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Real-time source localization is crucial for high-end automation and artificial intelligence (AI) products. However, a low signal-to-noise ratio (SNR) and limited processing time can reduce localization accuracy. This work proposes a new architecture for a time-domain feedback-based beamformer that meets real-time processing demands. The main objective of this design is to locate reflective sources by estimating their direction of arrival (DOA) and signal range. Incorporating a feedback mechanism in this architecture refines localization precision, a unique aspect of this approach. We conducted an in-depth analysis to compare the effectiveness of time-domain feedback beamforming against conventional time-domain methods, highlighting their benefits and limitations. Our evaluation of the proposed architecture, based on critical performance indicators such as peak-to-sidelobe ratio, mainlobe width, and directivity factor, demonstrates its ability to improve beamformer effectiveness significantly.

This paper proposes a joint estimation method for source number and DOA based on an improved convolutional neural network for unknown source number and undetermined DOA estimation. By analyzing the signal model, the paper designs a convolutional neural network model based on the existence of a mapping relationship between the covariance matrix and both the source number and DOA estimation. The model, which discards the pooling layer to avoid data loss and introduces the dropout method to improve generalization, takes the signal covariance matrix as input and the two branches of source number estimation and DOA estimation as outputs, and achieves the unfixed number of DOA estimation by filling in invalid values. Simulation experiments and analysis of the results show that the algorithm can effectively achieve the joint estimation of source number and DOA. Under the conditions of high SNR and a large snapshot number, both the proposed algorithm and the traditional algorithm have high estimation accuracy, while under the conditions of low SNR and a small snapshot, the algorithm is better than the traditional algorithm, and under the underdetermined conditions, where the traditional algorithm often fails, the algorithm can still achieve the joint estimation.

In automotive millimeter-wave (MMW) radar systems, achieving high-precision direction of arrival (DOA) estimation with a limited number of array elements is a crucial research focus. Compressive sensing (CS) techniques have been demonstrated to offer superior performance in DOA estimation compared to spectral estimation methods. However, traditional CS methods suffer from an off-grid effect, which causes their reconstruction results to deviate from the actual positions of the signal sources, thereby reducing the accuracy. Currently, as a gridless method, atomic norm minimization (ANM) has shown effectiveness in DOA estimation for uniform linear arrays (ULAs). However, the performance of ANM is suboptimal in non-uniform linear arrays (NULAs), and their computational efficiency is not satisfactory. In this paper, we propose a novel algorithm for DOA estimation in NULA, drawing inspiration from the alternating descent conditional gradient algorithm framework. First, we construct an atomic set based on the observation scene and select the atoms with the highest correlation to the residuals as potential signal sources for global estimation. Then, we construct a mapping function for the signal sources in the continuous domain and perform conditional gradient descent in the neighborhood of each signal source, addressing the bias introduced by the off-grid effect. We compared the proposed algorithm with ANM, Iterative Shrinkage Thresholding (IST), and Multiple Signal Classification (MUSIC) algorithms. Simulation experiments validate that the proposed algorithm effectively addresses the off-grid effect and is applicable to DOA estimation in coprime and random arrays. Furthermore, real data experiments confirm the effectiveness of the proposed algorithm.

Passive radar is an interesting approach in the context of non-cooperative target detection. Because the signal source takes advantage of the so-called illuminator of opportunity (IoO), the deployed system is silent, allowing the operator cheap, portable, and practically undetectable deployments. These systems match perfectly with the use of antenna arrays to take advantage of the additional gains provided by the coherent combination of the signals received at each element. To obtain these benefits, linear processing methods are required to enhance the system’s performance. In this work, we summarize the main beamforming methods in the literature to provide a clear picture of the current state of the art. Next, we perform an analysis of the benefits and drawbacks and explore the chance of increasing the number of antenna elements. Finally, we identify the major challenges to be addressed by researchers in the future.

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.

This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method.

