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There exist numerous multi‐path signals with impulsive noise (IN) in a multi‐path propagation environment. The direction‐of‐arrival (DOA) is highly challenging to be assessed because of the strong IN. For various military along with civilian applications, DOA estimation has turned into a hopeful technology. But, estimating DOA for multipath signals with IN environments is extremely complicated. A desirable output is not attained by several existent techniques, namely subspace‐centric approaches, maximum likelihood techniques, along with sparse representation‐centric methods, for DOA assessment. Therefore, an effective satin bowerbird optimization‐based deep learning neural network centered DOA estimation upon single snapshots is proposed in this paper for attaining robust and precise DOA estimation in multipath and IN environments. An arbitrary array configuration is employed by utilizing the proposed work as an input signal for establishing the received signal's model. Pre‐processing, time‐frequency domain conversion, feature extraction, feature reduction and DOA estimation are the proposed method's 5 disparate stages. To evince the proposed model's efficacy, its outcomes are analogized with other prevailing techniques regarding some performance metrics. The proposed model attains the root mean square error of 0.6484366‐AZ and 0.6484366‐EA, root mean squared percentage error (RMPSE) of 4.636107‐AZ and 5.628599‐EA and probability of resolution of 0.967999‐AZ and 0.962841‐EA, which are extremely less when compared to the prevailing methods; thus, depicting the superiority of the proposed model for an effective DOA estimation. [ABSTRACT FROM AUTHOR]

In this paper, an innovative cyclic noise reduction method and an improved CAPON algorithm (also the called minimum variance distortionless response (MVDR) algorithm) are proposed to improve the accuracy and reliability of DOA (direction of arrival) estimation. By processing the eigenvalues obtained from the covariance matrix of the received signal, the signal-to-noise ratio (SNR) can be increased by up to 5 dB by the cyclic noise reduction method, which will improve the DOA estimation accuracy. The improved CAPON algorithm has a convolution neural network (CNN) structure, whose input is the processed covariance matrix of the received signal, and the CAPON spectral value is used as the training label to obtain the estimated spatial spectrum. It retains the advantages of the CAPON algorithm, which can achieve blind source estimation, and simulations show that the proposed algorithm exhibits a better performance than the traditional algorithm in conditions of various SNRs and snapshot numbers. The simulation results show that, based on a certain SNR, the root mean square error (RMSE) of the improved CAPON algorithm can be reduced from 0.86° to 0.8° compared to traditional algorithms, and the angle estimation error can be decreased by up to about 0.3°. With the help of the cyclic noise reduction method, the angle estimation error decreases from 0.04° to 0.02°. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy. [ABSTRACT FROM AUTHOR]

With the development of deep learning techniques, the field of direction of arrival (DOA) estimation has also made significant progress. However, the accuracy of DOA estimation using end-to-end neural networks (NNs) heavily relies on the classification step of the networks, which necessitates the use of large and representative datasets. Additionally, conventional speech presence probability (SPP) estimation methods based on the ideal ratio mask (IRM) may misclassify time-frequency (T-F) bins dominated by non-speech and noise, which hinders the accurate extraction of directional information. To improve the robustness of existing DOA estimation algorithms, this paper proposes a DOA estimation method with T-F bin selection. In terms of output, instead of using IRM-based SPP, our proposed approach focuses on the a posteriori SPP, a deliberate choice aimed at circumventing potential confusion. For input optimization, we construct features that encompass spatial, temporal, and directional information concurrently, and these are coupled with a frequency bin-wise recurrent neural network (RNN) model to attain precise multi-channel SPP estimation. Subsequently, these SPP estimates are utilized to extract local information for DOA estimation. Moreover, the cascaded structure ensures that the model has the ability to complete out-of-label tasks, effectively reducing the dataset requirements by training only a subset of direction information to achieve omnidirectional DOA estimation. Besides, this contributes to the algorithm's ability to eliminate its reliance on the step size, setting it apart from other end-to-end methods. Simulation results validate that the proposed method achieves higher accuracy and lower error compared to both NN-based end-to-end approaches and traditional full-band approaches under various conditions of reverberation and signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In the field of direction of arrival (DOA) estimation for coherent sources, subspace-based model-driven methods exhibit increased computational complexity due to the requirement for eigenvalue decomposition. In this paper, we propose a new neural network, i.e., the signal space deep convolution (SSDC) network, which employs the signal space covariance matrix as the input and performs independent two-dimensional convolution operations on the symmetric real and imaginary parts of the input signal space covariance matrix. The proposed SSDC network is designed to address the challenging task of DOA estimation for coherent sources. Furthermore, we leverage the spatial sparsity of the output from the proposed SSDC network to conduct a spectral peak search for obtaining the associated DOAs. Simulations demonstrate that, compared to existing state-of-the-art deep learning-based DOA estimation methods for coherent sources, the proposed SSDC network achieves excellent results in both matching and mismatching scenarios between the training and test sets. [ABSTRACT FROM AUTHOR]

