Direction Of Arrival Estimation Error Research Articles

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.

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.

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.

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.

Sound source direction-of-arrival estimation method for microphone array based on ultra-weak fiber Bragg grating distributed acoustic sensor.

A sound source direction-of-arrival (DOA) estimation method for microphone array based on ultra-weak fiber Bragg grating (UW-FBG) distributed acoustic sensor is proposed. The principle of acoustic signal demodulation is introduced, the sound pressure sensitivity and frequency response range of a single UW-FBG microphone are analyzed, and a series linear array with three UW-FBG microphones is designed. Combined with convolutional recurrent neural networks, the DOA estimation method is developed. Log-Mel spectral features and SCOT/PHAT joint weighting generalized cross correlation features are used for DOA estimation. The corresponding system is established and experimentally verified. Results show that the measured sound pressure sensitivity of the UW-FBG microphone is in the range of 0.1032-3.306 rad/Pa within the frequency range of 1000-3000 Hz, and the peak sound pressure sensitivity is about 3.306 rad/Pa. The estimated mean error of 2D DOA estimation is about 2.85°, and the error of 3D DOA estimation is about 5.465°. This method has good application prospects in distributed sound source localization.

Effects of internal solitary waves on three-dimensional sound propagation and DOA estimation in the South China Sea

Internal solitary waves (ISWs) in the South China Sea, characterized by their large amplitude and strong nonlinearity, have attracted a lot of attention. In this paper, we use the Massachusetts Institute of Technology general circulation model (MITgcm) to construct the processes of generating and propagating ISWs in the South China Sea from the Luzon Strait to the continental shelf. The simulated east–west flow velocity is compared with remote sensing images, and the results demonstrate the accuracy of the ISW model in the South China Sea. Inserting the simulated three-dimensional (3D) sound speed from the ISW model into the Bellhop3D model, key findings emerge that ISWs cause depressions in the iso-sonic surface, which lead to drastic fluctuations in sound rays and the horizontal refraction effect in the progress of sound propagation. ISWs disturb the convergence zone of sound rays, but the position of the internal wave crest line is consistent with that of the collective deflection of rays. In addition, the results of direction of arrival (DOA) estimation under ISWs demonstrate that the internal wave increases the DOA estimation error. Together, ISWs induce fluctuations in sound propagation and degrade sonar performance. This study creatively combines ISWs with the underwater sound field and DOA estimation, which provides support for the 3D sound propagation mode and the arrangement of the sonar array in the internal wave environment.

High-resolution DOA estimation achieved by a single acoustic vector sensor under anisotropic noise

The acoustic vector sensor (AVS) has a wide application in the direction of arrival (DOA) estimation of sound sources including aircraft, underwater or on-land vehicles, search-and-rescue efforts, etc. The performance of only one acoustic vector sensor can compare favorably with a traditional acoustic array in DOA estimation. The anisotropic noise problem of the vector sensor has had a severe affective on the estimation accuracy and has caused little attention until now. In this paper, an AVS measurement system is designed, and an Anisotropic Sparse Bayesian Learning (SBL) method (the A-SBL method) is proposed to model and estimate the anisotropic noise of the AVS system. A high-resolution DOA estimation method is also introduced based on the noise estimation algorithm. The experimental results exhibit the necessity of modeling the anisotropic noise, and the estimation accuracy of the proposed A-SBL method based on the noise model is verified. The comparison of DOA methods shows the superiority of the proposed method, in which the DOA estimation error is not more than 1°. The proposed method’s utility may be found in applications for localization or tracking of targets with prominent acoustic characteristics when the environment is complicated.

Direction of Arrival Estimation for Single Microelectromechanical Systems Vector Hydrophone Using Modified Wavelet Packet De-Noising

The complex and variable ocean environment introduces complex noise to the signal received by microelectromechanical systems (MEMS) vector hydrophones, which seriously affects target location. To improve the detection efficiency and broaden the application range of vector hydrophone, this paper proposed a novel modified Wavelet packet de-noising method, known as the Wavelet packet energy (WPE) de-noising method. This method utilizes Shannon entropy to determine the optimal decomposition levels of Wavelet packets, and calculates the energy of reconstructed signals in each frequency band to construct feature vectors. The Wavelet packet with the larger energy is selected to reconstruct the signal until the root mean square error of the original signal and the reconstructed signal is minimized. thereby obtaining an optimal solution. The performance of this proposed method is evaluated through both indoor and outdoor experiments. The experimental results demonstrate that the developed method is effective in Direction of Arrival (DOA) estimation of single frequency signals and is feasible in low signal-to-noise ratio situations. The method improves the azimuth discrimination ability of the Minimum Variance Distortionless Response algorithm, and DOA estimation errors are all within 1°. Furthermore, the indoor and outdoor experiments also demonstrate that the WPE de-noising method solves the group delay and distortion of signals caused by conventional filtering.

