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.

High-Precision DOA Estimation Based on Synthetic Aperture and Sparse Reconstruction

The direction-of-arrival (DOA) estimation is predominantly influenced by the antenna's aperture size. However, space constraints on flight platforms often necessitate the use of antennas with smaller apertures and fewer array elements. This inevitably imposes limitations on the DOA estimation's resolution and degrees of freedom. To address these precision constraints, we introduce an accurate DOA estimation method based on spatial synthetic aperture model. This method adopts a two-stage strategy to ensure both efficiency and precision in DOA estimation. Initially, the orthogonal matching pursuit (OMP) reconstruction algorithm processes the original aperture data, providing a rough estimate of target angles that guides the aircraft's flight direction. Subsequently, the early estimations merge with the aircraft's motion space samples, forming equivalent spatially synthesized array samples. The refined angle estimation then employs the OMP-RELAX algorithm. Moreover, with the off-grid issue in mind, we devise an estimation method integrating Bayesian parameter estimation with dictionary sequence refinement. The proposed technique harnesses the spatial synthetic aperture for pinpoint estimation, effectively addressing the challenges of atomic orthogonality and angular off-grid on estimation accuracy. Importantly, the efficiency of deploying sparse reconstruction for angle estimation is bolstered by our phased strategy, eliminating the necessity for fine grid analysis across the entire observation scene. Moreover, the poor estimation accuracy caused by coherent source targets and angular-flickering targets is improved by sparse reconstruction. Through simulation and experiment, we affirm the proposed method's efficacy in angle estimation. The results indicate that target angle estimation errors are limited to within 1°. Furthermore, we assess the impact of variables such as target state, heading angle, spatial sampling points, and target distance on the estimation accuracy of our method, showcasing its resilience and adaptability.

Centroid Optimization of DNN Classification in DOA Estimation for UAV

Classifications based on deep learning have been widely applied in the estimation of the direction of arrival (DOA) of signal. Due to the limited number of classes, the classification of DOA cannot satisfy the required prediction accuracy of signals from random azimuth in real applications. This paper presents a Centroid Optimization of deep neural network classification (CO-DNNC) to improve the estimation accuracy of DOA. CO-DNNC includes signal preprocessing, classification network, and Centroid Optimization. The DNN classification network adopts a convolutional neural network, including convolutional layers and fully connected layers. The Centroid Optimization takes the classified labels as the coordinates and calculates the azimuth of received signal according to the probabilities of the Softmax output. The experimental results show that CO-DNNC is capable of acquiring precise and accurate estimation of DOA, especially in the cases of low SNRs. In addition, CO-DNNC requires lower numbers of classes under the same condition of prediction accuracy and SNR, which reduces the complexity of the DNN network and saves training and processing time.

Spectral Domain Sparse Representation for DOA Estimation of Signals with Large Dynamic Range

Recently, we proposed a Spectral Domain Sparse Representation (SDSR) approach for the direction-of-arrival estimation of signals incident to an antenna array. In the approach, sparse representation is applied to the conventional Bartlett spectra obtained from snapshots of the signals received by the antenna array to increase the direction-of-arrival (DOA) estimation resolution and accuracy. The conventional Bartlett spectra has limited dynamic range, meaning that one may not be able to identify the presence of weak signals in the presence of strong signals. This is because, in the conventional Bartlett spectra, uniform weighting (window) is applied to signals received by various antenna elements. Apodization can be used in the generation of Bartlett spectra to increase the dynamic range of the spectra. In Apodization, more than one window function is used to generate different portions of the spectra. In this paper, we extend the SDSR approach to include Bartlett spectra obtained with Apodization and to evaluate the performance of the extended SDSR approach. We compare its performance with a two-step SDSR approach and with an approach where Bartlett spectra is obtained using a low sidelobe window function. We show that an Apodization Bartlett-based SDSR approach leads to better performance with just single-step processing.

A-CRNN-Based Method for Coherent DOA Estimation with Unknown Source Number

Estimating directions of arrival (DOA) without knowledge of the source number is regarded as a challenging task, particularly when coherence among sources exists. Researchers have trained deep learning (DL)-based models to attack the problem of DOA estimation. However, existing DL-based methods for coherent sources do not adapt to variable source numbers or require signal independence. Herein, we put forward a new framework combining parallel DOA estimators with Toeplitz matrix reconstruction to address the problem. Each estimator is constructed by connecting a multi-label classifier to a spatial filter, which is based on convolutional-recurrent neural networks. Spatial filters divide the angle domain into several sectors, so that the following classifiers can extract the arrival directions. Assisted with Toeplitz-based method for source-number determination, pseudo or missed angles classified by the estimators will be reduced. Then, the spatial spectrum can be more accurately recovered. In addition, the proposed method is data-driven, so it is naturally immune to signal coherence. Simulation results demonstrate the predominance of the proposed method and show that the trained model is robust to imperfect circumstances such as limited snapshots, colored Gaussian noise, and array imperfections.

