Direction Of Arrival Estimation Research Articles

Robust Direction Estimation of Terrestrial Signal via Sparse Non-Uniform Array Reconfiguration under Perturbations

DOA (Direction of Arrival), as an important observation parameter for accurately locating the Signals of Opportunity (SOP), is vital for navigation in GNSS-challenged environments and can be effectively obtained through sparse arrays. In practical application, array perturbations affect the estimation accuracy and stability of DOA, thereby adversely affecting the positioning performance of SOP. Against this backdrop, we propose an approach to reconstruct non-uniform arrays under perturbation conditions, aiming to improve the robustness of DOA estimation in sparse arrays. Firstly, we theoretically derive the mathematical expressions of the Cramér–Rao Bound (CRB) and Spatial Correlation Coefficient (SCC) for the uniform linear array (ULA) with perturbation. Then, we minimize CRB as the objective function to mitigate the adverse effects of array perturbations on DOA estimation, and use SCC as a constraint to suppress sidelobes. By doing this, the non-uniform array reconstruction model is formulated as a high-order 0–1 optimization problem. To effectively solve this nonconvex model, we propose a polynomial-time algorithm, which can converge to the optimal approximate solution of the original model. Finally, through a series of simulation experiments utilizing frequency modulation (FM) signal as an example, the exceptional performance of this method in array reconstruction has been thoroughly validated. Experimental data show that the reconstructed non-uniform array excels in DOA estimation accuracy compared to other sparse arrays, making it particularly suitable for estimating the direction of terrestrial SOP in perturbed environments.

Trackable Electronic Deception Enabled by Space‐Time Coding Metasurface

AbstractSpace‐time coding metasurfaces (STCMs) have gained a great deal of achievements in the fields of radar and communication, but they have rarely been explored in the field of electronic jamming. The existing researches use time‐varying surface or phase‐switched screens to realize electronic deceptions, but the deceptions are completely passive and are limited in the time‐frequency domain. Here, a mechanism of STCM‐based deceptions is presented in the space and the time‐frequency domains, and precise designs of the STCM‐based deceptions are achieved by performing shifting operations on the space‐time coding sequences of the STCM. Moreover, STCM‐based DOA (direction‐of‐arrival) estimation is integrated with the deception procedure to achieve trackable electronic deception which cannot be realized by completely passive electronic jamming. A prototype system of the STCM‐based deception is built to verify the deception performance, and the experimental results agree well with the numerical simulations. This work extends the research and the applications of the STCMs, hence showing great scientific and engineering significance.

Research on the vector DOA estimation method with limited number of snapshots

The number of sample snapshots of array signals directly affects the performance of direction of arrival (DOA) estimation methods, and smaller snapshots often cannot represent all the features of array signals. However, in practical applications, owing to short-time abrupt changes, low intensity, large noise interference, and other factors of the target signal, the acoustic vector array sometimes cannot obtain sufficient signal data, making it difficult to achieve accurate DOA estimation. Therefore, this study proposes a transfer-learning-based DOA estimation method for acoustic vector arrays. This method extracts the spatial–temporal features of existing signal data by constructing a pre-trained network model based on a convolutional neural network (CNN) and long short-term memory (LSTM), and transfers the trained model to scenes with limited snapshot data through model fine-tuning, achieving the goal of improving the DOA estimation accuracy under a small number of snapshots. Simulation experiments show that the accuracy and RMSE of the proposed DOA estimation method are superior to those of traditional methods when only 1% of the target data are used. This indicates that the pre-training model based on LSTM and CNN can preserve the effective information of signal data and provides a new solution for the real-time prediction of acoustic vector arrays in scenes with a limited number of snapshots through transfer learning.