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l 2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a Toeplitz construction method based on eigenvalues and eigenvectors is proposed to combine with traditional denoising algorithms, including fractional low-order moment (FLOM), phased fractional low-order moment (PFLOM), and correntropy-based correlation (CRCO) methods. It can improve the direction of arrival (DOA) estimation of signals in impulsive noise. Firstly, the algorithm performs eigenvalue decomposition on the received covariance matrix to obtain eigenvectors and eigenvalues, and then the Toeplitz matrix is created according to the eigenvectors corresponding to its eigenvalues. Secondly, the spatial averaging method is used to obtain an unbiased estimate of the Toeplitz matrix, which is then weighted and added based on the corresponding eigenvalues. Next, the noise subspace of the Toeplitz matrix is reconstructed to obtain the one that has less angle information. Finally, the DOA of the coherent signal is estimated using the Multiple Signal Classification (MUSIC) algorithm. The improved method based on the Toeplitz matrix can not only suppress the effect of impulsive noise but can also solve the problem of aperture loss due to its decoherence. A series of simulations have shown that they have better performances than other algorithms. [ABSTRACT FROM AUTHOR]

The two-dimensional grid-free compressed sensing method with planar microphone arrays is expected to achieve super-resolution direction-of-arrival (DOA) estimation for acoustic sources in the hemispherical space in front of array. The existing methods are not yet well compatible with arbitrary planar array geometries. In this paper, we aim to break this limitation and explore a novel method applicable to arbitrary planar array geometries. First, the covariance between source-induced signals at arbitrary two microphones is formulated as related to the two-dimensional inverse Fourier transform of the source strength. Then, a mathematical model with a source sparsity constraint is built in the continuous domain to denoise the covariances of measured signals, which can be solved by decoupled positive semidefinite programming. Finally, the DOAs are extracted from the solution of the mathematical model via a matrix pencil and pairing method. Simulation and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, sparse arrays based on the fourth‐order difference coarray (FODCA) have received increased research attention due to their small number of array elements and large consecutive virtual arrays. The expanding and shift structure based on the nested array (NA) and coprime array (CPA) (EAS‐NA‐CPA) is the representative one. The EAS‐NA‐CPA comprises two sparse subarrays, wherein the NA is expanded and shifted according to the second‐order difference coarray of the CPA. Although the number of consecutive elements is large, there are many redundant elements in the FODCA of the EAS‐NA‐CPA. To decrease the number of redundant elements and increase the number of consecutive elements in the FODCA, the authors proposed the enhanced EAS‐NA‐CPA (EEAS‐NA‐CPA). Compared with the original EAS‐NA‐CPA, the EEAS‐NA‐CPA increases the adjacent physical sensor spacing further by using more fourth‐order cross‐correlation coarrays in the FODCA, which are not considered in the original EAS‐NA‐CPA. By performing a theoretical analysis of the FODCA provided by the proposed EEAS‐NA‐CPA, the sensor spacing in the expanded NA was further increased to obtain a larger number of consecutive elements compared with the original EAS‐NA‐CPA. Furthermore, the relationship between the number of physical sensors and corresponding number of consecutive elements provided by the FODCA was explicitly expressed. Experimental simulations were conducted to verify the effectiveness of the proposed sparse array for the fourth‐order cumulant‐based direction of arrival estimation. [ABSTRACT FROM AUTHOR]

Beamspace processing is widely applied in Direction‐of‐Arrival (DOA) estimation thanks to dimensional reduction and super‐resolution characterisations. However, the conventional atomic norm minimisation (ANM) based methods for beamspace DOA estimation are of high computational complexity for large arrays. To deal with this issue, the proposed method focuses on locating the sources in the mainlobe of the beamspace and encodes such prior information into the ANM problem without frequency‐selective constraints. The proposed method approximates the beamspace array manifold in the mainlobe sector with the truncated sector Fourier series. The theoretical analysis shows that such approximation with the properly designed fitting error relaxation on the boundary yields the low dimensional semidefinite programming (SDP) approximate implementation of the proposed ANM method and guarantees the support recovery inside the mainlobe. Furthermore, the low complexity Burer‐Monteiro factorisation based alternating direction method of multipliers method is proposed to solve the SDP problem. The complexity analysis and simulations show that the proposed method results in significant computational complexity reduction and slightly better performance compared with state‐of‐art benchmarks. [ABSTRACT FROM AUTHOR]

In practical applications, the hydrophone array has element position errors, which seriously degrade the performance of the direction of arrival estimation. We propose a direction of arrival (DOA) estimation method based on sparse Bayesian learning using existing array position errors to solve this problem. The array position error and angle grid error parameters are introduced, and the prior distribution of these two errors is determined. The joint probability density distribution function is established by means of a sparse Bayesian learning model. At the same time, the unknown parameters are optimized and iterated using the expectation maximum algorithm and the corresponding parameters are solved to obtain the spatial spectrum. The results of the simulation and the lake experiments show that the proposed method effectively overcomes the problem of array element position errors and has strong robustness. It shows a good performance in terms of its estimation accuracy, meaning that the resolution ability can be greatly improved in the case of a low signal-to-noise ratio or small number of snapshots. [ABSTRACT FROM AUTHOR]

Monitoring object displacement is critical for structural health monitoring (SHM). Radio frequency identification (RFID) sensors can be used for this purpose. Using more sensors enhances displacement estimation accuracy, especially when it is realized through the use of machine learning (ML) algorithms for predicting the direction of arrival of the associated signals. Our research shows that ML algorithms, in conjunction with adequate RFID passive sensor data, can precisely evaluate azimuth angles. However, increasing the number of sensors can lead to gaps in the data, which typical numerical methods such as interpolation and imputation may not fully resolve. To overcome this challenge, we propose enhancing the sensitivity of 3D-printed passive RFID sensor arrays using a novel photoluminescence-based RF signal enhancement technique. This can boost received RF signal levels by 2 dB to 8 dB, depending on the propagation mode (near-field or far-field). Hence, it effectively mitigates the issue of missing data without necessitating changes in transmit power levels or the number of sensors. This approach, which enables remote shaping of radiation patterns via light, can herald new prospects in the development of smart antennas for various applications apart from SHM, such as biomedicine and aerospace. [ABSTRACT FROM AUTHOR]