Direction of arrival estimation for BLE: Antenna array design and evaluation

The use of smart antenna arrays in wireless communication systems is becoming increasingly popular, as they improve the performance of the radio link and allow the integration of communication and sensing functions. In this paper, we present the design and performance evaluation of a uniform circular antenna array (UCAA) with 12 monopole antennas and RF switches to select the active antenna for the signal direction of arrival (DoA) estimation. The antenna configuration was optimized through simulations for a different number of antennas and antenna array radius. The frequency tuning of the antennas considered the coupling of the active antenna with adjacent antennas. The performance of the antenna array was evaluated by (1) simulations that examined the proximity of the antenna to the edge of the antenna array and the influence of adjacent antennas on the performance of the active antenna, and (2) measurements in outdoor and indoor environments. The results of the simulations show that antenna coupling can cause nulls in the radiation pattern, which affects the DoA estimation by reducing the signal-to-noise ratio. In a semi-controlled environment, we achieved a DoA estimation error of less than 1 degree by using the Bluetooth Low Energy (BLE) Angle of Arrival feature.

Research on DOA estimation method of single MEMS vector hydrophone based on pulse signal

With the rapid development and wide application of Micro-Electro-Mechanical System (MEMS) vector hydrophones, it is of higher requirement for the estimation method of direction of arrival (DOA) for a single vector hydrophone in complex environments. Although many classical methods for DOA estimation have been proposed in this field, the DOA estimation method in complex environments, such as multipath effects and reverberation, still needs to be further studied. When the target DOA is estimated in the environment with reflected waves, certain errors will be caused due to the reflection provided that the continuous wave method is used. Moreover, the influence of the reflected wave can be decreased once the pulse wave method is used, but it will low the accuracy due to the poor Signal to noise ratio (SNR) problem simultaneously. For that reason, a solution method for DOA estimation using pulsed waves in a reflective environment has been proposed in this paper. The detailed arrangements of this paper are as follows: firstly, the orientation error caused by the low SNR of the pulsed waves was processed by the segmentation and extraction of the pulsed waves; secondly, the effectiveness of the proposed method was tested by experiments and made a DOA estimation error comparison with the classic continuous wave method; finally, the experimental results showed that when MEMS vector hydrophone DOA was estimated in the reflection environment, the estimation error caused by the reflected wave could be effectively reduced by the method proposed in this paper. A solution method for DOA estimation using pulsed waves in a reflective environment has been proposed in this paper. • A solution method for DOA estimation using pulsed waves in a reflective environment has been proposed in this paper. • The orientation error caused by the low SNR was processed by the segmentation and extraction of the pulsed waves. • The effectiveness of the proposed method was tested by experiments and made a comparison with the continuous wave method.

An Intelligent DOA Estimation Error Calibration Method Based on Transfer Learning

Affected by various error factors in the actual environment, the accuracy of the direction of arrival (DOA) estimation algorithm will greatly decrease during an application. To address this issue, in this paper, we propose an intelligent DOA estimation error calibration method based on transfer learning, which learns error knowledge from a small number of actual signal samples and improves the DOA estimation accuracy in the real application. We constructed a deep convolutional neural network (CNN)-based intelligent DOA estimation model to learn the mapping between the input signals and their azimuths. We generated a large number of ideal simulation signal samples to train the CNN model and used it as the pretrained model. Then, we fine-tuned the CNN model with a small number of actual signal samples collected in the actual environment. We demonstrate the effectiveness of the proposed method through simulation experiments. The experimental results indicate that the proposed method can effectively improve the accuracy of DOA estimation in the actual environment.

