Direction Of Arrival Estimation Research Articles

Direction‐of‐Arrival Estimation of Electromagnetic Pulse Based on Energy Distribution

This paper investigates the direction‐of‐arrival (DOA) estimation of electromagnetic pulse (EMP) sources in modern radar system and proposes a novel EMP DOA estimation method. The method is based on energy distribution and improves the low accuracy and high computational complexity of the conventional estimation method. According to the characteristics of the EMP signal, the frequency point where 90% of the signal energy is concentrated is considered as the critical frequency point. Before this point, differently sized frequency sub‐blocks are determined depending on the energy. After the critical frequency point, identically sized frequency sub‐blocks are chosen at equal frequency intervals for processing. The proposed method is compared with the representative EMP DOA estimation methods. Simulation experiments are carried out to validate the effectiveness of the proposed method. The results illustrate that the computational complexity is significantly reduced while the accuracy is improved compared to the conventional method.

4D High-Resolution Imagery of Point Clouds for Automotive mmWave Radar

In the community of automotive millimeter wave radar, the recently developed concept of four-dimensional (4D) radar can provide high-resolution point clouds image with enhanced imaging performance. Currently, the density of point clouds for single-frame image is usually too sparse to satisfy the demands of target classification and recognition due to the limitation of Doppler and angle resolutions. To address the aforementioned issues, a novel algorithm is proposed for 4D high-resolution imagery generation of point clouds with extremely high Doppler and angle resolutions in this paper. For high Doppler resolution with high-dynamic, a novel velocity ambiguity resolution algorithm is proposed using a dual pulse repetition frequency (dual-PRF) waveform design embedded in an innovative time-division multiplexing & Doppler-division multiplexing MIMO (TDM-DDM-MIMO) framework. Meanwhile, an attractive complex-valued deep convolutional network (CV-DCN) of super-resolution direction-of-arrival (DOA) estimation is proposed only using single-frame data. To be specific, a spatial smoothing operator on array data is applied as input of the network, and a CV-DCN is designed to learn the transformation of the spatial spectrum from the end-to-end to effectively protect the spectrum extraction. Furthermore, experimental analysis is performed to confirm the effectiveness of the proposed super-resolution DOA estimation algorithm. Finally, the 4D high-resolution imagery of point clouds is obtained by experiments in the parking lot.

Parallel Complementary Virtual Arrays Algorithm for Direction of Arrival (DOA) Estimation

This Paper discusses the challenges faced by previous method 2D Direction of Arrival (DOA) systems, such as low degrees of freedom, poor resolution, and significant estimation errors in scenarios with small snapshots. In response to these issues, the present method proposes a low-complexity 2D Direction of Arrival (DOA) estimation algorithm based on a parallel complementary virtual array.
 The algorithm utilizes two mutually parallel complementary linear arrays to generate a virtual array, addressing the limitations of traditional parallel arrays. It constructs an extended matrix with enhanced 2D angular degrees of freedom using covariance and cross-covariance matrices. The final step involves obtaining automatic matching 2D angle estimates through Singular Value Decomposition (SVD) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT).
 In comparison to traditional 2D DOA estimation methods, the proposed algorithm better exploits the information from the array's received data. It can identify more incoming signals, offering high resolution without the need for 2D linear search or angle parameter matching. Importantly, it demonstrates effective estimation even in scenarios with low Signal-to-Noise Ratio (SNR) and small snapshots. Experimental simulation results validate the effectiveness and reliability of the proposed algorithm.