In this paper, we explore the problem of direction-of-arrival (DOA) estimation for a non-uniform linear array (NULA) under strong noise. The compressed sensing (CS)-based methods are widely used in NULA DOA estimations. However, these methods commonly rely on the tuning of parameters, which are hard to fine-tune. Additionally, these methods lack robustness under strong noise. To address these issues, this paper proposes a novel DOA estimation approach using a deep neural network (DNN) for a NULA in a low SNR. The proposed network is designed based on the denoising convolutional neural network (DnCNN) and the alternating direction method of multipliers (ADMM), which is dubbed as LDnADMM-Net. First, we construct an unfolded DNN architecture that mimics the behavior of the iterative processing of an ADMM. In this way, the parameters of an ADMM can be transformed into the network weights, and thus we can adaptively optimize these parameters through network training. Then, we employ the DnCNN to develop a denoising module (DnM) and integrate it into the unfolded DNN. Using this DnM, we can enhance the anti-noise ability of the proposed network and obtain a robust DOA estimation in a low SNR. The simulation and experimental results show that the proposed LDnADMM-Net can obtain high-accuracy and super-resolution DOA estimations for a NULA with strong robustness in a low signal-to-noise ratio (SNR). [ABSTRACT FROM AUTHOR]

Sparse arrays are widely employed in array signal processing due to their obvious advantages in array element distribution and uniform degrees of freedom (uDOFs). In this paper, a generalized augmented multi-subarray nested array (GAMSNA-I) and its variant, GAMSNA-II are proposed, with the objective of increasing uDOFs and reducing mutual coupling. Based on two subarrays of the prototype nested array (NA), GAMSNA-I is constructed by reconfiguring the dense uniform linear array (ULA) and forward-shifting the sparse ULA. GAMSNA-II is obtained by sparsifying the dense part of GAMSNA-I, ensuring constant uDOFs while further reducing mutual coupling. Subsequently, the closed-form expression for the uDOFs of GAMSNA-I with an arbitrary number of sensors is derived, and the proof is provided that the uDOFs of GAMSNA-II remain unchanged relative to that of GAMSNA-I. Compared to some existing array configurations, both GAMSNA-I and GAMSNA-II exhibit improved uDOFs, with GAMSNA-II achieving lower mutual coupling. Simulation results show the superior performance of the proposed GAMSNA-I and GAMSNA-II. [ABSTRACT FROM AUTHOR]

Receiver channels amplitude and phase calibration in smart antennas is a crucial process to achieve the systems requirement. The implementation of these functions in a programmable device and the procedures for selecting its parameters is not a widely disseminated topic in the specialized literature. This work solves the previous problem by implementing the calibration algorithm in FPGA based on the requirements to guarantee the estimation of the direction of arrival (DOA) with super resolution. The design implemented in Hardware Description Language (HDL) corrects in real time the amplitude and phase errors between channels of the multichannel reception system with low latency and resource consumption. Experimental verification with real signals demonstrates that the errors obtained after calibration are within the expected range and corroborates the effectiveness of the design. [ABSTRACT FROM AUTHOR]

Direction-of-arrival (DoA) estimation is an important part in sonar signal processing, providing a reliable foundation for tasks, such as underwater object detection and tracking. Although the deep learning model has powerful data fitting capabilities, accurately estimating the orientation of multiple targets with a single model remains a challenging task. To address this challenge, we enhance the permutation invariant training (PIT) technique and propose two different types of methods: multi-group classification with PIT (MC-PIT) and multi-group regression with PIT (MR-PIT). These two frame-level PIT schemes utilize a single model for both training and testing in multi-target scenarios. Furthermore, we evaluate the performance of MR-PIT and MC-PIT with different network backbones and demonstrate that the frame-level PIT has excellent portability. Compared with the model trained with the general multi-label strategy, simulation experiments show that our proposed methods have better multi-target DoA estimation performance. Finally, when the array configuration of simulated and recorded data are consistent, the model with frame-level PIT can achieve good performance on recorded data even only trained on simulation data. [ABSTRACT FROM AUTHOR]

A modified RELAX algorithm based on iterative coarray‐domain beamforming for fast source direction‐of‐arrival (DOA) estimation with fully augmentable sparse arrays is proposed. The authors exploit the deterministic centralised nature of the noise in the coarray domain and the Hermitian symmetry of the spatial autocorrelation function to efficiently incorporate source number estimation within the iterative framework. In doing so, the proposed algorithm allows low‐complexity, fast DOA estimation of more sources than sensors, without resorting to computationally expensive implementations of source number estimation using information theoretic criteria. Three variants of the proposed algorithm are presented, each differing in terms of the specific method employed for source number estimation. Extensive simulations are performed with a minimum redundancy array to compare and contrast the performance of the three variants in terms of their accuracy in estimating the number of sources in the field‐of‐view of the array. The results demonstrate that the modified RELAX algorithm can provide accurate estimates of the number and directions of sources, especially when the number of uncorrelated sources is equal to or higher than the number of sensors. [ABSTRACT FROM AUTHOR]