Coprime arrays have shown potential advantages for direction-of-arrival (DOA) estimation by increasing the number of degrees-of-freedom in the difference coarray domain with fewer physical sensors. In this paper, a new DOA estimation algorithm for coprime array based on the estimation of signal parameter via rotational invariance techniques (ESPRIT) is proposed. We firstly derive the observation vector of the virtual uniform linear array but the covariance matrix of this observation vector is rank-deficient. Different from the traditional Toeplitz matrix reconstruction method using the observation vector, we propose a modified Toeplitz matrix reconstruction method using any non-zero row of the covariance matrix in the virtual uniform linear array. It can be proved in theory that the reconstructed Toeplitz covariance matrix has full rank. Therefore, the improved ESPRIT method can be used for DOA estimation without peak searching. Finally, the closed-form solution for DOA estimation in coprime array is obtained. Compared to the traditional coprime multiple signal classification (MUSIC) methods, the proposed method circumvents the use of spatial smoothing technique, which usually results in performance degradation and heavy computational burden. The effectiveness of the proposed method is demonstrated by numerical examples.

Achieving accurate single snapshot direction of arrival (DOA) information significantly improves communication performance. This paper investigates an accurate and high-resolution DOA estimation technique by enabling single snapshot data collection and enhancing DOA estimation results compared to multiple snapshot methods. This is carried out by manipulating the incoming signal covariance matrix while suppressing undesired additive white Gaussian noise (AWGN) by actively updating and estimating the antenna array manifold vector. We demonstrated the estimation performance in simulation that our proposed technique supersedes the estimation performance of existing state-of-the-art techniques in various signal-to-noise ratio (SNR) scenarios and single snapshot sampling environments. Our proposed covariance-based single snapshot (CbSS) technique yields the lowest root-mean-squared error (RMSE) against the true DOA compared to root-MUSIC and the partial relaxation (PR) approach for multiple snapshots and a single signal source environment. In addition, our proposed technique presents the lowest DOA estimation performance degradation in a multiple uncorrelated and coherent signal source environment by up to 25.5% with nearly negligible bias. Lastly, our proposed CbSS technique presents the best DOA estimation results for a single snapshot and single-source scenario with an RMSE of 0.05° against the true DOA compared to root-MUSIC and the PR approach with nearly negligible bias as well. A potential application for CbSS would be in a scenario where accurate DOA estimation with a small antenna array form factor is a limitation, such as in the intelligent transportation system industry and wireless communication.

Unlike uniform linear arrays (ULAs), coprime arrays require fewer physical sensors yet provide higher degrees of freedom (DOF) and larger array apertures. However, due to the existence of “holes” in the differential co-array, the target detection performance deteriorates, especially in adaptive beamforming. To address these challenges, this paper proposes an efficient and robust adaptive beamforming algorithm leveraging coprime array interpolation. The algorithm eliminates unwanted signals and uses the Gauss–Legendre quadrature method to reconstruct an Interference-plus-Noise Covariance Matrix (INCM), thereby obtaining the beamforming coefficients. Unlike previous techniques, we utilize a virtual interpolated ULA to expand the aperture, enabling the acquisition of a high-dimensional covariance matrix. Additionally, a projection matrix is constructed to eliminate unwanted signals from the received data, greatly enhancing the accuracy of INCM reconstruction. To address the high computational complexity of integral operations used in most INCM reconstruction algorithms, we propose an approximation based on the Gauss–Legendre quadrature, which reduces the computational load while maintaining accuracy. This algorithm avoids the array aperture loss caused by using only the ULA segment in the difference co-array and improves the accuracy of INCM reconstruction. Simulation and experimental results show that the performance of the proposed algorithm is superior to the compared beamformers and is closer to the optimal beamformer in various scenarios.

In mixed-field source localization, the physical properties of a sensor array, such as the degrees of freedom (DOFs), aperture, and coupling leakage, directly affect the accuracy of estimating the direction of arrival (DOA). Compared to conventional symmetric uniform linear arrays, symmetric non-uniform linear arrays (SNLAs) have a greater advantage in mixed-field source localization due to their larger aperture and higher DOF. However, current SNLAs require improvements in their physical properties through modifications to the array structure in order to achieve more accurate source localization estimates. Therefore, this study proposes a symmetric double-supplemented nested array (SDSNA), which translates nested subarrays based on symmetric nested arrays to increase the aperture and inserts two symmetric supplemented subarrays to fill the holes created by the translation. This method results in longer consecutive difference coarray lags and larger apertures. The SDSNA is compared to existing advanced SNLAs in terms of their physical properties and DOA estimation. The results show that, with the same number of sensors, the SDSNA has a higher DOF, a larger aperture, and smaller coupling, indicating the advantages of the SDSNA in terms of its physical properties. Under the same experimental conditions, the SDSNA has a lower root-mean-square error of source location, thus indicating better performance in terms of both DOA and distance estimation.