DOA estimation of coherent signals in underdetermined problems using sparse-based Toeplitz covariance reconstruction

Direction-Of-Arrival (DOA) estimation in environments with coherent sources is a challenging problem, when the number of narrowband sources is more than elements and current coherent algorithms cannot accurately overcome such underdetermined problems. In this paper, we propose the Sparse-based Toeplitz Covariance Reconstruction (STCR) algorithm, which obtains a hole-free extended-aperture array with increased Degrees of Freedom (DOF) by exploiting a minimum redundancy array. This method provides superiority in estimating coherent sources by Toeplitz covariance matrix reconstruction. Also, using a Sparse Signal Representation (SSR) framework makes the DOA estimator stronger in source detection and robust to the noise power. Numerical results show the effectiveness of the proposed method even at low SNRs for over- and underdetermined DOA estimators compared to well-known methods. Also, it has high accuracy in DOA estimation of closely-located coherent sources using a small number of snapshots.

Direction-of-Arrival Estimation for a Random Sparse Linear Array Based on a Graph Neural Network.

This article proposes a direction-of-arrival (DOA) estimation algorithm for a random sparse linear array based on a novel graph neural network (GNN). Unlike convolutional layers and fully connected layers, which do not interact well with information between different antennas, the GNN model can adapt to the goniometry problem of non-uniform random sparse linear arrays without any prior information by applying neighbor nodes' aggregation and update operations. This helps the model in learning signal features under complex environmental conditions. We train the model in an end-to-end way to reduce the complexity of the network. Experiments are conducted on the uniform and sparse linear arrays for various signal-to-noise ratio (SNR) and numbers of snapshots for comparison. We prove that the GNN model has superior angle estimation performance on arrays with large sparsity that cannot be used by traditional algorithms and surpasses existing deep learning models based on convolutional or fully connected structures. The proposed algorithm shows excellent DOA estimation performance under the complex conditions of limited snapshots, low signal-to-noise ratio, and large array sparsity as well. In addition, the algorithm has a low time calculation cost and is suitable for scenarios that require low latency.

Antenna Pattern Calibration Method for Phased Array of High-Frequency Surface Wave Radar Based on First-Order Sea Clutter

The problem of accurate source localization has been an area of focus in high-frequency surface wave radar (HFSWR) applications. However, antenna pattern distortion (APD) decreases the direction-of-arrival (DOA) estimation performance of the multiple signal classification (MUSIC) algorithm. Up to now, limited studies have been conducted on the calibration of antenna pattern distortion for phased arrays in HFSWR. In this paper, we first analyze the effect of APD on the performance of the MUSIC algorithm through estimation of accuracy and angular resolution. We demonstrate that using the actual pattern (or say APD) can improve DOA estimation performance. Based on this proposition, we propose a novel iterative calibration method that employs the first-order sea clutter data and can jointly estimate DOA and APD in an iterative way. To obtain available calibration points, we introduce the extraction methods of the first-order sea clutter spectrum and single-DOA spectrum points. Meanwhile, in each iteration, the Beamspace MUSIC algorithm and artificial hummingbird algorithm (AHA) are utilized to estimate the DOA and APD, respectively. Numerical results reveal a good coincidence between the actual pattern and the estimated APD. We also apply this method to process the experimental data of HFSWR. We obtain the APD vector of the real phased array and improve the direction-finding performance of several real ship targets using this vector. Both numerical and experimental results prove the correctness of our proposed calibration method.

Robust cardinalized probability hypothesis density filter based underwater multi-target direction-of-arrival tracking with uncertain measurement noise

Direction-of-arrival (DOA) tracking of underwater targets is an important research topic in sonar signal processing. Considering the underwater DOA tracking is a typical multi-target scenario with uncertain measurement noise caused by unknown underwater environment, a robust underwater multi-target DOA tracking method with uncertain measurement noise is proposed by implementing a spatial matrix filtering (SMF) technique in the framework of the cardinalized probability hypothesis density (CPHD) filter. Firstly, the kinematic model of underwater targets and the measurement model based on the received signal of the hydrophone array (array signal) are established. Thus, the multi-target DOA tracking algorithm is derived by using the CPHD filter based on the established model. Moreover, to avoid the effect of the uncertain measurement noise, the SMF technique is implemented to process the array signal to extract the signal in the bearing angle of the target. Then, the output of the SMF is substituted into the CPHD filter. In this manner, the robust underwater multi-target DOA tracking method for uncertain measurement noise scenario is proposed. Finally, comprehensive simulations and experimental data processing are performed to prove the robustness of the proposed method in the scenario of multi-target DOA tracking with uncertain measurement noise. Compared with the existing DOA estimation and DOA tracking methods, the proposed methods significantly improve the robustness and the precision of the DOA of the underwater target.