Enhanced‐Resolution Learning‐Based Direction of Arrival Estimation by Programmable Metasurface

AbstractDue to its growing importance and wide range of applications, direction‐of‐arrival (DOA) estimation has become a major research topic, particularly in the field of communication systems. While traditional DOA estimation methods rely on antenna arrays and complex algorithms, recent progress achieved in the design and implementation of metasurfaces has proved their effectiveness as promising alternatives. This study presents a distinct approach for DOA estimation that combines the use of a programmable metasurface with deep learning. The programmable metasurface together with a radio‐frequency power detector placed at the focal point, acts as a parabolic reflector antenna with an adjustable pointing direction, which scans the azimuth plane in 5° increments to receive the power level of incoming signals. The collected data is then fed into a pre‐trained multilayer neural network to enable DOA estimation with a resolution of lower than 1° without requiring fine‐tuning of the scanning procedure. This approach ensures accurate and fast estimations, paving the way for advanced solutions in detection and localization for various applications.

Off-Grid Underwater Acoustic Source Direction-of-Arrival Estimation Method Based on Iterative Empirical Mode Decomposition Interval Threshold.

To solve the problem that the hydrophone arrays are disturbed by ocean noise when collecting signals in shallow seas, resulting in reduced accuracy and resolution of target orientation estimation, a direction-of-arrival (DOA) estimation algorithm based on iterative EMD interval thresholding (EMD-IIT) and off-grid sparse Bayesian learning is proposed. Firstly, the noisy signal acquired by the hydrophone array is denoised by the EMD-IIT algorithm. Secondly, the singular value decomposition is performed on the denoised signal, and then an off-grid sparse reconstruction model is established. Finally, the maximum a posteriori probability of the target signal is obtained by the Bayesian learning algorithm, and the DOA estimate of the target is derived to achieve the orientation estimation of the target. Simulation analysis and sea trial data results show that the algorithm achieves a resolution probability of 100% at an azimuthal separation of 8° between adjacent signal sources. At a low signal-to-noise ratio of -9 dB, the resolution probability reaches 100%. Compared with the conventional MUSIC-like and OGSBI-SVD algorithms, this algorithm can effectively eliminate noise interference and provides better performance in terms of localization accuracy, algorithm runtime, and algorithm robustness.

DOA estimation of noncircular signals with direction-dependent mutual coupling

In this paper, a reweighted sparse recovery algorithm based on the optimal weighted subspace fitting (WSF) for non-circular signals in direction-dependent mutual coupling (MC) is proposed. Firstly, a new augmented model is constructed by leveraging the characteristics of non-circular signals. Next, a new direction matrix without mutual coupling coefficients is obtained by a novel transformation method. Then, two sparse recovery models are constructed by utilizing the WSF technique, and the sparsity of the solution is increased by constructing a weighted matrix. Finally, the direction of arrival (DOA) is achieved by a sparse recovery approach. For both coherent and incoherent signals, the developed approach can achieve precise DOA estimation in the case of direction-dependent MC. The robustness and advantage of the developed approach are testified by various experiments.

Explicit Entropy Error Bound for Compressive DOA Estimation in Sensor Array

Compressive sensing (CS) simplifies software and hardware by sampling below the Nyquist rate, making it widely used in array signal processing. For the assessment of the compressive direction-of-arrival (DOA) estimation, a lower bound on the mean square error is essential. However, the most widely utilized Cramér-Rao bound (CRB) is only asymptotically tight. This paper proposes a globally tight bound with a closed-form expression for compressive DOA estimation in the uniform linear arrays employing Shannon information theory. Based on the a posteriori probability density function, we propose the indicator of the entropy error (EE) with compression to assess the DOA estimation. The theoretical EE bounds the compressive DOA estimation performance. Moreover, the explicit EE is derived by approximating the normalized differential entropy, which is comprehensive and captures the effect of the compression ratio, the SNR, the number of elements, and the mean square bandwidth. In Particular, the compression ratio has almost no influence on the EE in low SNR. Additionally, the asymptotic lower bound of the theoretical EE is identical to the CRB. Simulation results illustrate the superiority of EE over CRB in evaluating and predicting compressive DOA estimation performance in the uniform linear arrays.

