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The degree of freedom (DOF) is an important performance metric for evaluating the design of a sparse array structure. Designing novel sparse arrays with higher degrees of freedom, while ensuring that the array structure can be mathematically represented, is a crucial research direction in the field of direction of arrival (DOA) estimation. In this paper, we propose a novel L-shaped sparse sensor array by adjusting the physical placement of the sensors in the sparse array. The proposed L-shaped sparse array consists of two sets of three-level and single-element sparse arrays (TSESAs), which estimate the azimuth and elevation angles, respectively, through one-dimensional (1-D) spatial spectrum search. Each TSESA is composed of a uniform linear subarray and two sparse subarrays, with one single common element in the two sparse subarrays. Compared to existing L-shaped sparse arrays, the proposed array achieves higher degrees of freedom, up to 4 Q 1 Q 2 + 8 Q 1 − 5 , when estimating DOA using the received signal covariance. To facilitate the correct matching of azimuth and elevation angles, the cross-covariance between the two TSESA arrays is utilized for estimation. By comparing and analyzing performance parameters with commonly used L-shaped and other sparse arrays, it is found that the proposed L-shaped TSESA has higher degrees of freedom and array aperture, leading to improved two-dimensional (2-D) DOA estimation results. Finally, simulation experiments validate the excellent performance of the L-shaped TSESA in 2-D DOA estimation. [ABSTRACT FROM AUTHOR]

At present, there are few sparse arrays used in the mixed near‐field (NF) and far‐field (FF) localization based on non‐circular (NC) signals. Inspired by the symmetric flipped nested array (SFNA) used in the existing mixed NF and FF NC source, in order to further improve the parameter estimation accuracy of the mixed NF and FF NC signal, an improved symmetric flipped nested array (ISFNA) for mixed NF and FF NC sources localization was developed. First, the uniform subarrays in the SFNA are rearranged, ⌈N22⌉−1${\lceil \frac{N_2}{2}\rceil }-1$ elements are extracted from the uniform subarrays and rearranged into ISFNA. ISFNA is more sparse, the array aperture is larger, and the array degree of freedom (DOF) is higher; second, the formula of the maximum consecutive lags of ISFNA is given; third, a special fourth‐order cumulant is used to eliminate the range parameter and then use a one‐dimensional (1‐D) spectral peak search to obtain all Directions of Arrival (DOAs). By defining the range search, the range can be obtained by bringing in estimated DOAs. Finally, the superiority of the proposed array is proved by simulation. [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]

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]

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]

The performance of direction-of-arrival (DOA) estimation for sparse arrays applied to the distributed source is worse than that applied to the point source model. In this paper, we introduce the coprime array with a large array aperture into the DOA estimation algorithm of the exponential-type coherent distributed source. In particular, we focus on the fourth-order cumulant (FOC) of the received signal which can provide more useful information when the signal is non-Gaussian than when it is Gaussian. The proposed algorithm extends the array aperture by combining the sparsity of array space domain with the fourth-order cumulant characteristics of signals, which improves the estimation accuracy and degree of freedom (DOF). Firstly, the signal-received model of the sparse array is established, and the fourth-order cumulant matrix of the received signal of the sparse array is calculated based on the characteristics of distributed sources, which extend the array aperture. Then, the virtual array is constructed by the sum aggregate of physical array elements, and the position set of its maximum continuous part array element is obtained. Finally, the center DOA estimation of the distributed source is realized by the subspace method. The accuracy and DOF of the proposed algorithm are higher than those of the distributed signal parameter estimator (DSPE) algorithm and least-squares estimation signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm when the array elements are the same. Complexity analysis and numerical simulations are provided to demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]