Sparsity-Aware Noise Subspace Fitting for DOA Estimation

We propose a sparsity-aware noise subspace fitting (SANSF) algorithm for direction-of-arrival (DOA) estimation using an array of sensors. The proposed SANSF algorithm is developed from the optimally weighted noise subspace fitting criterion. Our formulation leads to a convex linearly constrained quadratic programming (LCQP) problem that enjoys global convergence without the need of accurate initialization and can be easily solved by existing LCQP solvers. Combining the weighted quadratic objective function, the ℓ1 norm, and the non-negative constraints, the proposed SANSF algorithm can enhance the sparsity of the solution. Numerical results based on simulations, using real measured ultrasonic, and radar data, show that, compared to existing sparsity-aware methods, the proposed SANSF can provide enhanced resolution with a lower computational burden.

A Novel Direction-of-Arrival Estimation via Phase Retrieval with Unknown Sensor Gain-and-Phase Errors

In signal array processing, high-resolution direction-of-arrival (DOA) estimation algorithms work well on the assumption that the system models are perfect. However, in practicality, there are imperfect system models in which sensor gain-and-phase errors are considered. In this paper, we propose a novel framework that can effectively solve direction-of-arrival estimation tasks in the presence of sensor gain-and-phase errors. In contrast to existing approaches based on phase retrieval, our method eliminates gain errors by using the compensated covariance matrix. Meanwhile, we propose a data preprocessing method by taking only one column of the compensated covariance matrix without losing any magnitude information. Additionally, the phase retrieval problem is formed by the proposed data preprocessing method. Furthermore, the phase retrieval problem is solved by the recently proposed sparse feasible point pursuit algorithm, and DOA estimates are obtained. To prevent the model from ambiguities, we employ the known DOA to place reference sources. Numerical results show that the proposed scheme achieves better performance compared to state-of-the-art approaches.

Two-Dimensional DOA Estimation for Coherently Distributed Sources with Symmetric Properties in Crossed Arrays

In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.

Target Tracking Using SePDAF under Ambiguous Angles for Distributed Array Radar

Distributed array radar can improve radar detection capability and measurement accuracy. However, it will suffer cyclic ambiguity in its angle estimates according to the spatial Nyquist sampling theorem since the large sparse array is undersampling. Consequently, the state estimation accuracy and track validity probability degrades when the ambiguous angles are directly used for target tracking. This paper proposes a second probability data association filter (SePDAF)-based tracking method for distributed array radar. Firstly, the target motion model and radar measurement model is built. Secondly, the fusion result of each radar’s estimation is employed to the extended Kalman filter (EKF) to finish the first filtering. Thirdly, taking this result as prior knowledge, and associating with the array-processed ambiguous angles, the SePDAF is applied to accomplish the second filtering, and then achieving a high accuracy and stable trajectory with relatively low computational complexity. Moreover, the azimuth filtering accuracy will be promoted dramatically and the position filtering accuracy will also improve. Finally, simulations illustrate the effectiveness of the proposed method.

Wearable Sensor Localization Considering Mixed Distributed Sources in Health Monitoring Systems

In health monitoring systems, the base station (BS) and the wearable sensors communicate with each other to construct a virtual multiple input and multiple output (VMIMO) system. In real applications, the signal that the BS received is a distributed source because of the scattering, reflection, diffraction and refraction in the propagation path. In this paper, a 2D direction-of-arrival (DOA) estimation algorithm for incoherently-distributed (ID) and coherently-distributed (CD) sources is proposed based on multiple VMIMO systems. ID and CD sources are separated through the second-order blind identification (SOBI) algorithm. The traditional estimating signal parameters via the rotational invariance technique (ESPRIT)-based algorithm is valid only for one-dimensional (1D) DOA estimation for the ID source. By constructing the signal subspace, two rotational invariant relationships are constructed. Then, we extend the ESPRIT to estimate 2D DOAs for ID sources. For DOA estimation of CD sources, two rational invariance relationships are constructed based on the application of generalized steering vectors (GSVs). Then, the ESPRIT-based algorithm is used for estimating the eigenvalues of two rational invariance matrices, which contain the angular parameters. The expressions of azimuth and elevation for ID and CD sources have closed forms, which means that the spectrum peak searching is avoided. Therefore, compared to the traditional 2D DOA estimation algorithms, the proposed algorithm imposes significantly low computational complexity. The intersecting point of two rays, which come from two different directions measured by two uniform rectangle arrays (URA), can be regarded as the location of the biosensor (wearable sensor). Three BSs adopting the smart antenna (SA) technique cooperate with each other to locate the wearable sensors using the angulation positioning method. Simulation results demonstrate the effectiveness of the proposed algorithm.