Theory of the cubic autoproduct and its utility for noisy direction of arrival estimation

Autoproducts are quadratic or higher products of frequency-domain acoustic fields that can mimic genuine fields at frequencies within or outside the original field's bandwidth. Past studies have found a variety of interesting autoproduct properties but have been limited to quadratic autoproducts. This paper presents cubic autoproduct theory and documents how noise suppression may be attained with the cubic frequency-difference autoproduct, a product of three frequency-domain acoustic fields. The cubic autoproduct's field equations, developed from the inhomogeneous Helmholtz equation, and analytical results in single- and two-path environments justify interpretating the cubic autoproduct as a pseudofield and underscore its similarities to the quadratic autoproducts. For nonzero field bandwidth, many frequency triplets satisfy the relationship for a single cubic autoproduct frequency. Thus, bandwidth averaging can lead to serendipitous noise suppression and is shown herein to facilitate field-phase-structure recovery from ideal free space fields corrupted by Gaussian noise. Cubic-autoproduct-based direction of arrival (DOA) estimation using signal and noise recordings collected in the ocean are found to be more accurate than conventional DOA estimates from the same data. In particular, cubic autoproduct results showed a 3–5 dB noise suppression advantage for 4- and 6-kHz direct- and reflected-path sounds broadcast 200 m to a four-element receiving array.

Augmented correlation matrix reconstruction for direction of arrival estimation using dual-spread array

Due to the large degrees of freedom (DOF) by generating difference coarray, nonuniform arrays have great potential in direction of arrival (DOA) estimation. However, some existing nonuniform arrays (e.g., (sparse) nested arrays) still have comparatively strong mutual coupling in physical array domain, whereas the others (e.g., coprime arrays) have holes or only used part available in difference coarray domain, for the performance loss of DOA estimation. To address these issues, we propose two kinds of dual-spread arrays which achieve more and continuous DOF by exploiting correlation matrix reconstruction, rather than the generation of difference coarray. All inter-antenna spacings of the proposed arrays are larger than half-wavelength, resulting in extended aperture and reduced mutual coupling. An ESPRIT-based estimation method is further provided for unique DOA estimation with high-accuracy and low-complexity. The analyses of mutual coupling and computational complexity are provided in detailed. The theoretical analyses and simulation results show the superiority of the proposed arrays and method over the existing techniques.

Robust Direction-of-Arrival Estimation in the Presence of Outliers and Noise Nonuniformity

In direction-of-arrival (DOA) estimation with sensor arrays, the background noise is usually modeled to be uncorrelated uniform white noise, such that the related algorithms can be greatly simplified by making use of the property of the noise covariance matrix being a diagonal matrix with identical diagonal entries. However, this model can be easily violated by the nonuniformity of sensor noise and the presence of outliers that may arise from unexpected impulsive noise. To tackle this problem, we first introduce an exploratory factor analysis (EFA) model for DOA estimation in nonuniform noise. Then, to deal with the outliers, a generalized extreme Studentized deviate (ESD) test is applied for outlier detection and trimming. Based on the trimmed data matrix, a modified EFA model, which belongs to weighted least-squares (WLS) fitting problems, is presented. Furthermore, a monotonic convergent iterative reweighted least-squares (IRLS) algorithm, called the iterative majorization approach, is introduced to solve the WLS problem. Simulation results show that the proposed algorithm offers improved robustness against nonuniform noise and observation outliers over traditional algorithms.

An improved histogram algorithm for DOA estimation based on single vector acoustic system

The integration of a singular vector acoustic system onto an unmanned underwater platform can lead to achieving unambiguous direction finding across the entire space. To enhance the direction-finding capabilities of the single vector acoustic system for low noise target, a refined histogram algorithm utilizing coherent spectrum weighting is suggested. A comparative evaluation and analysis of the target azimuth estimation performance of the enhanced histogram algorithm, traditional frequency-weighted histogram algorithm, and energy-weighted histogram algorithm are carried out. Through computer simulations, it is observed that the three Direction of Arrival (DOA) algorithms exhibit comparable direction-finding capabilities for wideband signals, whereas for single-frequency signals, the improved histogram algorithm surpasses the two conventional algorithms in direction-finding accuracy. Specifically, at a signal-to-noise ratio (SNR) of −40 dB, the azimuth estimation root mean square error (RMSE) is approximately 2°. Findings from sea trials indicate that the improved histogram algorithm displays a narrower spectral peak width and robust resistance to noise interference, thereby substantiating the effectiveness of the enhanced histogram algorithm.

