Direction Of Arrival Of Signals Research Articles

Sparsity-based direction-of-arrival estimation in the presence of near-field and far-field interferences for small-scale platform sonar arrays.

For the sonar arrays mounted on an unmanned underwater vehicle (UUV), the direction-of-arrival (DOA) estimation of the far-field (FF) weak sources is influenced by the near-field (NF) interferences generated from the radiated self-noise of the UUV and the FF interferences simultaneously. To address the problem, a sparsity-based DOA estimation method resistant to the NF and FF interferences is proposed in this paper. This method isolates the FF signals from the NF signals by sparse reconstruction. Additionally, subspace projection is applied to address the masking problem of the weak target signal by the strong interferences in the spatial domain, effectively enhancing the capacity of estimating the DOA of the weak target signal in the presence of strong interferences. Numerical simulations and experimental results demonstrate the effectiveness of the proposed method. Compared to other advanced DOA estimation methods, the proposed method exhibits better DOA estimation performance in the presence of strong NF and FF interferences.

Solar flare observations with the Radio Neutrino Observatory Greenland (RNO-G)

The Radio Neutrino Observatory – Greenland (RNO-G) seeks discovery of ultra-high energy neutrinos from the cosmos through their interactions in ice. The science program extends beyond particle astrophysics to include radioglaciology and, as we show herein, solar observations, as well. Currently seven of 35 planned radio-receiver stations (24 antennas/station) are operational. These stations are sensitive to impulsive radio signals with frequencies between 80 and 700 MHz and feature a neutrino trigger threshold for recording data close to the thermal floor. RNO-G can also trigger on elevated signals from the Sun, resulting in nanosecond resolution time-domain flare data; such temporal resolution is significantly shorter than from most dedicated solar observatories. In addition to possible RNO-G solar flare polarization measurements, the Sun also represents an extremely useful above-surface calibration source.Using RNO-G data recorded during the summers of 2022 and 2023, we find signal excesses during solar flares reported by the solar-observing Callisto network and also in coincidence with ∼2/3 of the brightest excesses recorded by the SWAVES satellite. These observed flares are characterized by significant time-domain impulsivity. Using the known position of the Sun, the flare sample is used to calibrate the RNO-G absolute pointing on the radio signal arrival direction to sub-degree resolution. We thus establish the Sun as a regularly observed astronomical calibration source to provide the accurate absolute pointing required for neutrino astronomy.

Adaptive Joint Carrier and DOA Estimations of FHSS Signals Based on Knowledge-Enhanced Compressed Measurements and Deep Learning.

As one of the most widely used spread spectrum techniques, the frequency-hopping spread spectrum (FHSS) has been widely adopted in both civilian and military secure communications. In this technique, the carrier frequency of the signal hops pseudo-randomly over a large range, compared to the baseband. To capture an FHSS signal, conventional non-cooperative receivers without knowledge of the carrier have to operate at a high sampling rate covering the entire FHSS hopping range, according to the Nyquist sampling theorem. In this paper, we propose an adaptive compressed method for joint carrier and direction of arrival (DOA) estimations of FHSS signals, enabling subsequent non-cooperative processing. The compressed measurement kernels (i.e., non-zero entries in the sensing matrix) have been adaptively designed based on the posterior knowledge of the signal and task-specific information optimization. Moreover, a deep neural network has been designed to ensure the efficiency of the measurement kernel design process. Finally, the signal carrier and DOA are estimated based on the measurement data. Through simulations, the performance of the adaptively designed measurement kernels is proved to be improved over the random measurement kernels. In addition, the proposed method is shown to outperform the compressed methods in the literature.

