Direction Of Arrival Estimation Research Articles

Exploration on 2D DOA estimation of linear array motion: Uniform linear motion

Generally, due to the limitation of the dimension of the array aperture, linear arrays cannot achieve two-dimensional (2D) direction of arrival (DOA) estimation. But the emergence of array motion provides a chance for that. In this paper, a generalized motion scheme and a novel method of 2D DOA estimation are proposed by exploring the linear array motion. To be specific, the linear arrays are controlled to move along an arbitrary direction at a constant velocity and snap per fixed time delay. All the received signals are processed to synthesize the comprehensive observation vector for an extended 2D virtual aperture. Subsequently, since most of 2D DOA estimation methods are not universal to our proposed motion scheme and the reduced-dimensional (RD) method fails to handle the case of the coupled parameters, a decoupled reduced-complexity multiple signals classification (DRC MUSIC) algorithm is designed specifically. Simulation results demonstrate that: a) our proposed scheme can achieve underdetermined 2D DOA estimation just by the linear arrays; b) our designed DRC MUSIC algorithm has the good properties of high accuracy and low complexity; c) our proposed motion scheme with the DRC method has better universality in the motion direction.

Deep learning-based DOA estimation for hybrid massive MIMO receive array with overlapped subarrays

As massive MIMO is a key technology in the future sixth generation (6G), the large-scale antenna arrays are widely considered in direction-of-arrival (DOA) estimation for they can provide larger aperture and higher estimation resolution. However, the conventional fully digital architecture requires one radio-frequency (RF) chain per antenna, and this is challenging for the high hardware costs and much more power consumption caused by the large number of RF chains. Therefore, an overlapped subarray (OSA) architecture-based hybrid massive MIMO array is proposed to reduce the hardware costs, and it can also have better DOA estimation accuracy compared to non-overlapped subarray (NOSA) architecture. The simulation results also show that the accuracy of the proposed OSA architecture has 6^{circ } advantage over the NOSA architecture with signal-to-noise ratio (SNR) at 10 dB. In addition, to improve the DOA estimation resolution, a deep learning (DL)-based estimator is proposed by combining convolution denoise autoencoder (CDAE) and deep neural network (DNN), where CDAE can remove the approximation error of sample covariance matrix (SCM) and DNN is used to perform high-resolution DOA estimation. From the simulation results, CDAE-DNN can achieve the accuracy lower bound at textrm{SNR}=-8 dB and the number of snapshots N=100, this means it has better performance in poor communication situation and can save more software resources compared to conventional estimators.

Low frequency three-dimensional DOA estimation for underwater gliders using an arbitrary tetrahedral array

This study proposes a method for estimating the three-dimensional (3-D) direction of arrival (DOA) of low-frequency line spectra with an arbitrary tetrahedral array on a moving underwater platform, such as underwater glider (UG). First, we provide the theoretical derivations of the 3-D DOA estimation algorithm. Four sensors are matched pairwise without duplication and the time difference of arrival (TDOA) of each pair is estimated using the cross-spectral method. The geometric relation between the space coordinate vector of the paired sensors and direction vector of the incoming signal is combined with the TDOA to establish the overdetermined equations. The algorithm solves the overdetermined equations to obtain the azimuth and elevation of the line spectra, and exploits all the information from sensors to enhance the accuracy of DOA estimation. And the Cramer–Rao lower bound (CRLB) of an arbitrary tetrahedral array is derived as a function of the signal-to-noise ratio (SNR), integration time, signal bandwidth, frequency, array arrangement, and DOA of the signal. Second, simulations and a sea trial verify the feasibility of the 3-D DOA estimation algorithm using a tetrahedral array on a moving UG. Finally, several factors that influence the algorithm are analyzed, including the DOA of the source, frequency, SNR, sensor position error and phase error. The upper frequency limit to avoid spatial aliasing is also derived as a function of the array aperture. The study shows that the tetrahedral array is suitable for various underwater mobile platforms owing to its small scale and irregularity.

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.

Direction‐of‐arrival estimation via coarray‐domain RELAX algorithm with source number estimation

AbstractA 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.

An enhanced expanding and shift sparse array based on the coprime array and nested array

AbstractIn 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.

