Direction Of Arrival Estimation Research Articles

Electromagnetic informed data model considerations for near-field DOA and range estimates

Localizing sources in the near-field is one of the emerging challenges for array signal processing, which has received a great deal of attention in recent years. The development of accurate localization algorithms requires the definition of a reliable model of the received signal that takes into account all wavefront characteristics, such as angle, range, and polarization, as well as electromagnetic effects, such as mutual coupling between antennas and the amplitude and phase behaviour of electromagnetic wavefronts. A system model that considers the electromagnetic-informed wave behaviour effects, independent of the type of receiver antennas, array structure, degree of correlation of sources signals and other electromagnetic effects, is considered an “ exact model ” in the literature. However, due to the mathematical complexity of this modeling approach, simplifications using several approximations are conventionally used. For instance, the phase of the exact model is approximated using the Fresnel approximation, while the magnitude of the exact model is simplified by assuming equal distances between the source and all elements in the array. In this work, we evaluate the accuracy of a localization algorithm, the multiple signal classification (MUSIC), using the exact and approximated models in the near-field region. Through a series of simulations, we demonstrate that the localization algorithm designed based on the electromagnetic-informed exact model outperforms the one designed using the approximated model. We also show that considering electromagnetic factors in the system model through the exact model results in a 13% improvement in the direction of arrival (DOA) root mean square error (RMSE) and a 57.7% improvement in range RMSE at signal-to-noise ratio (SNR) of 15 dB.

Spatial Spectrum Estimation of Weak Scattering Wave Signal in Range-Doppler Domain

How to enhance the desired signal with low signal-to-noise ratio (SNR) is a difficult problem in the estimation process of the direction-of-arrival (DOA) of the target scattering wave signal. In this paper, the feasibility of spatial spectrum estimation in the Range-Doppler (RD) domain is analyzed in principle, and the SNR gain expression of weak scattering wave signal is derived when constructing multi-snapshots virtual array data. On this basis, the mutual eigenvector singular value decomposition (MESVD) method based on RD domain mode excitation is proposed, which can robustly and effectively estimate the direction of the coherent weak signals. Simulation experiments verify that the RD domain spectral estimation method has the ability to simultaneously obtain the direction of multiple weak target scattering waves, and the direction-finding accuracy can reach the Cramer–Rao bound (CRB) of conventional spectral estimation method. The results of Monte Carlo experiments show that the root-mean-square-error (RMSE) of azimuth estimation of RD domain spatial spectrum estimation method is 5.76° lower than that of a conventional multiple signal classification (MUSIC) method. In addition, the practicability of the proposed method is demonstrated by comparing the DOA estimation results of a set of real data with Automatic Dependent Surveillance-Broadcast (ADS-B) data.

Joint parameter estimation algorithm for polarization-sensitive channel compression arrays based on atomic norm minimization

To reduce the complexity of direction-of-arrival (DOA) algorithms in polarization-sensitive arrays and maintain high estimation accuracy while decreasing runtime, this paper proposes a channel compression model based on orthogonal dipole arrays. In addition, a DOA estimation algorithm using atomic norm minimization (ANM) is introduced for this model. This algorithm performs eigenvalue decomposition on the covariance matrix of the data received from the polarization-sensitive channel compressed array. A new observation vector is constructed for the ANM problem under the channel compression model using the obtained eigenvalues and eigenvectors. Subsequently, a Toeplitz matrix is constructed from the optimal solution of the semi-positive definite programming (SDP) problem. The Vandermonde decomposition of the Toeplitz matrix provides estimates of the signal DOA parameters. By combining the vectorization result of the covariance matrix and the least-squares calculation, the polarization auxiliary angle and polarization phase angle information of the incident source are also obtained. Simulation experiments compare the root-mean-squared error (RMSE) of each algorithm at different angular intervals and signal-to-noise ratios (SNR) to confirm the validity of estimating DOA and polarization parameters.

Direction of Arrival (DOA) Estimation using Switched Beam Antenna with Butler Matrix at mm-Wave Frequency

This paper presents a butler matrix-based microstrip hexagonal patch antenna with a direction of arrival (DOA) estimation approach for mm-wave application. The hexagonal-shaped patch antenna had been designed with a Z-shaped slot with an eight-port butler matrix. The DOA estimation is also done for the switched beam antenna using a novel direction of arrival (DOA) estimation algorithm known as Cramer-Rao lower bound (CRLB). The proposed design leads to significant size reduction and loss minimization. In addition to this, the design had the advantages of being low-cost, lightweight, and small-volume. The entire proposed design provides an operating frequency range of 28 GHz to 39 GHz with a center frequency of 33 GHz. The proposed work makes use of two butler matrices with two 45° phase shifters and 120° phase shifters. The effectiveness of the proposed algorithm and antenna design using the Butler matrix is evaluated for various performance metrics separately. The antenna is designed using Rogers RT/duroid 5880(tm) substrate, and the fabricated prototype is studied. The designed antenna attains high radiation efficiency, and it ranges between 97 to 98% under both the measures and simulated scenarios under the operating frequency range of 28 GHz to 39 GHz.