High-resolution direction-finding algorithm using Qth−order cumulants tensor: Q−TMUSIC

To resolve more sources than sensors, the 2q−MUSIC algorithm has been developed recently by rearranging the 2qth−order circular cumulants tensor into a suitable size matrix. However, in 2q−MUSIC, the angular resolution and estimation accuracy have not attained their optimum values due to the loss of differential information by matricizing the cumulants tensor. This paper proposes a subspace-based MUSIC-like algorithm, namely Qth−order cumulants-based tensor MUSIC algorithm for the direction of arrival (DOA) estimation of statistically independent non-Gaussian sources by exploiting the Qth−order cumulants tensors, Q∈{3,4,5,⋯}, directly using multilinear algebra tools. The proposed algorithm offers an improved DOA estimation performance in terms of angular resolution and estimation accuracy compared to their equivalent matrix-based Q−MUSIC. Moreover, the computational complexity of the proposed Q-TMUSIC is lesser than that of their equivalent matrix-based Q−MUSIC for Q>4. However, the proposed Q−TMUSIC can identify atmost (M−1) sources using an array of M−sensors than that of (M⌊Q2⌋−1) with their equivalent matrix based Q−MUSIC.

Closed-Form Method for Unified Far-Field and Near-Field Localization Based on TDOA and FDOA Measurements

When the near-field and far-field information of a target is uncertain, it is necessary to choose a suitable localization method. The modified polar representation (MPR) method integrates the two scenarios and achieves a unified localization with direction of arrival (DOA) estimation in the far field and position estimation in the near field. Previous studies have only proposed solutions for stationary environments and have not considered the motion factor. Therefore, this paper proposes a new unified positioning algorithm using multi-sensor time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements without prior target source information. The method represents the position of the target source using MPR and describes the localization problem as a weighted least squares (WLS) problem with two constraints. We first obtain the initial estimates by WLS without considering the constraints and then investigate a two-step error correction method based on the constraints. The first step corrects the initial estimate using the Taylor series expansion technique, and the second step corrects the DOA estimate in the previous step using the direct error compensation technique based on the properties of the second constraint. Simulation experiments show that the method is effective for the unified positioning of moving targets and can achieve the Cramer–Rao lower bound (CRLB).

Multi-task recognition of modulation types and arrival directions of underwater acoustic signals based on convolutional neural networks

Abstract Nowadays, underwater acoustic communication reconnaissance technology is of great importance in military, marine science, and resource exploration fields. The fields involve military reconnaissance and intelligence collection, ocean monitoring and security, marine scientific research, and resource exploration. This article mainly focuses on the identification of modulation types and emission angles contained in underwater acoustic signals. Convolutional Neural Networks (CNNs) are used for deep learning to train, validate, and obtain final results on signal data. This network achieves the independent tasks of automatic modulation classification and Direction of Arrival (DOA) estimation of radio signals simultaneously. The model achieves efficient identification and filtering by designing different filter sizes and sizes, as well as different Y-shaped connection structures. It includes one input block and two output blocks, and the two output blocks correspond to the outputs of modulation classification and DOA estimation. At the same time, based on this, the parameters of the network layer are modified to achieve the generalization ability of the neural network. The training and validation data of the network consists of simulation data from underwater acoustic communication emissions and real data from the Songhua Lake experiment in Jilin Province, China, to test the network recognition efficiency.

Eliminating quantization errors in classification-based sound source localization

Sound Source Localization (SSL) involves estimating the Direction of Arrival (DOA) of sound sources. Since the DOA estimation output space is continuous, regression might be more suitable for DOA, offering higher precision. However, in practice, classification often outperforms regression, exhibiting greater robustness. Conversely, classification’s drawback is inherent quantization error. Within the classification paradigm, the DOA output space is discretized into several intervals, each treated as a class. These classes show strong inter-class correlations, being inherently ordered, with higher similarity as intervals grow closer. Nevertheless, this characteristic has not been fully exploited. To address this, we propose Unbiased Label Distribution (ULD) to eliminate quantization error in training targets. Furthermore, we introduce Weighted Adjacent Decoding (WAD) to overcome quantization error during the decoding stage. Finally, we tailor two loss functions for the soft labels: Negative Log Absolute Error (NLAE) and Mean Squared Error without activation (MSE(wo)). Experimental results show our approach surpasses classification quantization limits, achieving state-of-the-art performance. Our code and supplementary material are available at https://github.com/linfeng-feng/ULD.