Adaptive track approach for multiple sources scenarios during radar survey for space surveillance applications

The increasing population of resident space objects is currently fostering many space surveillance initiatives, which rely on the use of on-ground sensors. In particular, survey radars allow to first characterise the target orbit from a single transit, through measurements which are Doppler shift, slant range and angular profile. In this framework, the Music Approach for Track Estimate and Refinement (MATER) algorithm was developed to compute the angular track through the MUltiple SIgnal Classification (MUSIC), by solving possible ambiguities which may arise because of the receiver array geometry.This work presents the MATER extension to the case in which multiple sources are simultaneously detected by the sensor. For each detected source, the signal Direction of Arrival (DOA) is computed through MUSIC, and, if no prediction is exploited, possible ambiguous solutions arise. The computation is repeated for the entire observation, and all the estimations related to a specific target are grouped based on the angular sequence shape and the detection epochs. Finally, the possible ambiguity problem is solved, and the angular profile is obtained through a quadratic regression in time.The algorithm is numerically tested on a survey observation simulation. The detection length depends on the impinging signal intensity, and the angular accuracy is in the order of 1e-03 deg. A sensitivity analysis highlights that a transmitted power decrease shortens the detection length, with no remarkable angular accuracy deterioration. An additional simulation shows that in proximity operation monitoring MATER performance depends on the mutual geometry between target and chaser, as it may bring down the reciprocal angular distance under the resolution level. Nevertheless, it is always possible to identify the presence of both sources through the eigenvalues analysis of the signal correlation matrix. Finally, the simulation of a fragments cloud observation highlights that MATER performance depends both on the size of the observed fragment, as this is strictly linked to the signal detected by the receiver, and on the simultaneous detection of other fragments with a more effective signal.

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.

Research on direction of arrival estimation for mixed broadband signals

In practical applications, the signals received by a hydrophone array include coherent and incoherent signals, while estimating the direction of arrival (DOA) of coherent or incoherent signals has been studied for simplicity with poor performance for a mixed signal. The present study proposes a novel approach for estimating the DOA of mixed broadband signals to solve this problem, namely the oblique method. The unitary oblique method is simultaneously proposed to improve operational efficiency with the complex matrix shifted into a real valued matrix through a unitary transform. For independent signals, the incoherent signal subspace method (ISSM) is used to estimate the DOA. Matrix difference and oblique projection methods are adopted for multi-group coherent signals in order to eliminate the influence of incoherent signals and other groups of coherent signals. For broadband signals, the Tasseled Cap Transformation focusing transform is utilized to convert the broadband signal to the focusing frequency, and then the high-resolution Multiple Signal Classification algorithm method is employed to solve the problem. Simulation results indicate that the oblique method reconciles DOA estimation performance and computational efficiency and can be extended to other types of arrays.

DOA Estimation of Ultrasonic Signal by Indirect Phase Shift Determination

The paper presents the concept of the method of determining the direction of ultrasonic signal arrival, i.e., the azimuth and elevation angles. This method is an extension of the previous approach which was proposed to determine only the azimuth angle. The approach is based on the indirect phase determination. This makes it possible to tolerate spacing of receivers greater than half the wavelength of the received signal. At the same time, it provides increased measurement accuracy and reduced hardware requirements. To check the robustness of the method, simulations were carried out for the geometric arrangement of the receivers of the sonar module, for which the method was then implemented. This sonar module was used in the conducted experiments. The results of these simulations and experiments are included in the paper and discussed.

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Direction of Arrival Estimation Method Based on Eigenvalues and Eigenvectors for Coherent Signals in Impulsive Noise

In this paper, a Toeplitz construction method based on eigenvalues and eigenvectors is proposed to combine with traditional denoising algorithms, including fractional low-order moment (FLOM), phased fractional low-order moment (PFLOM), and correntropy-based correlation (CRCO) methods. It can improve the direction of arrival (DOA) estimation of signals in impulsive noise. Firstly, the algorithm performs eigenvalue decomposition on the received covariance matrix to obtain eigenvectors and eigenvalues, and then the Toeplitz matrix is created according to the eigenvectors corresponding to its eigenvalues. Secondly, the spatial averaging method is used to obtain an unbiased estimate of the Toeplitz matrix, which is then weighted and added based on the corresponding eigenvalues. Next, the noise subspace of the Toeplitz matrix is reconstructed to obtain the one that has less angle information. Finally, the DOA of the coherent signal is estimated using the Multiple Signal Classification (MUSIC) algorithm. The improved method based on the Toeplitz matrix can not only suppress the effect of impulsive noise but can also solve the problem of aperture loss due to its decoherence. A series of simulations have shown that they have better performances than other algorithms.