RDCSAE-RKRVFLN: A unified deep learning framework for robust and accurate DOA estimation

This paper introduces an innovative unified deep learning (DL) model, “reduced deep convolutional stack autoencoder (RDCSAE)-robust kernel-based random vector functional link network (RKRVFLN)” (RDCSAE-RKRVFLN), for addressing practical challenges like phase and gain uncertainty, mutual coupling effects, and element position errors in direction of arrival (DOA) estimation. The RDCSAE utilizes deep convolutional neural network (DCNN) and stack autoencoder (SAE) for robust feature extraction. The RKRVFLN integrates a concise SAE output with kernel-based learning. Thus, the integration of RDCSAE (suitable for unsupervised feature extraction) and RKRVFLN (for supervised learning) in the developed model results in efficient use of limited training data. Performance metrics of this method include among others the accuracy (separation between sources), root mean square error (RMSE), signal-to-noise ratio (SNR), etc. The method performs better than existing data driven methods in terms of computational efficiency, faster learning speed, enhanced model generalization, higher accuracy, and shorter event regression time and empirical methods. In the presence of above mentioned four perturbations, this method successfully resolves multiple sources with a resolution of 0.3° with a RMSE of 0.00376. For real time application, the paper implements RDCSAE-RKRVFLN on a high-speed reconfigurable Xilinx Virtex-5 field-programmable gate array (FPGA) realizing a digital DOA estimator for one source. The hardware estimates the DOA with a maximum error of 0.01953125 which follows closely the simulation results indicating the efficiency and feasibility of the method.

Robust DOA Estimation Using Multi-Scale Fusion Network with Attention Mask

To overcome the limitations of traditional methods in reverberant and noisy environments, a robust multi-scale fusion neural network with attention mask is designed to improve direction-of-arrival (DOA) estimation accuracy for acoustic sources. It combines the benefits of deep learning and complex-valued operations to effectively deal with the interference of reverberation and noise in speech signals. The unique properties of complex-valued signals are exploited to fully capture inherent features and rich information is preserved in the complex field. An attention mask module is designed to generate distinct masks for selectively focusing and masking based on the input. After that, the multi-scale fusion block efficiently captures multi-scale spatial features by stacking complex-valued convolutional layers with small size kernels, and reduces the module complexity through special branching operations. Experimental results demonstrate that the model achieves significant improvements over other methods for speaker localization in reverberant and noisy environments. It provides a new solution for DOA estimation for acoustic sources in different scenarios, which has significant theoretical and practical implications.

Kalman filter for radio source power and direction of arrival estimation

Images are an important source of information for spacecraft navigation. Based on an image and a known attitude, triangulation techniques (intersection or resection) are often used for positioning and navigation. In the resection problem, an observer estimate its unknown location by using angle measurements to points at known locations (i.e., landmarks), the localization performance depending on the accuracy of the angle measurements. As a contribution to resection for spacecraft navigation, we considers the dynamic image estimation problem based on radio interferometry, i.e., image of radio source power, where the measurements are sample covariance matrices (SCMs). Considering the case where several measurements are available as well as a known dynamic linear model of image evolution, a.k.a a linear state model, the minimum mean-squared error image estimator (MMSE) is given by the Kalman filter (KF) or one of its variants. However standard Kalman-like filters are not a priori suitable for the problem at hand since the measurements (i.e., SCMs) cannot be formulated analytically as a function of state parameters to be estimated (i.e., radio source power). In fact, this lack of analytical formulation can be circumvented by a statistical linear fitting allowing the SCMs to be expressed in terms of the state. This linear fitting introduces an additive residual noise, equivalent to a measurement noise, whose covariance matrix depends on the current state, a non-standard case for a measurement model. The covariance matrix of the residual noise is derived whatever the distributions of the radio sources and of the additive noise at the samples level, unveiling the contribution of their multivariate kurtosis. The proposed method is evaluated on simulated data representative of a dynamic radio interferometry framework. The results show that the proposed method is capable of effectively tracking moving radio sources in complex scenes with theoretical guaranties when the signal multivariate kurtosis is known.