A high-resolution DOA estimation via random forest virtual array extension

In sonar detection, underwater recognition, and similar fields, the challenge of using small-scale arrays is frequently encountered. With small-scale arrays, the degrees of freedom (DOFs) and accuracy of direction of arrival (DOA) estimation decrease significantly. Moreover, existing algorithms are less robust in complex environments and typically require substantial computing resources to ensure accurate estimation. To overcome these problems, this paper proposes a high-resolution DOA estimation via Random Forest virtual array extension (RFVAE). The algorithm first trains the random forest (RF) network using real array element data, and thus proposes a virtual covariance reconstruction technique. This technique allows for a substantial increase in the number of virtual array elements. Then, based on the virtual covariance reconstruction technique, a high resolution estimation network technique is proposed, which can increase the accuracy and DOFs of DOA estimation. Experimental results show that the proposed algorithm reduces error by 30% to 80% compared to recent technologies and can provide up to twice as many virtual elements. Additionally, the estimation speed can be increased by 3 to 1000 times, and it has significantly stronger robustness, functioning normally at signal-to-noise ratios 10 dB lower than the conditions under which other algorithms fail.

DOA Estimation on One-Bit Quantization Observations through Noise-Boosted Multiple Signal Classification.

Due to the low-complexity implementation, direction-of-arrival (DOA) estimation-based one-bit quantized data are of interest, but also, signal processing struggles to obtain the demanded estimation accuracy. In this study, we injected a number of noise components into the receiving data before the uniform linear array (ULA) composed of one-bit quantizers. Then, based on this designed noise-boosted quantizer unit (NBQU), we propose an efficient one-bit multiple signal classification (MUSIC) method for estimating the DOA. Benefiting from the injected noise, the numerical results show that the proposed NBQU-based MUSIC method outperforms existing one-bit MUSIC methods in terms of estimation accuracy and resolution. Furthermore, with the optimal root mean square (RMS) of the injected noise, the estimation accuracy of the proposed method for estimating DOA can approach that of the MUSIC method based on the complete analog data.

Near-field DOA estimation oriented sparse array design via symmetric augmentation of three ULAs

A symmetric sparse array, via symmetric augmentation of three (SAT) uniform linear subarrays, has been designed for direction of arrival (DOA) estimation of uncorrelated near-field or coexisted near-field and far-field narrowband source signals. With an explicit design of the subarray structures and positions, this SAT array 1) involves only two closely spaced antenna pairs (with quarter-wavelength spacing); 2) has a large uniform degree of freedom (uDOF) and difference co-array; 3) can have either even or odd number of antennas; and 4) has closed form expressions for antenna positions, uDOF and weight functions. Simulation results show that the SAT array is superior to the current symmetric sparse arrays in both antenna mutual coupling and consecutive virtual aperture.

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.

DOA method based on CSI and improved neural network

Abstract In wireless communication systems, accurate estimation of signal direction has always been a key research area. Channel State Information (CSI) is an important parameter that can be used to estimate the Direction of Arrival (DOA) of a signal. In order to improve the accuracy and robustness of DOA estimation, this study aims to explore a DOA estimation method based on CSI and improved neural networks. Firstly, the role of CSI in localization technology and related theories are detailed. Subsequently, the application of neural network-based fingerprint matching algorithms, including BP neural networks, Whale Optimization Algorithm (WOA), and chaotic mapping techniques, is analyzed. In light of this, an improved BP neural network integrating chaotic mapping and adaptive weighting is proposed to improve the positioning accuracy and convergence rate of the algorithm. Finally, through the collection and training of experimental data, an algorithm proposed in this article achieves a test set accuracy of 96.4286% and a training set accuracy of 82.7243%. The better training effect is obtained, which verifies the efficacy and superiority of the proposed approach.