To improve the data utilization of the sensor array and direction-of-arrival-(DOA)-estimation performance for coherent signals, a DOA-estimation method with a modified spatial-smoothing technique is proposed. The covariance matrix of the received data of the sensor array is decomposed to obtain the signal subspace vectors, and the obtained vectors are smoothed in the proposed method. Then, a new data covariance matrix is constructed by using the autocorrelation covariance matrix of the intra-subarrays and the cross-correlation covariance matrix of the inter-subarrays. Finally, the DOA of the incident signal is estimated, using the new data covariance matrix with the multiple-signal-classification-(MUSIC) algorithm. The data-processing results of the simulation and lake test show that the modified method has stronger decoherence ability, as it utilizes more comprehensive coherent signal information. It also has better azimuth-estimation performance and robustness in the case of a low signal-to-noise ratio (SNR), few snapshots, and small incident-angle intervals when compared to the traditional method. Therefore, the modified method has great engineering application value. [ABSTRACT FROM AUTHOR]

This letter presents a method to optimize the estimation of direction of arrival (DOA) using the uniform linear array (ULA) with one‐bit signals in the presence of non‐uniform noise. With the Toeplitz properties and the rank characteristics of the signal subspace matrix formed by the ULA, the alternating minimization (AM) method is employed to optimize the estimation problem. To address this challenge further, we utilize the singular value thresholding (SVT) method and the approximate projection method. The angle deviations caused by non‐uniform noise can be effectively corrected and a significant improvement in the estimation performance can be achieved. The feasibility and effectiveness of the proposed method are demonstrated through simulation results. [ABSTRACT FROM AUTHOR]

To reduce the influence of gain-phase errors and improve the performance of direction-of-arrival (DOA) estimation, a robust sparse Bayesian two-dimensional (2D) DOA estimation method with gain-phase errors is proposed for L-shaped sensor arrays. The proposed method introduces an auxiliary angle to transform the 2D DOA estimation problem into two 1D angle estimation problems. A sparse representation model with gain-phase errors is constructed using the diagonal element vector of the cross-correlation covariance matrix of two submatrices of the L-shaped sensor array. The expectation maximization algorithm derives unknown parameter expression, which is used for iterative operations to obtain off-grid and signal precision. Using these parameters, a new spatial spectral function is constructed to estimate the auxiliary angle. The obtained auxiliary angle is substituted into a sparse representation model with gain and phase errors, and then the sparse Bayesian learning method is used to estimate the elevation angle of the incident signal. Finally, according to the relationship of the three angles, the azimuth angle can be estimated. The simulation results show that the proposed method can effectively realize the automatic matching of the azimuth and elevation angles of the incident signal, and improves the accuracy of DOA estimation and angular resolution. [ABSTRACT FROM AUTHOR]

In this work, we propose the unfolded versions of the coprime transformed nested array (CTNA), which exploits the sum difference coarray (SDCA). We know that the CTNA has attractive properties in achieving more degrees of freedom (DOF) in direction-of-arrival estimation. However, the mutual coupling of the CTNA cannot be neglected. Here, we present the unfolded versions of the CNTA, specifically UCTNA-I (Unfolded CTNA) and UCTNA-II, which are obtained by flipping two different subarrays of the CTNA. The proposed configurations significantly reduce the mutual coupling of the CTNA without compromising the DOF it achieves. Vectorized conjugate augmented MUSIC algorithm is used to explore the SDCA of the array. The detailed properties of the arrays with the weight functions are provided in the paper. The optimization of the arrays is also carried out. Simulations are performed to prove the superiority of the proposed arrays by comparing them with the other existing arrays. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation with nested arrays has been widely investigated in the field of array signal processing, but most studies assume that the noise is Gaussian white noise. In practical situations, there may exist impulsive noise (a kind of heavy-tailed noise), wherein the performance of traditional subspace-based DOA estimation algorithms deteriorates significantly. In this paper, we propose a correlation entropy-based infinite norm preprocessing algorithm, which can be applicable to any type of impulsive noise. Each snapshot of the sensor array data is processed by an exponential kernel function with the infinite norm, which can effectively combat the outliers. Furthermore, we construct the equivalent second-order covariance matrix and perform DOA estimation using classical subspace methods. Simulation results demonstrate the effectiveness of the proposed method for both symmetric α -stable distribution and the Gaussian mixture model. [ABSTRACT FROM AUTHOR]

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]

An investigation on fractal-based sub-array (FBSA), of isotropic elements, that evolves from two Non-uniform Linear arrays, i.e. the minimum redundancy array and fractal Array, with a hole-free difference co-array shows competitive performance in direction of arrival estimation using (spatial smoothing-) MUSIC algorithm. Numerical experiments demonstrate that the algorithm can resolve 2° separation between sources. Considering mutual coupling, in terms of RMSE, the FBSA performs better than other competing configurations. [ABSTRACT FROM AUTHOR]

This paper presents an underwater soundfield visualisation method for passive-sonar applications employing circular hydrophone arrays. The method operates by segregating the space by means of beamforming into angular sectors scanning the whole horizontal plane and then computing acoustic parameters within each sector. The information from these directionally constrained parameters is fused in order to produce spatial spectra which depict the distribution of acoustic energy over bearing. The evaluation is performed on simulated data of circular hydrophone arrays mounted on rigid cylindrical baffles. Comparisons against baseline methods of similar computational complexity suggest that, for moderate to high signal-to-noise ratio levels, the proposed method offers improved performance in terms of background noise suppression, angular resolution, and direction-of-arrival estimation accuracy. Additionally, it is demonstrated that, with the appropriate choice of sector pattern, the proposed method can, at least in some cases, achieve superior performance to the baseline methods in the presence of interferers even at low signal-to-interference ratio levels. Last, the sector-based parameter diffuseness, which is directly related to the direct-to-diffuse ratio, may be used both as a weight function to further attenuate the background noise level and as a confidence measure of the estimation accuracy. [ABSTRACT FROM AUTHOR]