DOA-guided source separation with direction-based initialization and time annotations using complex angular central Gaussian mixture models

By means of spatial clustering and time-frequency masking, a mixture of multiple speakers and noise can be separated into the underlying signal components. The parameters of a model, such as a complex angular central Gaussian mixture model (cACGMM), can be determined based on the given signal mixture itself. Then, no misfit between training and testing conditions arises, as opposed to approaches that require labeled datasets to be trained. Whereas the separation can be performed in a completely unsupervised way, it may be beneficial to take advantage of a priori knowledge. The parameter estimation is sensitive to the initialization, and it is necessary to address the frequency permutation problem. In this paper, we therefore consider three techniques to overcome these limitations using direction of arrival (DOA) estimates. First, we propose an initialization with simple DOA-based masks. Secondly, we derive speaker specific time annotations from the same masks in order to constrain the cACGMM. Thirdly, we employ an approach where the mixture components are specific to each DOA instead of each speaker. We conduct experiments with sudden DOA changes, as well as a gradually moving speaker. The results demonstrate that particularly the DOA-based initialization is effective to overcome both of the described limitations. In this case, even methods based on normally unavailable oracle information are not observed to be more beneficial to the permutation resolution or the initialization. Lastly, we also show that the proposed DOA-guided source separation works quite robustly in the presence of adverse conditions and realistic DOA estimation errors.

Direction-of-arrival estimation by asymmetric amplitude interpolation

Amplitude comparison is a traditional method to estimate Direction-of-arrival(DOA) based on beamforming. Due to its low computational complexity, the method has been widely used in many fields especially for radar and sonar systems. However, the original “amplitude comparison” method considers the spatial spectrum and beampattern to be axis-symmetric, and the DOA estimation error rises sharply when the true DOA deviates from 0°. Considering the beamwidth difference between the left and right halves, asymmetric method is presented in this paper. Linear, quadratic and Gaussian interpolation methods are revised to be asymmetric through theoretical derivation. Asymmetric interpolation functions are adjusted to the steering angle. Furthermore, the influence of signal-to-noise ratio(SNR) is analyzed, and an amendment is employed to improve the robustness of the method at low SNR. Compared with the symmetric methods, the asymmetric methods can reduce the DOA estimation error significantly. The effectiveness of the proposed methods are demonstrated by numerical simulation and processing of experimental data on the lake.

Interpolating the Directional Room Impulse Response for Dynamic Spatial Audio Reproduction

Virtual reality (VR) is increasingly important for exploring the real world, which has partially moved to virtual workplaces. In order to create immersive presence in a simulated scene for humans, VR needs to reproduce spatial audio that describes three-dimensional acoustic characteristics in the counterpart physical environment. When the user moves, this reproduction should be dynamically updated, which provides practical challenges because the bandwidth for continuously transmitting audio and video scene data may be limited. This paper proposes an interpolation approach for dynamic spatial audio reproduction using acoustic characteristics of direction and reverberation at limited numbers of positions, which are represented using a first order Ambisonics encoding of the room impulse response (RIR), called the directional RIR (DRIR). We decompose two known DRIRs into reflection components, before interpolating early dominant components for DRIR synthesis and utilizing DRIR recordings for accuracy evaluation. Results indicate that the most accurate interpolation is obtained by the proposed method over two comparative approaches, particularly in a simulated small room where most direction of arrival estimation errors of early components are below five degrees. These findings suggest precise interpolated DRIRs with limited data using the proposed approach, which is vital for dynamic spatial audio reproduction for VR applications.

A Spatially Confined, Platform-Based HF Direction Finding Array

A spatially-confined, platform-based HF antenna array with enhanced bandwidth and direction-finding (DF) accuracy is presented. As the HF band is widely used in many important civilian and military applications, HF DF systems are of great interest in electronic warfare support applications. However, due to the large wavelength, practical DF arrays mounted on moving platforms tend to be electrically small, resulting in fundamental limitations on antenna bandwidth and DF accuracy. Furthermore, many applications require mounting the array at a single location on the platform due to limited space and mobility considerations. To alleviate these issues, we employ the platform as the major radiator by exciting several of its significant characteristic modes (CMs) using a spatially-confined antenna array. Specifically, we examined four DF array designs mounted on a representative, mid-size passenger airplane operating at 10 MHz in simulation, each of which is confined within a virtual sphere with a 3-m diameter. A scaled model of one design was fabricated and characterized. Cramer-Rao bounds and Monte-Carlo test results are also reported. Our results demonstrate that the proposed DF array can provide a 15% lower DoA estimation error than the theoretical limit of a standalone array possessing the same volume and having the same bandwidth.

