHOR]

Owing to increased degrees of freedom (DOFs) and reduced mutual coupling effect, sparse linear arrays can improve the performance of direction‐of‐arrival estimation compared with uniform linear arrays. In this study, a novel sparse linear array is presented based on fourth‐order cumulants, which consists of five sparse sub‐arrays. The sensor locations of the five sub‐arrays are determined by a closed‐form expression. Closed‐form expressions of DOFs for the proposed array with any number of sensors are also derived. By optimising the allocation of sensors in each sub‐array, the DOFs of the proposed array with M sensors achieve OM4 $\mathcal{O}\left({M}^{4}\right)$. Because each sub‐array is sparse, the number of pairwise sensors with small separation is significantly alleviated. Theoretical analysis shows that the proposed array can provide a higher number of DOFs and is more robust in scenarios with heavy levels of mutual coupling than most sparse linear arrays. Numerical simulations are conducted to demonstrate the merits of the proposed array over other sparse linear arrays. [ABSTRACT FROM AUTHOR]

In the coprime planar array (CPA), the existing tensor DOA estimation has the problem that the statistics are not fully utilized. We propose a two-dimensional DOA estimation method based on tensor self-correlation, which realizes the high-resolution and high-precision joint estimation of elevation angle and azimuth angle. Firstly, we represent the received signals of two subarrays with tensors and then obtain the self-correlation covariance tensor of the subarrays themselves and the cross-correlation covariance tensor of the two subarrays. Then, we extract the covariance tensor corresponding to the maximum continuous virtual array and prove the expression of the maximum continuous virtual array aperture of the proposed method. Compared with the existing methods, the proposed method effectively improves the maximum aperture of the continuous virtual array. Finally, the signal subspace is solved by tensor expansion and tensor decomposition. Simulation results show that under the same conditions, the proposed method has higher estimation accuracy and degree of freedom than the cross-correlation tensor method, and the resolution is also improved significantly. [ABSTRACT FROM AUTHOR]

As we all know, the non‐uniform array is widely used in the mixed near‐field (NF) and far‐field sources localization. The nested array contains a uniform linear array, it is easy to be affected by mutual coupling, so we propose a symmetric thinned coprime array (STCA) to reduce the mutual coupling effect of mixed source localization. In this paper, the STCA configuration consists of two sparse uniform linear arrays, the first subarray is composed of 2N − 1 sensors, and the sensor element spacing is Md. The second subarray is composed of 2M+2⌊M2⌋ $2M+2\lfloor \frac{M}{2}\rfloor $ sensors, and the sensor element spacing are Nd and Md respectively. The two subarrays form the symmetric coprime array, which shares a reference sensor. Under the same number of physical array sensors, compared with the latest symmetric nested array, although STCA has lower consecutive lags, the array sensors have larger inter‐sensor spacing and larger physical array aperture, which can significantly reduce the mutual coupling effect between physical sensors, and better estimation performance of direction‐of‐arrival (DOA) estimation can be achieved. Finally, simulation results show that STCA can achieve better performance than other symmetric nested arrays under the same array sensors and mutual coupling effects. [ABSTRACT FROM AUTHOR]

Recently, sparse linear arrays have aroused significant attention because they can provide increased degrees of freedom (DOFs) and enlarged inter‐element spacing, which are the critical factors to improve the accuracy of direction of arrival (DOA) estimation. In this paper, to alleviate the high mutual coupling caused by the dense part of transformed nested arrays (TNAs), we present a super transformed nested array (STNA) for the DOA estimation of non‐circular signals. It can be obtained by removing some sensors from the dense part of transformed nested arrays and relocating them appropriately. The proposed array structure possesses a higher DOF and a sparser physical structure, resulting in less mutual coupling compared to TNA. For the proposed array structure, we provide theoretical proof of the DOFs and deduce the weight functions. Numerical simulations are conducted to demonstrate the advantages of the STNA over existing sparse arrays. [ABSTRACT FROM AUTHOR]