COUPLED C-ESPRIT-BASED AZIMUTH AND ELEVATION ANGLE ESTIMATION WITH MINIMUM VARIANCE

This paper presents a method for conjugate estimation of azimuth and elevation angles based on the minimum variance C-ESPRIT method. The conjugate estimation method with minimum variance is a modification of the robust method based on the ESPRIT method with minimum variance and differs from it in that it does not require prior matching of signal duplicates. When modeling the signal acquisition from a unmanned aerial vehicle and processing it with the ESPRIT method, the data were distorted. Several signals were not displayed and noise appeared, which prevented the estimation of the signal arrival direction. The paper presents an efficient algorithm that can estimate the direction of arrival based on uncorrelated and one-dimensional signals. The method of conjugate estimation with minimum variance, when compared to the method of conjugate estimation without minimum variance, has been shown to improve the signal by a factor of 10. This improvement in signal quality allows one to conclude that the method is highly efficient. The C-ESPRIT-based minimum variance conjugate azimuth and location angle estimation method uses a robust minimum variance method with a conjugate rotation matrix to process a second subarray of data. An important aspect of the method is that it uses information from all array elements without grouping them and without computing the mean of the covariance matrices.

Spatial Filtering of Signals under Imprecise Calibration of Antenna Arrays

Introduction. Spatial filtering of signals is performed for the selection the signals of interest when the signals spectra overlap. The quality of spatial filtering depends on the accuracy of antenna array (AA) calibration, which allows estimation of the amplitude-phase distribution (APD) at all possible directions of arrival, thus ensuring the identity of reception paths. A mismatch between the actual and measured APD values leads to quality degradation in all spatial filtering methods.Aim. To develop a method for improving the quality of signal spatial filtering based on the estimates of the desired and interfering signal arrival directions formed by the MUSIC and ESPRIT algorithms under a priori uncertainty and imprecise AA calibration.Materials and methods. The quality of spatial filtering is improved by rejecting the interfering signals unsuppressed due to imprecisely measured APD of an AA. Statistical simulation modeling was carried out in the MATLAB environment; the data obtained experimentally were analyzed.Results. A method for spatial filtering based on MUSIC and ESPRIT completed with an additional rejection of unsuppressed interfering signals due to imprecise AA calibration is developed. An algorithm for basis construction for rejection under of a priori uncertainty of the signal-interference environment is substantiated. The results of statistical simulation modeling and experimental data processing have shown the feasibility of additional rejection applied to the selected signals by spatial filtering.Conclusion. The developed method for spatial filtering under the conditions of a priori uncertainty of the signal-interference situation and imprecise calibration of AA and reception paths ensures high quality characteristics across a wide dynamic range of desired and interfering signals. Whereas the Capon's method, which requires a priori knowledge of the arrival direction of the desired signal or its estimation, is capable of selecting only weak signals and suppressing strong ones under the conditions of imprecise APD.