Single acoustic vector sensor DOA enhanced by unsaturated bistable stochastic resonance with linear amplitude response constrained

Acoustic vector sensors (AVS) are increasingly utilized for remote target passive perception, but accurate direction-of-arrival (DOA) estimation remains a formidable challenge, particularly in the presence of heavy background noise. In this paper, we propose a novel DOA estimation method that utilizes complex acoustic intensity measurements (CAIM) and unsaturated bistable stochastic resonance with linear amplitude response constrained (LAR-UBSR). The proposed method aims to exploit the excellent denoising performance of stochastic resonance (SR) to enhance the accuracy of DOA estimation. The proposed LAR-UBSR method is based on the theoretical analysis of the signal pre-processing requirements of CAIM, which determines the linear amplitude response and fixed phase shift. LAR-UBSR achieves a stable phase shift and linear amplitude response by utilizing the unsaturated potential well and limited potential parameters adjustment method of SR. We analyze the amplitude response linearity of LAR-UBSR under different signal-to-noise ratios (SNRs) and a wide range of frequencies, demonstrating a larger linear amplitude response interval that meets the signal pre-processing requirements of CAIM. Numerical analysis and application verification show that the proposed DOA method outperforms existing methods, particularly under low SNR conditions. The results suggest the potential for high-accuracy DOA estimation using nonlinear signal processing strategies in the presence of heavy background noise.

Design of relocating sparse nested arrays for DOA estimation of non-circular signals

Recently, the ability of sparse arrays to achieve higher degrees of freedom (DOFs) and to be less sensitive to the mutual coupling (MC) effect has aroused increasing attention. Aiming at this, we investigate the sparse array design problem for direction of arrival (DOA) estimation of non-circular (NC) signals. Then, we propose two novel relocating sparse nested array (RSNA) structures, named RSNA-I and RSNA-II, respectively, and derive simple explicit expressions for their array locations and DOFs. Specifically, the RSNA-I is composed of two subarrays plus a separate sensor. By utilizing the separate sensor to enable the virtual sum and difference co-array (SDCA) with a longer consecutive segment and to alleviate the MC effect. In addition, to further make the array structure more robust to the MC effect, RSNA-II relocates the dense subarray of RSNA-I. Theoretical analysis and numerical simulation results demonstrate that the proposed RSNA-I and RSNA-II achieve a better balance between DOFs and the MC effect, which in turn effectively solves DOA estimation of NC signals and yields better DOA estimation performance.

An Enhanced DOA Estimation Method for Coherent Sources via Toeplitz Matrix Reconstruction and Khatri–Rao Subspace

The Toeplitz matrix reconstruction methods are capable of resolving coherent signals, playing a crucial role in the direction-of-arrival (DOA) estimation of acoustic sources. However, the decoherence processing sacrifices the array aperture and further results in a reduced resolution capability for the number of identifiable sources. To solve this issue, we propose an enhanced method using the Khatri–Rao subspace to resolve more coherent sources than that of the existing Toeplitz matrix reconstruction methods. Firstly, a full set of Toeplitz matrices with full rank is obtained. Then, the virtual array aperture can be obtained using the Khatri–Rao product of the array response, and the degree of freedom provided inherently in the virtual array structure is about twice the size of that of the existing Toeplitz methods. Next, linear processing is further used to achieve complexity reduction without losing the effective degree of freedom. Finally, the DOA estimation for more coherent sources can be achieved by combining it with conventional methods. Numerical simulations verify the superiority of the proposed method.

Passive localization of wideband near-field sources using Sparse Bayesian learning and envelope alignment

Most studies about passive localization of near-field signals are limited to narrowband sources. In this paper, a novel efficient algorithm is developed for direction of arrival (DOA) and range estimation of wideband near-field sources. Using the specific structure of symmetric linear array, the direction information is extracted and the off-grid Sparse Bayesian learning (SBL) framework is established for DOA estimation. The generalized approximate message passing (GAMP) strategy is applied for fast implementation. Then the envelope aligned approach is proposed for the range estimation in time domain and the linear searching concept is applied to accelerate the computation. Compared with the existing wideband near-field localization methods, the proposed algorithm has better performance of accuracy and resolution probability. Simulation results validate the feasibility and effectiveness of the proposed algorithm.

DOA Estimation for Coherent Sources Based on Uniformly Distributed Two Concentric Rings Array.

The direction estimation of the coherent source in a uniform circular array is an essential part of the signal processing area of the array, but the traditional uniform circular array algorithm has a low localization accuracy and a poor localization effect on the coherent source. To solve this problem, this paper proposes a two-dimensional direction of arrival (DOA) estimation for the coherent source in broadband. Firstly, the central frequency of the coherent sound source is estimated using the frequency estimation method of the delayed data, and a real-valued beamformer is constructed using the concept of the multiloop phase mode. Then, the cost function in the beam space is obtained. Finally, the cost function is searched in two dimensions to locate the sound source. In this paper, we simulate the DOA of the sound source at different frequencies and signal-to-noise ratios and analyze the resolution of the circular array. The simulation results show that the proposed algorithm can estimate the direction of arrival with high precision and achieve the desired results.