As we all know, nested array can obtain a larger array aperture and more degrees of freedom using fewer sensors. In this study, we not only designed an enhanced symmetric nested array (ESNA), which achieved more consecutive lags and more unique lags compared with a generalized nested array but also developed a special cumulant matrix, in the case of a given number of sensors, which can automatically generate the largest consecutive lags of the array. First, the direction-of-arrivals (DOAs) of mixed sources are estimated using the special cumulant matrix. Then, we can estimate the range of the near-field source in the mixed source using a one-dimensional spectral search through estimated DOAs, and in the mixed sources, the near-field and far-field sources are classified by bringing in the range parameter. The largest consecutive lags and composition method of ESNA are also given, under a given number of sensors.Our algorithm has moderate computation complexity, which provides a higher resolution and improves the parameters' estimation accuracy. Numerical simulation results demonstrate that the proposed array showed an outstanding performance under estimation accuracy and resolution ability for both DOA and range estimation compared with existing arrays of the same physical array sensors. [ABSTRACT FROM AUTHOR]

As we all know, the model mismatch, primarily when the desired signal exists in the training data, or when the sample data is used for training, will seriously affect algorithm performance. This paper combines the subspace algorithm based on direction of arrival (DOA) estimation with the adaptive beamforming. It proposes a reconstruction algorithm based on the interference plus noise covariance matrix (INCM). Firstly, the eigenvector of the desired signal is obtained according to the eigenvalue decomposition of the subspace algorithm, and the eigenvector is used as the estimated value of the desired signal steering vector (SV). Then the INCM is reconstructed according to the estimated parameters to remove the adverse effect of the desired signal component on the beamformer. Finally, the estimated desired signal SV and the reconstructed INCM are used to calculate the weight. Compared with the previous work, the proposed algorithm not only improves the performance of the adaptive beamformer but also dramatically reduces the complexity. Simulation experiment results show the effectiveness and robustness of the proposed beamforming algorithm. [ABSTRACT FROM AUTHOR]

When there is coexistence of uncorrelated and coherent signals in sparse arrays, the conventional algorithms for direction-of-arrival (DOA) estimation using difference coarray fail. In order to solve the problems, this paper analyzes the feasibility of using spatial smoothing in sparse arrays. Firstly, we summarize the two types of sparse arrays, one consisting of identical sparse subarrays and the other consisting of several uniform linear subarrays. Then, we give the feasibility analysis and the processes of applying spatial smoothing. At last, we discuss the performance of the number of detectable coherent signals in different sparse arrays. Numerical experiments prove the conclusions proposed by the paper. [ABSTRACT FROM AUTHOR]

The sparse arrays using two uniform linear arrays have attracted considerable interest due to the capability of giving analytical expression of sensor location and owning robust direction-of-arrival (DOA) facing strong mutual coupling and sensor failure. In order to achieve the maximum consecutive virtual uniform linear array in difference coarray, in this paper, a design method of a novel sparse array using two uniform linear arrays (NSA-U2) is proposed. We first analyze the relationship between the values of displacement of two subarrays and difference coarray, and then we give the analytical expressions of the displacement and the number of consecutive lags. By discussing the selection of number of subarray sensors, the design of NSA-U2 is completed. Moreover, through choosing a proper compressed interelement spacing, NSA-U2 can be robust to mutual coupling effect. Numerical experiments prove the effectiveness and favorable performance of DOA estimation with mutual coupling. [ABSTRACT FROM AUTHOR]

Recently, the design of sparse linear array for direction of arrival (DOA) estimation of non-Gaussian signals has attracted considerable interest due to the fact that the fourth-order difference coarray offered by non-Gaussian significantly increases the aperture of a virtual linear array, which improves the performance of DOA estimation. In this paper, a super four-level nested array (S-FL-NA) configuration based on fourth-order cumulants (FOC) is proposed. The S-FL-NA consists of uniform linear arrays which have different interelement spacing. The proposed array configuration is designed based on interelement spacing, which, for a given number of sensors, is uniquely determined by a closed-form expression. We also derive the closed-form expression for the degrees of freedom (DOFs) of the proposed array. The optimal distribution of the number of sensors in each uniform linear array of the proposed array is given for an arbitrary number of sensors. Compared with the existing sparse arrays, the proposed array can provide a higher number of degrees of freedom and a larger physical array aperture. In addition, to improve the calculation speed of the fourth-order cumulant matrix, we simplify the FOC matrix by removing some redundancy. Numerical simulations are conducted to verify the superiority of the S-FL-NA over other sparse arrays. [ABSTRACT FROM AUTHOR]