Direction Of Arrival Algorithm Research Articles

High-Resolution and Robust One-Bit Direct-of-Arrival Estimation via Reweighted Atomic Norm Estimation.

In recent years, one-bit quantization has attracted widespread attention in the field of direction-of-arrival (DOA) estimation as a low-cost and low-power solution. Many researchers have proposed various estimation algorithms for one-bit DOA estimation, among which atomic norm minimization algorithms exhibit particularly attractive performance as gridless estimation algorithms. However, current one-bit DOA algorithms with atomic norm minimization typically rely on approximating the trace function, which is not the optimal approximation and introduces errors, along with resolution limitations. To date, there have been few studies on how to enhance resolution under the framework of one-bit DOA estimation. This paper aims to improve the resolution constraints of one-bit DOA estimation. The log-det heuristic is applied to approximate and solve the atomic norm minimization problem. In particular, a reweighted binary atomic norm minimization with noise assumption constraints is proposed to achieve high-resolution and robust one-bit DOA estimation. Finally, the alternating direction method of multipliers algorithm is employed to solve the established optimization problem. Simulations are conducted to demonstrate that the proposed algorithm can effectively enhance the resolution.

Joint DOA-Distance Estimation Method for Radar Using a Novel Time-Domain Wideband Synthesis System

In this paper, a joint direction of arrival (DOA) and distance estimation (JDDE) method using a novel time-domain wideband synthesis signal system is proposed. In contrast to traditional time-domain synthesis methods, which transmit sub-pulses separately, a uniform linear array is used, and all stepped linear frequency modulated (SLFM) sub-pulses are transmitted simultaneously. The echo signal is mixed with each transmitted signal of the corresponding antenna and filtered to separate the single-frequency components from different targets and array elements for synthesis. Single-frequency components have different frequencies and discontinuous phases due to wave-way differences. To solve the problem that single-frequency components cannot be synthesized directly, the frequency and phase of single-frequency components need to be calibrated, including frequency conversion and phase shift, which require DOA information of the targets. Consequently, a high-precision DOA algorithm that employs phase difference fitting, along with the corresponding generic phase unwrapping algorithm, is designed for the characteristics of the arrays and signal system in this paper. After obtaining the DOA information, the wideband synthesis algorithm is applied to synthesize the single-frequency components to obtain high-resolution ranging results. The theoretical analysis and simulation results show that the method has high distance resolution and JDDE accuracy. In a multi-target environment, the number of targets is not limited by the number of antennas. In addition, unlike traditional wideband synthesis methods, the method utilizes multiple transmitting antennas to send SLFM signal pulses simultaneously rather than sequentially, which enhances the response speed of the radar.

DOA Estimation of Underwater Acoustic Array Signal Based on Wavelet Transform With Double Branch Convolutional Neural Network

In underwater acoustic communications, a hydrophone array is often used to receive the underwater acoustic signals to improve the gain of the received signal. The direction of arrival (DOA) estimation is a basic task in underwater acoustic array signal processing. In underwater signal transmission, due to the channel complexity, a large signal transmission loss, and heavy noise interference, the received signal is seriously distorted, and the DOA estimation is poor. In order to improve the accuracy of DOA estimation for underwater acoustic array signals, in this work, we propose continuous wavelet transform with convolutional neural network (CWT-CNN) method. We use a linear factor to improve the calculation process of continuous wavelet transform. The characteristics of time-frequency fusion of signals are calculated by constructing time-frequency array model with modified wavelet factors. The fused features are then used to train the proposed double branch CNN. As compared with other DOA algorithms based on neural networks, the proposed algorithm shows a 5%–20% higher accuracy and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.479^{\circ }-1.172^{\circ }$</tex-math></inline-formula> lower RMSE at 7 different values of SNR. In addition, the proposed algorithm is less computationally complex.

A Joint Angle and Frequency Spectrum Estimation Algorithm Using Difference Coarray

The spectrum sensing that jointly estimates direction-of-arrival (DOA) and frequency spectrum is an important issue for cognitive radio. Existing off-grid DOA estimation algorithms using difference coarray require a large number of snapshots to guarantee the estimation accuracy. Meanwhile, inaccurate DOA estimation renders inaccurate frequency spectrum estimation due to coupled estimation process. In order to overcome these disadvantages, we propose a joint angle and frequency spectrum estimation algorithm using difference coarray in this work. The proposed algorithm first transforms the received signal into the coarray domain and then adopts an “estimate and subtract” method to separate multiple signals. Subsequently, the DOA estimate of each source is corrected iteratively based on the proposed simple interpolation method. Finally, the frequency spectra are obtained by estimating the frequency response matrix based on the previous estimated DOAs. The shortage of requiring a large number of snapshots are overcome by utilizing the deterministically orthogonal signal model in which the signals are completely uncorrelated. Simulation results demonstrate the effectiveness of the proposed algorithm for off-grid DOA and frequency spectrum estimation using difference coarray with few snapshots.