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

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

A Novel Underdetermined Blind Source Separation Algorithm of Frequency-Hopping Signals via Time-Frequency Analysis

To address the significant performance degradation of conventional underdetermined blind source separation algorithms for frequency-hopping (FH) signals under time-frequency (TF) overlapping conditions, this paper presents a novel three-stage scheme based on the TF distribution of FH signals. In the first stage, key parameters of the FH signal are estimated using a TF binary graph. In the second step, the initial mixing matrix is estimated for non-overlapping and overlapping carrier frequencies employing density peaks clustering and tensor decomposition methods, respectively. In the third step, the final mixing matrix, directions of arrival (DOA), and source signals are estimated using the expectation-maximization algorithm within the nonnegative matrix factorization model. Finally, different segments of the FH signals are spliced together based on the DOAs of different source signals. Comprehensive experimental results demonstrate the superior performance of the proposed algorithm compared to state-of-the-art algorithms. Even at a signal-to-noise ratio of 5 dB, the correlation coefficient of the estimated source signals can still reach 0.91.

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

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.

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.

An Enhanced Spatial Smoothing Technique of Coherent DOA Estimation with Moving Coprime Array.

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios.

Performance Comparison of Several Algorithms for Localization of Wideband Sources

In recent years, researchers have tried to estimate the direction-of-arrival (DOA) of wideband sources and several novel techniques have been proposed. In this paper, we compare six algorithms for calculating the DOA of broadband signals, namely coherent subspace signal method (CSSM), two-sided correlation transformation (TCT), incoherent multiple signal classification (IMUSIC), test of orthogonality of frequency subspaces (TOFS), test of orthogonality of projected subspaces (TOPS), and squared TOPS (S-TOPS). The comparison is made through computer simulations for different parameters, such as signal-to-noise ratio (SNR), in order to establish the efficiency and performance of the discussed methods in noisy environments. CSSM and TCT require initial values, but the remaining approaches do not need any preprocessing.

Satellite Interference Source Direction of Arrival (DOA) Estimation Based on Frequency Domain Covariance Matrix Reconstruction.

Direction of arrival (DOA) estimation is an effective method for detecting various active interference signals during the satellite navigation process. It can be utilized for both interference detection and anti-interference applications. This paper proposes a DOA estimation algorithm for satellite interference sources based on frequency domain covariance matrix reconstruction (FDCMR) to address various types of active interference that may occur in the satellite navigation positioning process. This algorithm can estimate the DOA of coherent signals from multiple frequency points under low signal-to-noise ratio (SNR) conditions. The signals received from the array are transformed from the time domain to the frequency domain using a fast Fourier transform (FFT). The data corresponding to the frequency point of the target signal is extracted from the signal in the frequency domain. The frequency domain covariance matrix of the received array signals is reconstructed by utilizing its covariance matrix property. The spatial spectrum search method is used for the final DOA estimation. Simulation experiments have shown that the proposed algorithm performs well in the DOA estimation under low SNR conditions and also resolves coherency. Moreover, the algorithm's effectiveness is verified through comparison with three other algorithms. Finally, the algorithm's applicability is validated through simulations of various interference scenarios.

Polarization Direction of Arrival Estimation Using Dual Algorithms Based on Time-Frequency Cross Terms

In radar array signal processing, weak nonstationary polarization signal direction of arrival (DOA) estimation is a challenging and significant issue when both strong and weak nonstationary signals coexist. Time-frequency (T-F) analysis is an effective method to deal with nonstationary signals. In the last decade, spatial time-frequency distributions (STFDs) have been proposed for multiple dual-polarization antenna arrays and efficaciously used for nonstationary signal DOA estimation. In this article, we introduced a novelty means for estimating weak nonstationary polarization signal DOA by utilizing spatial polarimetric time-frequency distributions (SPTFDs) of cross terms when there are strong nonstationary polarization interference signals and additive Gaussian white noise. The cross terms’ SPTFDs are considered via a replaceability matrix for data covariance in multiple signal classification (MUSIC) and the estimation of signal parameters using the rotational invariance technique (ESPRIT). Combining the STFDs of cross terms with polarization information about weak nonstationary signals improves signal DOA estimation accuracy. The combined MUSIC and ESPRIT are used in the algorithm to further ensure the success probability and accuracy of DOA estimation. Through simulation analyses, the proposed algorithm is more suitable for the required application scenarios than other algorithms and is superior to other algorithms.