Multiplicative Basis Function Based Adaptive DOA Estimation in Optimal MIMO Sparse Antenna Reconfiguration Model

Direction of arrival (DOA) estimation using sparse signal representation has gained significant attention in recent decades. The spatial signals utilized for DOA estimation are reconstructed through a novel compressive sensing (CS) approach. In this study, we used a CS approach to ascertain the adaptive underdetermined DOA for multiple inputs and multiple output (MIMO) sparse media. Accurate DOA estimation through the CS approach contributes to enhanced signal investigation and the suppression of undesired noise in a sparse channel. The method proposed herein encompasses the development and execution of a novel multiplicative basis function known as the multi-kernel supported non-negative sparse Bayesian learning (NNSBL) algorithm, which is implemented on predefined grid values. Concurrently, stochastic grey wolf optimization (GWO) is virtually applied to increase the degrees of freedom (DOF) on a minimum redundancy array (MRA) while considering an optimal antenna reconfiguration model. The advantages of this proposed approach include the generation of a distinct manifold matrix for precise beam steering, resulting in improved DOA estimation accuracy. Additionally, an augmentation of DOF using GWO was observed, with low computational complexity. The simulated result of proposed algorithm leads to the attainment of optimal minimum root mean square error (RMSE) across various optimal wavelengths of the stochastic sources. Finally, a comparative analysis of RMSE and convergence plots confirms the superior performance and high potentiality of the proposed method in comparison to existing techniques across different SNR values. Notably, there is significant reduction in RMSE which is suitable for precise DOA estimation in signal processing applications.

Enhanced Underwater Single Vector-Acoustic DOA Estimation via Linear Matched Stochastic Resonance Preprocessing

Underwater acoustic vector sensors (UAVSs) are increasingly utilized for remote passive sonar detection, but the accuracy of direction-of-arrival (DOA) estimation remains a challenging problem, particularly under low signal-to-noise ratio (SNR) conditions and complex background noise. In this paper, a comprehensive theoretical analysis is conducted on UAVS signal preprocessing subjected to gain-phase uncertainties for average acoustic intensity measurement (AAIM) and complex acoustic intensity measurement (CAIM)-based vector DOA estimation, aiming to explain the theoretical restrictions of intensity-based vector acoustic preprocessing approaches. On this basis, a generalized vector acoustic preprocessing optimization model is established in which the principle can be described as “maximizing the denoising performance under the constraints of an equivalent amplitude-gain response and phase-bias response”. A novel vector acoustic preprocessing method named linear matched stochastic resonance (LMSR) is proposed within the framework of matched stochastic resonance theory, which can naturally guarantee the linear gain-phase restrictions, as well achieving effective denoising performance. Numerical analyses demonstrate the superior vector DOA estimation performance of our proposed LMSR-AAIM and LMSR-CAIM methods in comparison to classical intensity-based AAIM and CAIM methods, especially under low-SNR conditions and non-Gaussian impulsive noise circumstances. Experimental verification conducted in the South China Sea further verifies its the effectiveness for practical application. This work can lay a solid foundation to break through the challenges of underwater remote vector acoustic DOA estimation under low-SNR conditions and complex ocean ambient noise and can provide important guidance for future research work.

Motion-guided large aperture ULA to enhance DOA estimation: An inverse synthetic aperture perspective

Direction-of-arrival (DOA) estimation is a critical issue in array signal processing, especially in radar applications. However, the array aperture of high-frequency radars is constrained by the site and platform, which in turn leads to limited DOA estimation performance. In this paper, inspired by the inverse synthetic aperture radar, we design a novel DOA estimation method based on motion-guided large-aperture uniform linear array (ULA). Referring to the concept of inverse synthetic aperture, the novel method utilizes the relative motion between the radar and the target to construct a larger ULA. We demonstrate that the key condition for reconstructing ULAs is suitable data segmentation and reshaping within the coherent integration time. However, the correct segmentation position is related to the target's motion trajectory. For non-cooperative targets, the uncertain segmentation position is regarded as a mismatch problem between the steering and weighting vectors, such that the spatial spectrum becomes a product of two sinc-like functions. With the analysis of the main lobe and grating lobes, the maximum peak-to-grating-lobe ratio criterion is introduced to find the ambiguity-free DOA. The experimental results demonstrate the performance advantages of the proposed DOA estimation algorithm in terms of noise robustness and resolution.

Improving the Accuracy of Direction of Arrival Estimation with Multiple Signal Inputs Using Deep Learning.