Direction-of-arrival estimation for a nested array with gain-phase error and impulse noise

To solve direction-finding problems for nested arrays under conditions of impulse noise and gain–phase errors, this paper proposes a direction-of-arrival (DOA) estimation method. First, a correntropy with an adaptive kernel length combined with an infinite norm of a variable weight value is proposed to suppress impulse noise. Then, the auxiliary array elements are used to realize the initial calibration of the amplitude and phase errors. On this basis, a DOA estimation method without a spectral peak search is proposed; this method is robust for arrays that still have residual gain–phase errors after calibration. Our method overcomes the difficulties of DOA estimation for nested arrays under conditions of gain–phase errors and impulse noise. Compared with traditional methods, the proposed method does not require prior knowledge, does not require a spectral peak search and has high superiority and robustness; a series of experiments have verified its superiority. In addition, a Cramér‒Rao bound (CRB) for angle estimation under conditions of gain–phase errors and impulse noise is proposed in this paper.

Direction of Arrival Estimation and Highlighting Characteristics of Testing Wideband Echoes from Multiple Autonomous Underwater Vehicles.

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.

Phased array antenna controlled by FPGA-ARM Cortex-M Processor

This paper discusses the architecture of an adaptive transmitting antenna array that allows highly flexible beamsteering. Antenna arrays are used in many digital signal processing applications due to their ability to locate signal sources. The Direction of Arrival (DOA) estimation is a key task of array signal processing, with the Taguchi method and Multiple Signal Classification (MUSIC). Although various algorithms have been developed for DOA estimation, their high complexity prevents their use in real-time applications. In this paper, we design and develop an implementation using Field Programmable Gate Array (FPGA Artix-7), which is the most widely used ARM processor in embedded systems. The antenna array is digitally controlled with the phases synthesized by the Taguchi method.

Direction-of-arrival and power spectral density estimation using a single directional microphone and group-sparse optimization

In this paper, two approaches are proposed for estimating the direction of arrival (DOA) and power spectral density (PSD) of stationary point sources by using a single, rotating, directional microphone. These approaches are based on a method previously presented by the authors, in which point source DOAs were estimated by using a broadband signal model and solving a group-sparse optimization problem, where the number of observations made by the rotating directional microphone can be lower than the number of candidate DOAs in an angular grid. The DOA estimation is followed by the estimation of the sources’ PSDs through the solution of an overdetermined least squares problem. The first approach proposed in this paper includes the use of an additional nonnegativity constraint on the residual noise term when solving the group-sparse optimization problem and is referred to as the Group Lasso Least Squares (GL-LS) approach. The second proposed approach, in addition to the new nonnegativity constraint, employs a narrowband signal model when building the linear system of equations used for formulating the group-sparse optimization problem, where the DOAs and PSDs can be jointly estimated by iterative, group-wise reweighting. This is referred to as the Group-Lasso with l_1-reweighting (GL-L1) approach. Both proposed approaches are implemented using the alternating direction method of multipliers (ADMM), and their performance is evaluated through simulations in which different setup conditions are considered, ranging from different types of model mismatch to variations in the acoustic scene and microphone directivity pattern. The results obtained show that in a scenario involving a microphone response mismatch between observed data and the signal model used, having the additional nonnegativity constraint on the residual noise can improve the DOA estimation for the case of GL-LS and the PSD estimation for the case of GL-L1. Moreover, the GL-L1 approach can present an advantage over GL-LS in terms of DOA estimation performance in scenarios with low SNR or where multiple sources are closely located to each other. Finally, it is shown that having the least squares PSD re-estimation step is beneficial in most scenarios, such that GL-LS outperformed GL-L1 in terms of PSD estimation errors.

Performance analysis of two-dimensional DOA estimation for uniform circular array

Perturbation analysis of direction of arrival (DOA) estimation has been studied mostly on one-dimensional arrays rather than planar arrays, which remains room for exploration. For uniform circular arrays with various model errors, we establish the corresponding system model. Then a performance analysis of the two-dimensional MUSIC algorithm is proposed by first-order error analysis and verified by simulation. The results show that the root-mean-squared error of DOA estimation is proportional to the standard deviation of the model errors, including gain-phase errors, sensor position errors, and mutual coupling effect.