Monopulse based DOA and polarization estimation with polarization sensitive arrays

In this paper, the vector sensor array (VSA) and the scalar sensor array (SSA) with polarization sensitivity (PS) are placed under the same framework of polarization sensitive arrays (PSAs), whose direction-dependent PS factor is larger than zero. This commonality of their PS factors enables both VSA and SSA to perform polarization estimation effectively. Based on this new PSA model, a generalized monopulse algorithm is proposed to jointly estimate direction-of-arrival (DOA) and polarization parameters, by expanding the existing monopulse angle estimation in spatial domain to both spatial and polarization domains. Both the DOA and polarization parameters can be effectively and efficiently estimated by comparing the outputs of the sum and spatial/polarized difference beams with only one snapshot. Then, closed-form expressions for joint DOA and polarization estimation error variances are derived and the polarization estimation variance is proved to decrease monotonically with the PS factor. Simulations are carried out on an X-band 5×5 planar array composed of microstrip patch antennas to demonstrate the effectiveness of the proposed algorithm.

2D Direction of Arrival Estimation Using Uniform Circular Arrays With Radiation Pattern Reconfigurable Antennas

This paper focuses on direction of arrival (DoA) estimation using adaptive arrays that consist of radiation pattern reconfigurable antenna (RPRA) elements for 2D direction finding (i.e., azimuth and elevation DoA estimation). In particular, uniform circular arrays (UCAs) are explored that use RPRA elements with two different elevation radiation pattern states to achieve unambiguous estimates over all possible incident angles. Theoretical cardioid-type directional patterns are investigated to determine the pattern states that minimize overall DoA estimation error, and the performance of 3-, 4-, and 5-element RPRA UCAs is compared with baseline theoretical arrays composed of isotropic elements. The results demonstrate that RPRA UCAs with optimized cardioid patterns can achieve similar accuracy to the baseline arrays, but with fewer antennas/front-ends. For example, a 4-element RPRA UCA can achieve approximately the same root mean square error (RMSE) as a 6-element uniform spherical array composed of isotropic elements. Furthermore, unambiguous estimates can be achieved over all incident angles with electrically large UCA radii using optimized RPRA elements, which can further improve accuracy and increase bandwidth. To demonstrate the feasibility of the technique, a practical RPRA was designed at 6 GHz with a pattern that approximates the optimized cardioid, and the performance meets or exceeds the theoretical pattern performance for RMSEs less than 3°.

Maximum Element Dichotomous Coordinate Descent Based Minimum Variance Distortionless Response DoA Estimator

In this paper, we devise an efficient approach for estimating the direction of arrival (DoA). The proposed DoA estimation approach is based on minimum variance distortionless response (MVDR) criteria within a recursive least squares (RLS) framework. The dichotomous coordinate descent algorithm is used to modify the calculation of the output power spectrum, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance. A numerical comparison confirms that the proposed DoA estimator outperforms the conventional RLS DoA estimator in terms of the computational complexity and DoA estimation error. Finally, the proposed theoretical DoA estimator is implemented on a field-programmable gate array (FPGA) board to verify the feasibility of the method. The numerical results of a fixed-point implementation demonstrate that the performance of the proposed method is very close to that of its floating-point counterpart.

Fast digital multi-beam search method for active phased array antenna system with full azimuth beam steering

This paper proposes a multi-beam search method based on an active phased array antenna system using digital beamforming. It includes initial beamforming, valid beam selection, and beam angle estimation using phase comparison mono pulses for multi-channel signals. To verify DoA estimation error, simulation and measurement are performed using the proposed antenna system. As a result, we confirm the performance of estimating each channel's angle and the beam directional error within 0.5°.

Alternative Formulation of Antenna Arrays for DF Systems Considering Active-Element Patterns and Scattering Matrices.

Direction finding (DF) systems are used to determine the direction-of-arrival (DoA) of electromagnetic waves, thus allowing for the tracking of RF sources. In this paper, we present an alternative formulation of antenna arrays for modeling DF systems. To improve the accuracy of the data provided by the DF systems, the effects of mutual coupling in the array, polarization of the received waves, and impedance mismatches in the RF front-end receiver are all taken into account in the steering vectors of the DoA algorithms. A closed-form expression, which uses scattering parameter data and active-element patterns, is derived to compute the receiver output voltages. Special attention is given to the analysis of wave polarization relative to the DF system orientation. Applying the formulation introduced here, a complete characterization of the received waves is accomplished without the need for system calibration techniques. The validation of the proposed model is carried out by measurements of a 2.2 GHz DF system running a MUSIC algorithm. Tests are performed with a linear array of printed monopoles and with a planar microstrip antenna array having polarization diversity. The experimental results show DoA estimation errors below 6° and correct classification of the polarization of incoming waves, confirming the good performance of the developed formulation.