To address the problems of traditional two‐level nested arrays (TTNA) with low degrees of freedom and high mutual coupling, a generalised two‐level nested MIMO radar array with high degrees of freedom and low mutual coupling for the direction of arrival (DOA) estimation is proposed. First, two coprime expansion factors are introduced in the TTNA to mitigate mutual coupling among array elements and enhance its degrees of freedom. Secondly, the range of consecutive lags and the total number of virtual array elements are derived in closed form under the structures of 'sum–difference co‐array'. Finally, utilising the atomic norm minimisation theory, the authors address the issue of discrete holes caused by different coprime expansion factors through filling in virtual arrays at discontinuities. Furthermore, a convex optimisation model to recover equivalent received signals from these filled virtual arrays is established, which is combined with a multiple signal classification algorithm for DOA estimation. Simulation results validate the rationality of the array structure and demonstrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this article, an effective algorithm is proposed for direction‐of‐arrival (DOA) estimation of coherent signals using the l2‐norm with moving coprime arrays. The proposed algorithm exhibits high accuracy and robustness in decorrelation of coherent signals compared to existing methods. Firstly, the received signal is filtered on the moving coprime array and a signal model is constructed that is compatible with the moving coprime array. Next, virtual sensors is inserted into the holes of the moving coprime array and the received signals are initialised. Then, the Toeplitz matrix is reconstructed based on the covariance matrix of the initial signal and perform low‐rank matrix recovery to eliminate signal coherence by compensating the matrix for zero. Finally, the DOA estimation for the signal is performed using spectral peak search. Simulation results verify that the estimation accuracy of our proposed algorithm outperforms various existing algorithms. [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]

The authors propose a computationally efficient approach to estimate the directions of arrival of far‐field sources impinging on a sensor array. The proposed estimator is formed using a sparse reconstruction framework, employing a novel adaptive grid selection technique to reduce the dimensionality of the used dictionary matrix. The method further makes use of a SPICE‐inspired dictionary to adaptively select an appropriate regularisation parameter and to select the active grid set. An adaptive stepsize selection strategy is also introduced to reduce computation complexity further. The proposed method allows for accurate direction‐of‐arrival (DOA) estimates using even a single snapshot, also from weak sources. Numerical simulations indicate that the method offers preferable performance in comparison to existing state‐of‐the‐art DOA estimation algorithms. [ABSTRACT FROM AUTHOR]

To reduce mutual coupling of an improved nested array (INA), the authors propose an augmented improved nested array (AINA) by splitting the dense subarray of the INA into two parts and rearranging one of them on the right side of the last element in the INA, which enhances the number of unique lags in difference coarray and reduces the number of element pairs with small separations. The closed‐form expressions for the physical element locations, the range of consecutive lags and the number of unique lags are derived for any given element number. It is indicated that the AINA possesses higher degrees of freedom and less mutual coupling than the common sparse arrays. Numerical simulations verify the superiority of the proposed configuration. [ABSTRACT FROM AUTHOR]

The traditional coprime parallel array (TrCPA) is prone to suffer from the problem of angle ambiguity, due to its larger inter-element spacing and limited array aperture, for two-dimensional direction of arrival estimation. And the classic multiple signal classification (MUSIC) algorithm has heavy complexity and has poor estimation ability in some unsatisfactory situations. Both restrict the improvement of angle estimation performance. In this paper, we design a novel displaced coprime parallel array termed NDCPA, by rearranging and misplacing all subarrays of TrCPA along the coordinate axis, which brings about larger array aperture making contributions to superior angle estimation accuracy. Besides, we propose an improved two-step reduced-dimensional MUSIC algorithm to further enhance angle estimation accuracy. The proposed method reconstructs the covariance matrix, which can fully exploit the information contained in uniform linear subarrays. Meanwhile, the transformation of angle domain divides the original two-dimensional search into two one-dimensional searches, reducing complexity to a certain extent. Finally, simulation results verify the effectiveness and applicability of the proposed configuration and method compared with the other structures and methods. [ABSTRACT FROM AUTHOR]

To improve the performance of underdetermined direction of arrival (DOA) estimation in the scenario of strong mutual coupling and unknown nonuniform noise, this paper presents a novel coprime polarization sensitive array (PSA) with limited antenna number and proposes a low-complexity DOA estimation method via iterative covariance matrix reconstruction. The proposed synthetic array is composed of two single-polarized subarrays with dipole or loop antennas. Owing to the polarization domain, it can efficiently reduce the mutual coupling between subarrays, which dominates the effect of mutual coupling in the existing coprime arrays. For effectively eliminating the nonuniform noise, the cross-covariance matrix between subarrays is utilized. Based on it, the full aperture and all degrees of freedoms of the difference coarray with holes are obtained, and then, initial DOAs are estimated by using orthogonal matching pursuit algorithm. The oblique projection operators depending on initial DOAs are constructed to fill holes in difference coarray, in order to generate a larger covariance matrix for refined angle estimation. Then, a fast iterative procedure associated with covariance matrix reconstruction is given to achieve final DOA estimation, for further enhancing estimation performance. Theoretical analysis and simulation results verify the effectiveness of the proposed array and method. [ABSTRACT FROM AUTHOR]