A Novel Nested Array Structure for DOA Based on CCM of Subarrays

An innovative nested array structure that can notably increase the DOF and the linear arrays’ direction of arrival (DOA) estimated performance is proposed. For the conventional nested array, we vectorize the ACM’s output of the whole array and then remove the repeated rows to get a virtual array’s output. In contrast with classical nested arrays, the superiority of the new nested array is that it utilizes the combination of reverse ordering and conjugation of the inner uniform linear array (ULA) for one of the two subarrays and the sparse outer ULA for another to increase the array aperture. This means the outer sparse ULA’s sensor spacing is approximately the length of the entire inner ULA in the classical nested array structure. Yet, it is about twice the length in the new nested array structure. We generate one lengthy consecutive virtual uniform array excluding any redundant virtual sensors by vectorizing the two subarrays’ cross-correlation matrix (CCM), which is mentioned above. With the export signal of the virtual array and its conjugate form of it, an equivalent covariance matrix of full rank is constructed, which is called the Toeplitz matrix, to compensate for the rank lack of the virtual array’s ACM. For the sake of obtaining the DOA of input signals, the conventional DOA estimation method will be implemented on the ACM. The increase in outer sparse ULA’s sensor spacing ensures an increase in virtual array aperture in principle, which means it is capable of increasing the number of DOA estimations, which is called DOF, and optimizing the DOA estimated performance in contrast with the ULA and classical nested arrays. Results from trials certify the preponderance of the proposed structure in the aspect of DOF and the accuracy of DOA estimation.

In Situ Calibration of Antenna Arrays for Positioning With 5G Networks

Owing to the ubiquity of cellular communication signals, positioning with the fifth-generation (5G) signal has emerged as a promising solution in global navigation satellite system-denied areas. Unfortunately, although the widely employed antenna arrays in 5G remote radio units (RRUs) facilitate the measurement of the direction of arrival (DOA), DOA-based positioning performance is severely degraded by array errors. This article proposes an in situ calibration framework with a user terminal (UT) transmitting 5G reference signals at several known positions in the actual operating environment and the accessible RRUs estimating their array errors from these reference signals. Further, since sub-6 GHz small-cell RRUs deployed for indoor coverage generally have small-aperture antenna arrays, while 5G signals have plentiful bandwidth resources, this work segregates the multipath components via super-resolution delay estimation based on the maximum likelihood criteria. This differs significantly from existing in situ calibration works which resolve multipaths in the spatial domain. The superiority of the proposed method is first verified by numerical simulations. We then demonstrate via field test with commercial 5G equipment that, a reduction of 46.7% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1{\text -}\sigma$</tex-math> </inline-formula> DOA estimation error can be achieved by in situ calibration using the proposed method.

Assistant vehicle locating based on DOA estimation of deep unfolded network

In view of the decline in the positioning accuracy of the vehicles with small snapshots, this paper proposes a direction of arrival(DOA) estimation method based on deep unfolded network to assist the global positioning system to achieve high-precision locating. Firstly, the signal emitted from the on board unit installed on the vehicle is received by the array antenna of the road side unit(RSU), then RSU transmits the array data to cloud service platform, in which the traditional fixed point continuation algorithm is improved by using l1 norm instead of l2 norm, and the adaptive outlier point tracking algorithm is used to deal with the problem of symbol flipping caused by noise. Then we unfold the improved fixed point continuous algorithm for obtaining a neural network. In order to improve the DOA estimation performance and convergence speed, this paper uses the black widow optimization algorithm to determine the soft threshold shrinkage parameters. According to the mapping between the signal and the array manifold matrix, the DOA of the target is estimated, and its location can be evaluated from the geometry relation between vehicle and RSU. The simulation results show that the algorithm proposed in this paper has better direction finding performance and improves the vehicle positioning accuracy under small snapshots and high signal-to-noise ratio effectively.

Data-Driven DOA Estimation Methods Based on Deep Learning for Underwater Acoustic Vector Sensor Array

Abstract Direction of arrival (DOA) estimation is a fundamental problem in underwater acoustic vector sensor array signal processing. Because of the advantages of deep learning technology, this paper proposes two categories of data-driven DOA estimation methods for underwater acoustic vector sensor array, which transform the DOA estimation problem into a neural network classification problem. Specifically, one is the DOA estimation method of convolutional neural network based on teacher-student noise reduction (TS-CNN), which considers the covariance matrix as the training data set; the other is a DOA estimation method based on long-short term memory network and attention mechanism (LSTM-ATT), which applies the time-domain signal as the training data set. The experimental simulation results show that: 1) when the number of array elements is small, the accuracy of the DOA estimation method based on TS-CNN is equivalent to that of traditional methods, and it can effectively suppress the influence of noise when the signal-to-noise ratio (SNR) is low; 2) the accuracy of DOA estimation method based on LSTM-ATT is much higher than that of traditional Multiple Signal Classification method, especially in the case of low SNR, which also proves the importance of temporal characteristics for DOA estimation in a real environment.