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°.

Improved Underwater Single-Vector Acoustic DOA Estimation via Vector Convolution Preprocessing

Remote passive sonar detection with underwater acoustic vector sensor (UAVS) has attracted increasing attention due to its merit in measuring the full sound field information. However, the accurate estimation of the direction-of-arrival (DOA) remains a challenging problem, especially under low signal-to-noise ratio (SNR) conditions. In this paper, a novel convolution (COV)-based single-vector acoustic preprocessing method is proposed on the basis of the single-vector acoustic preprocessing model. In view of the theoretical analysis of the classical single-vector acoustic DOA estimation method, the principle of preprocessing can be described as “to achieve an improved denoising performance in the constraint of equivalent amplitude gain and phase response.” This can be naturally guaranteed by our proposed COV method. In addition, the upper bound with matched filtering (MF) preprocessing is provided in the consideration of the optimal linear signal processing for weak signal detection under Gaussian noise. Numerical analyses demonstrate the effectiveness of our proposed preprocessing method with both vector array signal processing-based and intensity-based methods. Experimental verification conducted in South China Sea further verifies the effectiveness of our approach for practical applications. This work can lay a solid foundation in improving underwater remote vector acoustic DOA estimation under low SNR, and can provide important guidance for future research work.

An automated multi-layer perceptron discriminative neural network based on Bayesian optimization achieves high-precision one-source single-snapshot direction-of-arrival estimation

This paper proposes an innovative global solution which is a pioneering work applying automated machine learning algorithms to remarkable precision sparse underwater direction-of-arrival (DOA) estimation that views the subaquatic sparse-sampling DOA estimation problem as a classification prediction task. The proposed solution, termed automated multi-layer perceptron discriminative neural network (AutoMPDNN), is built upon a Bayesian optimization framework. AutoMPDNN transforms sparsely sampled time-domain signals into the complex domain, preserving essential components in a one-source single-snapshot scenario. Leveraging Bayesian optimization principles, the algorithm embeds necessary hyperparameters into the loss function, effectively defining it as a maximum likelihood problem using the upper confidence bound function and incorporating sparse signal features. We also explore the model space architecture and introduce variants of AutoMPDNN, denoted as AutoMPDNNs_ln (n = 2,3,4). Through a series of plane wave simulation experiments, it is demonstrated that AutoMPDNN achieves the highest prediction performance for one-source single-snapshot scenarios compared to classical DOA estimation algorithms that incorporate sparse representation approaches, as well as contemporary deep learning DOA methods under varying conditions.

High-accuracy 2D DOA estimation with three parallel sparse nested array

To improve the performance for two-dimensional (2D) direction of arrival (DOA) estimation in the presence of limited antennas in practice, we propose a novel three parallel sparse nested array with extended aperture and reduced mutual coupling. The proposed array consists of three subarrays where locations of antennas have closed-form expressions, to efficiently achieve increased degrees of freedom in difference coarray domain. The unit inter-antenna spacings and the displacements among subarrays are all expanded by D1, D2 or D3 fold for aperture extension and mutual coupling reduction in physical array domain. By exploiting the configuration, the two methods, i.e., BOMP-based and CMT-BCS-based methods, are further explored for high-precision but ambiguous angle estimation, and then the coprime-ness between the displacements is utilized to solve the angle ambiguities. Simulation results demonstrate the superiority of the proposed array and methods for 2D DOA estimation over the existing technologies.

Reduced-complexity multiple parameters estimation via toeplitz matrix triple iteration reconstruction with bistatic MIMO radar

In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output (MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovatively addresses the joint estimation of the Direction of Departure (DOD), Direction of Arrival (DOA), and Doppler frequency for incoherent targets. We propose a novel approach that significantly reduces computational complexity by utilizing the Temporal-Spatial Nested Sampling Model (TSNSM). Our methodology begins with a multi-linear mapping mechanism to efficiently eliminate unnecessary virtual Degrees of Freedom (DOFs) and reorganize the remaining ones. We then employ the Toeplitz matrix triple iteration reconstruction method, surpassing the traditional Temporal-Spatial Smoothing Window (TSSW) approach, to mitigate the single snapshot effect and reduce computational demands. We further refine the high-dimensional ESPRIT algorithm for joint estimation of DOD, DOA, and Doppler frequency, eliminating the need for additional parameter pairing. Moreover, we meticulously derive the Cramér-Rao Bound (CRB) for the TSNSM. This signal model allows for a second expansion of DOFs in time and space domains, achieving high precision in target angle and Doppler frequency estimation with low computational complexity. Our adaptable algorithm is validated through simulations and is suitable for sparse array MIMO radars with various structures, ensuring higher precision in parameter estimation with less complexity burden.