Multi-user communications for line-of-sight large intelligent surface systems

In this paper, we propose a new interference-suppression beamformer design and a Direction-of-Arrival (DoA) estimation method for Line-of-Sight (LoS) multi-user communication systems with circular Large Intelligent Surfaces (LISs). This symmetrical circular-shaped LIS allows signals defined on it to be formed by combining Fourier and Bessel series. The Fourier harmonics are orthogonal along the rotational direction and the Bessel functions constituting the Bessel series are orthogonal along the radial direction. Synthesizing basis functions from these two series results in the proposed interference-suppression beamformer, with their coefficients designed to cancel inter-user interference. Also by exploiting signal structure of a circular LIS communicating with Mobile Stations (MSs), we devise a DoA estimation method to obtain directional information of incoming signals. Under LoS channel, the DoA corresponds to elevation and Azimuth angles of MSs relative to the LIS. This method is numerically demonstrated to have promising performance with high-frequency carriers.

Fast and accurate wideband sparse spatial spectrum estimation in an underwater strong interference environment.

Wideband sparse spatial spectrum estimation is an important direction-of-arrival (DOA) estimation method that can obtain a high resolution with few snapshots and a low signal-to-noise ratio. However, in an underwater strong interference environment, the accuracy of DOA estimation may be seriously affected, and even the weak targets could be completely masked. In this paper, we propose a fast matrix filter design method based on truncated nuclear norm regularization to attenuate strong interferences while passing weak targets. The matrix filter operator and the exact covariance matrix after filtering can be obtained simultaneously by solving a convex optimization problem that contains the output power term and non-Toeplitz error propagation control term. Then the modified sparse spectrum fitting algorithm based on the matrix filter is used to estimate spatial spectrum over closely spaced wideband signals. Compared with existing methods, the proposed method achieves higher DOA estimation accuracy and lower computational time for matrix filter design. Meanwhile, the estimation accuracy of the proposed method is verified with the experimental results.

Joint Polarization and DOA Estimation Based on Improved Maximum Likelihood Estimator and Performance Analysis for Conformal Array

The conformal array can make full use of the aperture, save space, meet the requirements of aerodynamics, and is sensitive to polarization information. It has broad application prospects in military, aerospace, and communication fields. The joint polarization and direction-of-arrival (DOA) estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array. To solve these problems, this paper establishes the wave field signal model of the conformal array. Then, for the case of a single target, the cost function of the maximum likelihood (ML) estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms. On this basis, rapid parameter estimation is achieved with the idea of manifold separation technology (MST). Compared with the modified variable projection (MVP) algorithm, it reduces the computational complexity and improves the parameter estimation performance. Meanwhile, the MST is used to solve the partial derivative of the steering vector. Then, the theoretical performance of ML, the multiple signal classification (MUSIC) estimator and Cramer-Rao bound (CRB) based on the conformal array are derived respectively, which provides theoretical foundation for the engineering application of the conformal array. Finally, the simulation experiment verifies the effectiveness of the proposed method.

