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For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

In this paper, a direction of arrival (DOA) estimation algorithm for non-circular signal by a large-spacing uniform array with an auxiliary element has been presented. The auxiliary element is placed away from the last element of the large-spacing uniform array. The spacing between arbitrary two elements of the whole array is not limited by the half-wavelength of the signal. Firstly, two initial signal subspaces corresponding to the large-spacing uniform array and two row vectors corresponding to the auxiliary element are obtained by eigenvalue decomposition (EVD) of the correlation matrix. The two row vectors are expanded into two virtual signal subspaces by using the two initial signal subspaces. Then, the relationship between the virtual signal subspaces and the initial signal subspaces are used to form a high-dimensional signal subspace corresponding to a uniform linear array with half-wavelength spacing. Finally, DOA estimation can be got by using the estimation of signal parameters via the rotational invariance techniques (ESPRIT) algorithm. Compared with the traditional ESPRIT algorithm and non-circular ESPRIT (NC-ESPRIT) algorithm based on a conventional uniform linear array, the proposed algorithm has higher accuracy for DOA estimation and stronger robustness to the mutual coupling.

Statistical properties of signals play an essential role in designing algorithms for Direction of Arrival (DoA) estimation. Many times, signals are assumed to be circular, and circular moments are used thereof. Practically, non-circular signals exist and provide extra statistical information in terms of pseudo/non-circular moments/cumulants which can be used to improve the performance of any parameter estimation algorithm. This paper uses the 2qth-order non-circular cumulants along with circular cumulants to solve the underdetermined non-Gaussian non-circular system. A generalized method based on higher-order non-circularity has been proposed to design the physical array such that the corresponding virtual array provides the larger degree of freedoms than existing arrays. The weight function, an important metric, to measure the stability of the corresponding virtual array, has also been evaluated analytically. Numerical simulation demonstrates performance gain due to the proposed array structure.

Sparse arrays can increase the array aperture and degrees of freedom through the construction of either sum or difference co-arrays or both. In order to exploit the advantages of sparse arrays while estimating directions of arrival (DOAs) of a mixture of circular and non-circular signals, in this paper, a gridless DOA estimation method is proposed by employing a recently introduced enhanced nested array, whose virtual arrays have no holes. The virtual signals derived from both sum and difference co-arrays are constructed based on atomic norm minimization. It is shown that the proposed method also works when the circular and non-circular signals come from the same set of directions. Simulation results are provided to demonstrate the performance of the proposed method.

In this paper, a robust DOA estimation scheme based on sparse Bayesian learning (SBL) for non-circular signals in impulse noise and mutual coupling (MC) is proposed. Firstly, the Toeplitz property of the MC matrix is used to eliminate the effect of array MC, and the array aperture is extended by using the properties of the non-circular signal. To eliminate the effect of impulse noise, the outlier part of the impulse noise is reconstructed together with the original signal in the signal matrix, and the DOA coarse estimation is obtained by balancing the accuracy and efficiency of parameter estimation using the alternating SBL update algorithm. Finally, a one-dimensional search is used in the vicinity of the searched spectral peaks to achieve a high-precision DOA estimation. The effectiveness and robustness of the algorithm for dealing with the above errors are demonstrated by extensive simulations.

This study focuses on the direct position determination (DPD) of non-circular (NC) sources with multiple nested arrays (NAs). Under impulsive noise modeled as a complex symmetric alpha stable ( S α S ) process, traditional DPD algorithms suffer from significant degradation in localization performance. To address this problem, a phase fractional lower-order moment (PFLOM) based DPD algorithm for NC sources using multiple NAs, combined with a reduced-dimension subspace data fusion (RD-SDF) technique, termed PNNR-SDF, is proposed in this paper. By employing the PFLOM-based covariance matrix instead of the second-order covariance matrix, the sharp amplitude of the impulsive noise can be effectively suppressed, thus improving the estimation accuracy. Moreover, the RD-SDF technique is exploited to reduce high computational complexity. Numerical results demonstrate the superiority of the PNNR-SDF method compared to conventional DPD algorithms under impulsive noise.

In this study, a moving single-station direct position determination (DPD) algorithm based on virtual interpolated arrays is proposed. Existing moving single-station algorithms face challenges such as the incomplete utilization of sparse array apertures and insufficient consideration of mixed circular and non-circular signals. To address these issues, we propose an enhanced gridless DPD algorithm, suitable for multiple mixed circular and non-circular sources. Through constructing a non-zero unconjugated covariance matrix from the non-circular components of the mixed signals, the data dimensionality is expanded, and the gridless method is used to fill the voids in the coarray, significantly improving localization performance. Additionally, a unitary transformation method is applied to reduce computational complexity. This method transforms complex operations into real operations by applying unitary transformations to steering vectors and subspaces. Simulation results demonstrate that the proposed algorithm offers significant advantages in terms of array degrees of freedom and localization accuracy.

We study the problem of angle estimation for non-circular sources in bistatic multiple-input multiple-output (MIMO) radar system and propose a low-complexity ESPRIT–Root-MUSIC algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation. By taking the non-circularity characteristics of the impinging signals, the received data can be extended, which corresponds to double the number of elements in MIMO radar. Then a novel signal subspace, based on the multistage wiener filter, can be determined directly from the extended data, which does not involve the estimation of covariance matrix and its eigenvalue decomposition (EVD), thus implying that the proposed method is computationally efficient. Finally, the DOD and DOA are estimated by ESPRIT and Root-MUSIC, respectively. Compared with EVD-based algorithms, the proposed method provides the comparable angle estimation performance with lower computational complexity. Some simulation results verify the validity of the proposed method.

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. Improve Symmetric Flipped Nested Array for Mixed Near‐Field and Far‐Field Non‐Circular Sources Localization.

In recent years, direct position determination (DPD) with multiple arrays for non-circular (NC) signals is a hot topic to research. Conventional DPD techniques with spectral peak search methods have high computational complexity and are sensitive to the locations of the observation stations. Besides, there will be loss when the signal propagates in the air, which leads to different received signal-to-noise ratios (SNRs) for each observation station. To attack the problems mentioned above, this paper derives direct position determination of non-circular sources for multiple arrays via weighted Euler estimating signal parameters viarotational invariance techniques (ESPRIT) data fusion (NC-Euler-WESPRIT) method. Firstly, elliptic covariance information of NC signals and Euler transformation are used to extend the received signal. Secondly, ESPRIT is applied to avoid the high-dimensional spectral function search problem of each observation station. Then, we combine the information of all observation stations to construct a spectral function without complex multiplication to reduce the computational complexity. Finally, the data of each observation station is weighted to compensate for the projection error. The consequence of simulation indicates that the proposed NC-Euler-WESPRIT algorithm not only improves the estimation performance, but also greatly reduces the computational complexity compared with subspace data fusion (SDF) technology and NC-ESPRIT algorithm.