Multiple source direction-of-arrival estimation applicable under near-, far-, and mixed-field scenarios.

Traditionally, direction-of-arrival (DOA) estimations under near- and far-field scenarios are treated as independent tasks based on the corresponding acoustic model, hence necessitating a proper soundfield detector as an upstream processing tool, whereas there may not be a distinct boundary between different soundfield types, especially the mixed-field scenarios where both near- and far-field sources coexist simultaneously. To handle this issue, this article investigates a multisource DOA estimator that equally localizes multiple near-, far-, and mixed-field sources, not requiring any specialized adjustments. We (i) define a signal-invariant multichannel feature denoted generalized relative harmonic coefficients in the spherical harmonics domain; (ii) derive the analytical expression of this feature and summarize its unique properties, exhibiting consistence for both near- and far-field sources; (iii) estimate source elevation and azimuth using the magnitude and phase parts of this feature, respectively; (iv) detect single-source dominated periods from the mixed measurements based on an investigated distance measure; and (v) count the number of sources and localize their DOAs by clustering the single-source dominated estimates. Extensive experimental results, in both simulated and real-life environments, finally confirm the effectiveness of the proposed algorithm under diverse acoustic scenarios, and a superiority over baseline approaches in localizing mixed-field sources.

Enhancing azimuth estimation in low-resolution underwater acoustic lens systems for advanced communication and positioning

Here we aimed to enhance azimuth estimation to accurately locate a communication partner’s position by utilizing a low-resolution underwater acoustic lens system for communication. We proposed a method to accurately estimate the direction-of-arrival (DoA) by finding the center of gravity of the focal distribution using two adjacent elements of the transducer array. Ranging was to be based on time-of-flight (ToF). The method’s effectiveness was evaluated by two-dimensional finite difference time domain simulation. The lens’s focused sound field was calculated and the array was designed based on the result. DoA and ToF were estimated from the received signals and evaluated by comparing them with the true values under conditions involving 1-, 2-, and 3- users. The results confirmed DoA estimation with an error of almost 4°, even when using a lens system with an azimuth resolution of 10°. As the number of users increased, the maximum error value increased, though slightly.

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐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.

Advanced Interference Mitigation Method Based on Joint Direction of Arrival Estimation and Adaptive Beamforming for L-Band Digital Aeronautical Communication System

The L-band digital aeronautical communication system (LDACS) is one of the candidate technologies for future broadband digital aeronautical communications, utilizing the unused L-band spectrum between distance measuring equipment (DME) channels. However, the higher signal power of DME complicates LDACS implementation. This paper proposes an advanced DME mitigation approach for the LDACS, integrating joint direction of arrival (DOA) estimation with adaptive beamforming techniques. The proposed method begins by exploiting the cyclostationary characteristics of signals, accurately obtaining the preliminary direction of the LDACS signal using the Cyclic-MUSIC method. Subsequent precise steering vectors (SVs) are selected through Capon spectrum search, followed by the reconstruction of the interference plus noise covariance matrix (INCM). Using the obtained SV and INCM, the weight vector is calculated and beamforming is performed. Simulation results validate that the proposed method not only accurately estimates the direction of LDACS signal but also efficiently mitigates DME interference, demonstrating a superior performance and reduced algorithmic complexity, even in scenarios with lower signal-to-noise ratios (SNRs) and the presence of DOA estimation errors. Additionally, the proposed method achieves a low bit error rate (BER), further validating its ability to ensure communication quality and enhance the reliability of LDACS.

Improved moving scheme for coprime arrays in direction of arrival estimation

Coprime array motions are known to improve direction of arrival (DOA) estimation due to the synthetic aperture technique and the concept of difference coarray (DCA) are combined to achieve an increased number of degrees of freedom (DOFs). In this paper, an improved moving scheme for coprime array is presented, where the array spans a carefully designed large displacement. The benefit by doing this is that the overlapping lags induced by the original DCA and the shifted DCA can be avoided as much as possible, thereby significantly enhancing the number of consecutive DOFs (cDOFs). Then, the closed-form expressions of the displacement, cDOFs, and DOFs are derived. We also prove that the synthetic array has the same robustness against mutual coupling as the original array. It shows that the proposed moving scheme is more attractive than the other existing schemes. Finally, numerical examples are provided to demonstrate the superiority of the proposed moving scheme in both the absence and presence of mutual coupling.