Direction of Arrival Estimation With Gain-Phase Uncertainties in Unknown Nonuniform Noise

This paper considers the problem of direction-of-arrival (DOA) estimation for narrowband source signals under the coexistence of gain-phase uncertainties and nonuniform noise. Firstly, by exploiting the low-rank property of the covariance of signal components, and the diagonal property of noise covariance, an optimization problem with low-rank constraints is formulated to estimate the nonuniform noise covariance matrix, which is then solved efficiently by the alternating direction method of multipliers (ADMM). Secondly, a linear transformation operator is employed to construct a rank reduction (RARE) estimator, and subsequently an initial DOA and gain-phase uncertainties are obtained via one-dimensional (1-D) spectral search. With initial estimates, an augmented DOA estimation is finally achieved by constructing a weighted and structured sparse total least-squares (WSS-TLS) optimization problem, which is solved using the block coordinate descent algorithm. Simulation results show the superior performance of the proposed method, and it achieves better tradeoff between computational complexity and performance, compared to existing methods.

High-resolution DOA estimation in the hydrophone array shape with uncertainty based on dynamic compressed sensing

Compressed sensing (CS) technology is a popular method for the direction of arrival (DOA) estimation of underwater acoustic radiation noise due to its high resolution. However, in practical applications such as buried arrays and other arrays, uncertainty in the hydrophone array shape can lead to model mismatch which significantly reduces DOA estimation accuracy. This paper focuses on high-resolution wideband DOA estimation in the radiated noise from underwater targets of interest using dynamic compressed sensing. The study introduces phase error into the signal model to simulate the model mismatch, and improves DOA estimation accuracy by jointly estimating both the DOA and phase error. Simulation results demonstrate that the proposed algorithm is effective in improving the accuracy of DOA estimation.

Structural-Missing Tensor Completion for Robust DOA Estimation with Sensor Failure

Array sensor failure poses a serious challenge to robust direction-of-arrival (DOA) estimation in complicated environments. Although existing matrix completion methods can successfully recover the damaged signals of an impaired sensor array, they cannot preserve the multi-way signal characteristics as the dimension of arrays expands. In this paper, we propose a structural-missing tensor completion algorithm for robust DOA estimation with uniform rectangular array (URA), which exhibits a high robustness to non-ideal sensor failure conditions. Specifically, the signals received at the impaired URA are represented as a three-dimensional incomplete tensor, which contains whole fibers or slices of missing elements. Due to this structural-missing pattern, the conventional low-rank tensor completion becomes ineffective. To resolve this issue, a spatio-temporal dimension augmentation method is developed to transform the structural-missing tensor signal into a six-dimensional Hankel tensor with dispersed missing elements. The augmented Hankel tensor can then be completed with a low-rank regularization by solving a Hankel tensor nuclear norm minimization problem. As such, the inverse Hankelization on the completed Hankel tensor recovers the tensor signal of an unimpaired URA. Accordingly, a completed covariance tensor can be derived and decomposed for robust DOA estimation. Simulation results verify the effectiveness of the proposed algorithm.

Robust Sparse Bayesian Two-Dimensional Direction-of-Arrival Estimation with Gain-Phase Errors

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.

Coherent DOA Estimation Algorithm with Co-Prime Arrays for Low SNR Signals

The Direction of Arrival (DOA) estimation of coherent signals in co-prime arrays has become a popular research topic. However, traditional spatial smoothing and subspace algorithms fail to perform well under low signal-to-noise ratio (SNR) and small snapshots. To address this issue, we have introduced an Enhanced Spatial Smoothing (ESS) algorithm that utilizes a space-time correlation matrix for de-noising and decoherence. Finally, an Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is used for DOA estimation. In comparison to other decoherence methods, when the SNR is −8 dB and the number of snapshots is 150, the mean square error (MSE) of the proposed algorithm approaches the Cramér–Rao bound (CRB), the probability of resolution (PoR) can reach over 88%, and, when the angular resolution is greater than 4°, the estimation accuracy can reach over 90%.

Direction of Arrival Estimation with Nested Arrays in Presence of Impulsive Noise: A Correlation Entropy-Based Infinite Norm Strategy

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.