Low-Elevation Target DOA Estimation Based on Multi-Scattering Center Equivalent Model

In very-high-frequency (VHF) radar, the direction-of-arrival (DOA) estimation performance of low-angle targets tracking is strongly affected by the multipath phenomenon. Especially in the complex terrain conditions, the multipath echo comes from a region where the different scattering media make the multipath echo show the characteristics of multi-channel and uneven energy distribution. In this case, the received signal mismatches with the signal model, which leads to performance degradation and even failure of the traditional DOA algorithm. To deal with this problem, the authors propose a new signal model based on multiple scattering center. A multipath signal equivalent model is deduced and analyzed using multipath vector synthesis. Subsequently, the fitness function is established based on the equivalent model, and the target elevation angle is estimated by particle swarm optimization (PSO) algorithm. Simulation results and real data analysis show that the proposed model and algorithm can effectively improve the DOA estimation accuracy of low elevation target under complex terrain and less snapshot condition.

Robust high-resolution direction-of-arrival estimation method using DenseBlock-based U-net.

Direction-of-arrival (DOA) estimation is widely used in underwater detection and localization. To address the high-resolution DOA estimation problem, a DenseBlock-based U-net structure is proposed in this paper. U-net is a U-shaped fully convolutional neural network, which yields a two-dimensional image. DenseBlock is a more efficient structure than typical convolutional layers. The proposed network replaces the concatenated convolutional layers in the original U-net with DenseBlocks. Through training, the network can remove the interference of sidelobes and noise in a conventional beam forming bearing-time record (BTR) and get a clean BTR; hence, this method has narrow beam width and few sidelobes. In addition, the network can be trained by simulation data and applied in actual data when the simulated and actual data are similar in BTR features, so the method has high generalization. For a multi-target problem, the network does not need to be trained on all cases with different target quantities and therefore can reduce the training set size. As a data-driven method, it does not rely on prior assumptions of the array model and possesses better robustness to array imperfections than typical model-based DOA algorithms. Simulations and experiments verify the advantages of the proposed method.

An Overview of Direction-of-Arrival Estimation Methods Using Adaptive Directional Time-Frequency Distributions

Direction of arrival (DOA) is one of the essential topics in array signal processing that has many applications in communications, smart antennas, seismology, acoustics, radars, and many more. As the applications of DOA estimation are broadened, the challenges in implementing a DOA algorithm arise. Different environments require different modifications to the existing methods. This paper reviews the DOA algorithms in the literature. It evaluates and compares the performance of the three well known algorithms, including MUSIC, ESPRIT, and Eigenvalue Decomposition (EVD), with and without using adaptive directional time–frequency distributions (ADTFD) at the preprocessing stage. We simulated a case with four sources and three receivers. The sources were well separated. Signals were received at each sensor with an SNR value of −5 dB, 0 dB, 5 dB, and 10 dB. The angles of the sources were 15, 30, 45, and 60 degrees. The simulation results show that the ADTFD algorithm significantly improved the performance of MUSIC, while it did not provide similar results for the ESPRIT and EVD methods. As expected, the computation time of the algorithms was increased by implementing the ADTFD algorithm as a preprocessing step.

Design of efficient single target real-time beam tracking system

This paper builds a system for real-time tracking of a single target Radio Frequency (RF) signal source, in which the transmitter uses a low-cost HackRF One software radio transceiver platform, and the receiving antenna array uses two monopole antennas to form a 1×2 receiving array. The receiver uses Xilinx 7-Series development board Zedboard and AD9361 RF transceiver to build a wireless receiving platform to process the received signal. In this RF beam tracking system, it needs to perform Direction of Arrival (DOA) estimation on the calibrated signal, the DOA algorithm plays a crucial role in the accuracy of beam pointing and system running time, the MUSIC algorithm takes some time to conduct spectrum peak search, so the Root-Music algorithm is used here to avoid the spectrum peak search problem. To enable the Root-MUSIC algorithm to be better executed on this two-element receiving platform, this work simplifies the entire calculation process, requiring only a small amount of calculation and running time to complete the DOA estimation step, which effectively save FPGA processing time and computing resources. It provides a guarantee for the real-time performance of the system.

Detection, Estimation and Radiation Formation Using Smart Antennas for the Spatial Location

The Electromagnetic (EM) waves are impinging on the base station from all the directions, Equally Spaced Uniform Linear Antenna Array (ESULA) are used to process these incoming EM waves to Detect and Estimate the directions of the mobile transmitters. After the process of Detection and Estimation, Electronic Beamforming is used to provide the narrow sharper beam towards the detected user. This Detection, Estimation and Beamforming plays a key role in variety of use cases like Radar, Wireless Communication and Sonar based systems. Smart Antenna Systems are implemented using two strategies namely Direction of Arrival (DoA) and Beamforming (BF). Direction of Arrival is a mechanism of Detecting and Estimating the directions of the mobile transmitters. Beamforming on the other hand is a process of transmission of the EM waves towards the source in a specific direction and providing the Spectral Nulls to other Interfering users. To increase the user capacity and to enhance the user experience Spatial Location based Spatial Division Multiple Access (SDMA) technology is used. To improve the overall performance of the smart antenna systems energy and packet delivery is majorly focused on specific source directions rather than using blind transmission strategy. In this paper performance analysis of algorithms for Direction of Arrival methods as well as the Beamforming methods have been performed. Experimental simulations are conducted and comparison is done with respect to Bias, Resolution and Time complexity for the Direction of Arrival methods. Noise Subspace Method (NSM) DoA algorithm consistently delivered the optimal bias, high resolution detection of the user location in spatial domain and provided lesser time complexity for both the scenarios which uses fewer antenna elements or larger number of antenna array elements at the base station. Similarly for the case of Beamforming methods the Mean Square Error and Beam-directions have been compared.