Multiple autonomous underwater vehicles (AUVs) have gradually become the trend in underwater operations. Identifying and detecting these new underwater multi-targets is difficult when studying underwater moving targets. A 28-element transducer is used to test the echo of multiple AUVs with different layouts in a lake. The characteristics of the wideband echo signals are studied. Under the condition that the direction of arrival (DOA) is not known, an autofocus coherent signal subspace (ACCSM) method is proposed. The focusing matrix is constructed based on the received data. The spatial spectrum of the array signal of multiple AUVs at different attitudes is calculated. The algorithm estimates the DOA of the echo signals to overcome the shortcomings of traditional wideband DOA estimation and improve its accuracy. The results show that the highlights are not only related to the number of AUVs, but are also modified by scale and attitude. The contribution of the microstructure of the target in the overall echo cannot be ignored. Different parts of the target affect the number of highlights, thus resulting in varying numbers of highlights at different attitude angle intervals. The results have significant implications for underwater multi-target recognition. [ABSTRACT FROM AUTHOR]

Nonuniform linear arrays (NLAs) have attracted considerable attention owing to their capability to enhance the degrees of freedom (DOF) and increase the array aperture, which is essential for improving performance in terms of both the direction of arrival estimation and adaptive beamforming. This paper presents two new NLAs, namely interleaved coprime array (ICA) and augmented interleaved array (AIA). The ICA consists of two uniform linear subarrays, whose inter-element spacings are coprime integers. The ICA can obtain more uniform degrees of freedom (uDOF), while maintaining weak mutual coupling effects, because its configuration includes only minority sensors interleaved. The optimal configuration of the ICA is deduced using the principle of maximizing the uDOF. Moreover, the AIA geometry is obtained by removing a redundant element in the ICA and appropriately designing the location of the additional element. For a fixed total number of sensors, the AIA can gain more uDOF and DOF than the ICA, while exhibiting lower mutual coupling effects. The closed-form expressions for the properties of the proposed array structures involving an arbitrary number of sensors are also derived. Numerical simulations are performed to verify the superiority of the proposed arrays over other sparse arrays. [ABSTRACT FROM AUTHOR]

In this letter, a localization algorithm for mixed‐field sources based on fourth‐order cumulant matrix rank reduction is proposed. First, a cumulant matrix is constructed, and a spectral peak search function associated with the direction‐of‐arrival (DOA) of the sources only is constructed using the rank reduction principle to achieve DOA estimation. Then the range estimation is also obtained by a spectral peak search. Compared to existing algorithms, the algorithm is able to utilize all the elements of the cumulant matrix and has a higher accuracy and degrees‐of‐freedom. The simulation results verify the excellence of the algorithm. [ABSTRACT FROM AUTHOR]

Direction‐of‐arrival (DOA) estimation methods for wideband linear frequency modulated (LFM) signals based on fractional Fourier transform (FRFT) typically use the single snapshot vector in the fractional Fourier (FRF) domain. However, the low‐rank problem of the second‐order statistics in the single snapshot vector can decrease the DOA estimation resolution and cause issues in DOA estimation for coherent sources. In order to address these problems, a weighted l1‐norm method based on FRFT is proposed. The proposed method utilises the energy aggregation property of FRFT for LFM signals. This allows for obtaining a single snapshot vector in the FRF domain. Subsequently, a sparse representation DOA estimation model is established by taking advantage of the sparsity of the target distribution in the spatial domain. The DOA estimation is then obtained by minimising the l1‐norm. To further enhance the DOA estimation performance, we construct a matrix by rearranging the elements of the eigenvectors corresponding to the nonzero eigenvalue of the covariance matrix in the FRF domain. The rank of this matrix is equal to the number of sources, ensuring the orthogonality of the subspace obtained by the reconstructed matrix. Finally, a weighted matrix is constructed by exploiting the subspace orthogonality principle to adjust the sparsity penalty of the l1 constraint model. Simulation results demonstrate that our method is capable of achieving high angular resolution and accuracy even at low SNR and can process coherent signals directly. [ABSTRACT FROM AUTHOR]

Polarimetric Airborne Scientific INstrument, mark 2 (PASIN2) is a 150 MHz coherent pulsed radar with the purpose of deep ice sounding for bedrock, subglacial channels and ice‐water interface detection in Antarctica. It is designed and operated by the British Antarctic Survey from 2014. With multiple antennas, oriented along and across‐track, for transmission and reception, it enables polarimetric 3D estimation of the ice base with a single pass, reducing the gridding density of the survey paths. The off‐line data processing stream consists of channel calibration; 2D synthetic aperture radar (SAR) imaging based on back‐projection, for along‐track and range dimensions; and finally, a direction of arrival estimation (DoA) of the remaining across‐track angle, by modifying the non‐linear MUSIC algorithm. Calibration flights, during the Antarctic Summer campaigns in 16/17 and 19/20 seasons, assessed and validated the instrument and processing performances. Imaging flights over ice streams and ice shelves close to grounding lines demonstrate the 3D sensing capabilities. By resolving directional ambiguities and accounting for reflector across‐track location, the true ice thickness and bed elevation are obtained, thereby removing the error of the usual assumption of vertical DoA, that greatly influence the output of flow models of ice dynamics. [ABSTRACT FROM AUTHOR]