Polarization Direction of Arrival Estimation for Vector Array of Unmanned Aerial Vehicle Swarm

Aiming at the problem of the excessive error of direction of arrival (DOA) estimation caused by the position disturbance of a UAV swarm during flight, a robust polarization-DOA estimation method based on sparse Bayesian learning (SBL) is proposed. First, the algorithm decomposes the covariance matrix of the received data of the UAV swarm vector array and then constructs the determination matrix of the UAV position coordinates by exploiting the orthogonality of the eigenvalues and eigenvectors. Then, the optimal solution of the semi-positive definite programming (SDP) problem is solved using the constrained global least square method, and the exact self-positioning coordinates of UAVs are obtained. Second, we construct a spatially discrete grid to model the received data of the UAV group vector array. The SBL theory is then applied to obtain the posterior probability distribution of the sparse signal matrix. The sparsity of the signal matrix is controlled with a hyperparameter, and the estimation of the DOA is conducted using a fixed-point iteration to obtain the maximum posterior estimate of the signal matrix. Finally, according to the estimated DOA, the polarization parameter is obtained from the constructed objective function of the polarization parameter estimation. The simulation results show that the proposed algorithm achieves higher accuracy and robustness than the traditional 2D DOA estimation algorithm in the direction-finding system for UAV swarm vector arrays.

Deep Unfolding Sparse Bayesian Learning Network for Off-Grid DOA Estimation with Nested Array

Recently, deep unfolding networks have been widely used in direction of arrival (DOA) estimation because of their improved estimation accuracy and reduced computational cost. However, few have considered the existence of a nested array (NA) with off-grid DOA estimation. In this study, we present a deep sparse Bayesian learning (DSBL) network to solve this problem. We first establish the signal model for off-grid DOA with NA. Then, we transform the array output into a real domain for neural networks. Finally, we construct and train the DSBL network to determine the on-grid spatial spectrum and off-grid value, where the loss function is calculated using reconstruction error and the sparsity of network output, and the layers correspond to the steps of the sparse Bayesian learning algorithm. We demonstrate that the DSBL network can achieve better generalization ability without training labels and large-scale training data. The simulation results validate the effectiveness of the DSBL network when compared with those of existing methods.

UNet-rootMUSIC: A high accuracy direction of arrival estimation method under array imperfection

In the practical direction-finding systems, the accuracy and resolution of the direction of arrival (DOA) estimation are affected not only by the Gaussian noise and array size but also by hardware configuration imperfections, such as errors in element manufacturing and mounting. These impairments cause phase and amplitude errors in estimating the DOA of signal sources. To address this issue, this paper proposes to combine a U-shape deep neural network (UNet) with the multiple signal classification via the root of the polynomial (rootMUSIC) algorithm (so-called UNet-rootMUSIC) to improve the DOA estimation accuracy. In this approach, the UNet model plays a role in converting a covariance matrix of received signals containing phase and gain errors into a nearly perfect one of the ideal antenna array. The rootMUSIC algorithm is then employed to estimate the signal DOA based on the converted covariance matrix. The DOA estimation performance of the uniform linear array of eight elements with an inter-element distance of λ/2 is analyzed through experimental simulations. The simulation results demonstrate that our method can significantly reduce the root mean square error of DOA estimation compared to the conventional MUSIC, rootMUSIC, ESPRIT methods and two deep neural network-based angular classification methods.

A Gridless DOA Estimation Method for Sparse Sensor Array

Direction-of-arrival (DOA) estimation is still a pivotal research direction in array signal processing. Traditional algorithms based on the signal subspace and compressed sensing theory usually suffer from off-grid and computational complexity. Deep-learning-based methods usually face difficulty in obtaining labeled datasets. With the development of array technology, sparse sensor arrays can effectively reduce the number of sensors, which in turn reduces the complexity of the hardware. Therefore, effective DOA estimation algorithms for sparse sensor arrays need to be further investigated. An unsupervised deep learning method is proposed here to address the above issues. A training model was built based on the residual network structure. The DOA estimation was implemented using Vandermonde decomposition. Finally, the experimental findings confirmed the efficacy of the proposed algorithms presented in this article.