In this paper, a modified high-efficiency Convolutional Neural Network (CNN) with a novel Supervised Contrastive Learning (SCL) approach is introduced to estimate direction-of-arrival (DOA) of multiple targets in low signal-to-noise ratio (SNR) regimes with uniform linear arrays (ULA). The model is trained using an on-grid setting, and thus the problem is modeled as a multi-label classification task. Simulation results demonstrate the robustness of the proposed approach in scenarios with low SNR and a small number of snapshots. Notably, the method exhibits strong capability in detecting the number of sources while estimating their DOAs. Furthermore, compared to traditional CNN methods, our refined efficient CNN significantly reduces the number of parameters by a factor of sixteen while still achieving comparable results. The effectiveness of the proposed method is analyzed through the visualization of latent space and through the advanced theory of feature learning. [ABSTRACT FROM AUTHOR]

This paper presents a tracking algorithm for joint estimation of direction of arrival (DOA) and polarization parameters, which exhibit dynamic behavior due to the movement of signal source carriers. The proposed algorithm addresses the challenge of real-time estimation in multi-target scenarios with an unknown number. This algorithm is built upon the Multi-target Multi-Bernoulli (MeMBer) filter algorithm, which makes use of a sensor array called Circular Orthogonal Double-Dipole (CODD). The algorithm begins by constructing a Minimum Description Length (MDL) principle, taking advantage of the characteristics of the polarization-sensitive array. This allows for adaptive estimation of the number of signal sources and facilitates the separation of the noise subspace. Subsequently, the joint parameter Multiple Signal Classification (MUSIC) spatial spectrum function is employed as the pseudo-likelihood function, overcoming the limitations imposed by unknown prior information constraints. To approximate the posterior distribution of MeMBer filters, Sequential Monte Carlo (SMC) method is utilized. The simulation results demonstrate that the proposed algorithm achieves excellent tracking accuracy in joint DOA-polarization parameter estimation, whether in scenarios with known or unknown numbers of signal sources. Moreover, the algorithm demonstrates robust tracking convergence even under low Signal-to-Noise Ratio (SNR) conditions. [ABSTRACT FROM AUTHOR]

Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests. [ABSTRACT FROM AUTHOR]

Uncertainty quantification (UQ) of deep learning (DL)-based acoustic estimation methods is useful for establishing confidence in the predictions. This is crucial to enable the real-world applicability of DL-based systems for acoustic tasks. Specifically, it is proposed to use conformal prediction (CP) for UQ in direction-of-arrival (DOA) estimation. CP is a statistically rigorous method to provide confidence intervals for an estimated quantity without making distributional assumptions. With CP, confidence intervals are computed via quantiles of user-defined scores. This easy-to-use method can be applied to any trained classification/regression model if an appropriate score function is chosen. The proposed approach shows the potential to enhance the real-time applicability of DL methods for DOA estimation. The advantages of CP are illustrated for different DL methods for DOA estimation in the presence of commonly occurring environmental uncertainty. Codes are available online (https://github.com/NoiseLabUCSD/ConformalPrediction). [ABSTRACT FROM AUTHOR]

The estimation of the direction of electromagnetic (EM) waves from a radio source using electrically short antennas is one of the challenging problems in the field of radio astronomy. In this paper we have developed an algorithm which performs better in direction and polarization estimations than the existing algorithms. Our proposed algorithm Snapshot Averaged Matrix Pencil Method (SAM) is a modification to the existing Matrix Pencil Method (MPM) based Direction of Arrival (DoA) algorithm. In general, MPM estimates DoA of the incoherent EM waves in the spectra using unitary transformations and least square method (LSM). Our proposed SAM modification is made in context to the proposed Space Electric and Magnetic Sensor (SEAMS) mission to study the radio universe below 16 MHz. SAM introduces a snapshot averaging method to improve the incoherent frequency estimation thereby improving the accuracy of DoA estimation. It can also detect polarization to differentiate between Right Hand Circular Polarlization (RHCP), Right Hand Elliptical Polarlization (RHEP), Left Hand Circular Polarlization (LHCP), Left Hand Elliptical Polarlization (LHEP) and Linear Polarlization (LP). This paper discusses the formalism of SAM and shows the initial results of a scaled version of a DoA experiment at a resonant frequency of ∼ 72 MHz. [ABSTRACT FROM AUTHOR]

This paper presents a novel measurement method and briefly discusses the basic properties of direction of arrival (DoA) measurement in a multiple-input multiple-output (MIMO) radar system by using orthogonality with time-division multiplexing (TDM), where only one transmitting antenna element is active in each time slot. This paper presents the mathematical model of the TDM-MIMO radar operating at 10 GHz, transmitting a string of pulses, the method of transmitting and receiving the signal, and the method of measuring the angle of arrival of the signal based on the use of the Capon algorithm and its modifications. Finally, the correctness of the theory, algorithm and method of measuring the direction of arrival of the signal is verified by experimental simulation. The work discussed in this paper is of great significance to practically demonstrate the capabilities of the TDM MIMO radar sensor in practical implementations like reconnaissance and electronic warfare systems. [ABSTRACT FROM AUTHOR]

The adaptive beamforming algorithm can realize interference suppression and navigation signal enhancement, and has been widely used. However, achieving high-precision real-time estimation of the direction of arrival (DOA) parameters of navigation signals in strong-interference scenarios with low complexity is still a challenge. In this paper, a blind adaptive beamforming algorithm for a Global Navigation Satellite System (GNSS) array receiver based on direction lock loop is proposed without using the prior information of the DOA parameter. The direction lock loop is used for DOA tracking and estimation after interference suppression, which uses the spatial correlation of the array beam pattern to construct a closed direction-tracking loop. The DOA estimation value is adjusted in real time based on the loop errors. A blind beamformer is constructed using the DOA estimation results to provide gain by forming a beam in the satellite direction. This method improves the accuracy and dynamic adaptability of DOA estimation while significantly reducing the computational complexity. The theoretical analysis and simulation results verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Electromagnetic vector sensor (EMVS) arrays bring an epochal opportunity for direction finding, as they enable the estimation of two-dimensional direction of arrival (2D-DOA) and polarization characteristics. In this paper, we revisit the 2D-DOA estimation problem in an EMVS rectangle array under multipath propagation. An improved subspace estimator is proposed, which addresses the rank-deficit problem through matrix arrangement, and the 2D-DOA and polarization parameters are estimated via combining the normalized vector cross-product with the least squares method. Our proposed method is suitable for a single snapshot scenario and offers superior accuracy compared to existing methods. To validate its effectiveness, several numerical simulations have been designed and conducted. [ABSTRACT FROM AUTHOR]

The performance of traditional direction of arrival (DOA) estimation methods always deteriorates at a low signal-to-noise ratio (SNR) or without sufficient observations. This paper investigates the Bayesian DOA estimation problem aided by the prior knowledge from the target tracker. The Bayesian Cramér–Rao lower bounds (CRLB) and the expected CRLB are first derived to evaluate the theoretical performance of Bayesian DOA estimation. Based on the maximum a posterior (MAP) estimator in the Bayesian framework, two methods are proposed. One is a two-step grid search method for a single target DOA case. The other is a gradient-based iterative solution for multiple targets DOA case, which extends the traditional Newton method by incorporating the prior knowledge. We also propose a minimum mean square error (MMSE) estimator using a Monte Carlo method, which requires trading off accuracy against computational complexity. By comparing with the maximum likelihood (ML) estimators and the MUSIC algorithm, the proposed three Bayesian estimators improve the DOA estimation performance in low SNR or with limited snapshots. Moreover, the performance is not affected by the correlation between sources. [ABSTRACT FROM AUTHOR]

The canonical polyadic decomposition (CPD) of higher-order tensors, a.k.a. PARAFAC, has shown excellent performance in two-dimensional direction of arrival (DOA) estimation using the acoustic vector sensor array (AVSA). However, most existing studies pay little attention to the manifold matrix structure of the AVSA during the CPD and are designed for uncorrelated sources. This paper presents a constrained CPD-based algorithm for DOA estimation using a uniform linear AVSA, whose manifold matrix is highly structured. Specifically, the manifold matrix equals to the Khatri-Rao product of a Vandermonde matrix and a proportional column-norm matrix. We show that DOA estimation accuracy is further improved by incorporating the prior structured information. Besides, we also extend the Toeplitz decorrelation technique to the AVSA to handle possibly correlated sources. The algorithm does not require iteration or peak searching and thus is computationally effective. Numerical simulations verify the effectiveness and superior performance of the algorithm. [ABSTRACT FROM AUTHOR]

For improving performance of the towed array sonar during the manoeuvring period, a processing framework is proposed based on joint estimation of direction of arrival (DOA) and the array shape. The sparse Bayesian learning (SBL) algorithm is utilised to accurately estimate the DOAs of interesting targets. Meanwhile, the towed array shape is modelled as a parabola array, and the array element positions are estimated using the bow of the parabola. Then, an approximate posterior covariance is implemented to the SBL for a fast converging speed required by practical applications. Besides, the co‐prime array structure is considered for the uniform linear array to further reduce the computational load. The numerical simulations have verified the effectiveness of the fast converging SBL method. MAPEX2000 experimental data processing results have shown that the proposed framework performs well in detection of weak targets during slow turns. [ABSTRACT FROM AUTHOR]

Direction-of-arrival estimation is difficult for signals spatially undersampled by more than half the wavelength. Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018–3029] offers an alternative approach to avoid such spatial aliasing by using multifrequency signals and processing them at a lower frequency, the difference-frequency. As with the conventional beamforming method, lowering the processing frequency sacrifices spatial resolution due to a beam broadening. Thus, unconventional beamforming is detrimental to the ability to distinguish between closely spaced targets. To overcome spatial resolution deterioration, we propose a simple yet effective method by formulating the frequency-difference beamforming as a sparse signal reconstruction problem. Similar to compressive beamforming, the improvement (compressive frequency-difference beamforming) promotes sparse nonzero elements to obtain a sharp estimate of the spatial direction-of-arrival spectrum. Analysis of the resolution limit demonstrates that the proposed method outperforms the conventional frequency-difference beamforming in terms of separation if the signal-to-noise ratio exceeds 4 dB. Ocean data from the FAF06 experiment support the validity. [ABSTRACT FROM AUTHOR]

In this letter, a computationally efficient multiple signal classification (MUSIC)‐based evolutionary algorithm for angle estimation of bistatic multiple‐input multiple‐output (MIMO) radar is proposed. The existing MUSIC algorithms require a computationally cumbersome two‐dimensional (2D) peak searching and the performance is highly related to the grid that set, which leads to a conflict between the computational efficiency and estimation performance. To address this difficulty, a multimodal quantum‐inspired salp swarm algorithm, integrating kmeans clustering technique, is proposed to substitute the 2D peak searching to obtain multiple maxima of the MUSIC algorithm. The resulting computationally efficient algorithm obviously reduces the computational complexity of the MUSIC algorithm, avoids grid errors, and further exploits the potential of the MUSIC algorithm. Numerical simulations in various scenarios are carried out to verify the superiority of the method. [ABSTRACT FROM AUTHOR]