Robust 2-D DOA Estimation in a Polarization Sensitive Single User Environment

Apart from the conventional parameters (such as signal-to-noise ratio (SNR), array geometry and size, and the number of samples), several other factors (e.g., alignment of the antenna elements, polarization parameters) influence the performance of direction of arrival (DOA) estimation algorithms. When all the antenna elements are aligned in the same direction, the polarization parameters uniformly affect the steering vectors, which is the underlying assumption of almost all conventional DOA algorithms. Unfortunately, in this case, for a given set of DOA angles, there exists a range of polarization parameters resulting in a very low SNR across all the antenna elements in the array and vice versa. To avoid this type of unwanted event, different antenna elements must be aligned differently. However, this fact will make almost all commonly used DOA estimation algorithms inoperable since the steering vectors are contaminated unevenly by the polarization parameters. To the best of our knowledge, no work in the literature handles this issue using simple hardware and signal processing techniques even for a single user environment. In this paper, that line of inquiry is pursued. We consider a circular array with the minimum number (i.e., 4) of short dipole antenna elements and propose an antenna alignment scheme. This ensures that at any given point no more than one element will suffer significantly from low SNR due to the contribution of polarization. A thresholding technique to isolate the antenna element after being seriously contaminated by the polarization parameters is developed and analyzed. Two algorithms that are suited for operating reliably in all possible DOA and polarization environments are addressed. The first algorithm follows the working principle of the popular MUSIC algorithm after cleaning the polarization contributions from the non-signal subspace. The other one, which is found as a byproduct of the process of cleaning the non-signal subspace, can estimate the DOA angles in a closed form manner. The implementations of the above algorithms for an arbitrary number of antenna elements greater than or equal to 4 are also presented. Finally, a thorough performance and complexity analysis are illustrated for those two algorithms considering various polarization and DOA scenarios.

Recurrent NEAT Assisted 2D-DOA Estimation With Reduced Complexity for Satellite Communication Systems

Direction-of-arrival (DOA) estimation plays a vital role in the field of array signal processing. However, the need for heavy computing tasks in most traditional DOA algorithms, e.g., multiple signal classification (MUSIC), makes their engineering practicality significantly compromised in satellite communication systems. The neuroevolution of augmenting topologies (NEAT) can quickly search for appropriate topologies and weights of neural network functions, but its computational complexity is still too high for satellite systems. This paper proposes a modified NEAT architecture featuring a recurrent structure (RNEAT) that only needs a small number of phase components of the received signal covariance matrix as inputs to reduce the complexity and simplify the neural network architecture. The proposed RNEAT incorporated with multiple signal classification (RNEAT-MUSIC) features low complexity to achieve high resolution and low complexity simultaneously. Validation has been done by applying the proposed method in a two-dimensional direction of arrival estimation (2D-DOA) problem. Results show that the proposed RNEAT-MUSIC efficiently restricts the scanning region before forwarding the covariance matrix to the MUSIC stage. Consequently, the computational workload is reduced by 3/4 compared with the traditional 2D-MUSIC algorithm while maintaining satisfactory DOA resolution.

DOA Estimation With Non-Uniform Linear Arrays: A Phase-Difference Projection Approach

Phase wrapping is a major problem in direction-of-arrival (DOA) estimation using phase-difference observations. For an antenna pair with an inter-antenna spacing greater than half of the wavelength ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda /2$ </tex-math></inline-formula> ) of the signal, phase wrapping occurs at certain DOA angles leading to phase-difference ambiguities. Existing phase unwrapping methods exploit either frequency or spatial diversity. These techniques work by imposing restrictions on the utilized frequencies or the receiver array geometry. In addition to these restrictions, sensitivity to noise and calibration errors is another limitation of these methods. We propose a grid-less <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">phase-difference projection</i> (PDP) DOA algorithm to overcome these issues. The concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wrapped phased-difference pattern</i> (WPDP) is introduced, which allows us to compute most of the parameters required for DOA estimation in an offline manner. This results in a superior computational speed in real-time compared to methods with similar DOA estimation performance. Simulation results demonstrate the excellent performance of the proposed algorithm, both in terms of accuracy and speed.

Velocity‐independent two‐dimensional direction‐of‐arrival estimation algorithm with three parallel linear arrays

In order to eliminate the influence of acoustic velocity variable on the estimation accuracy when the signal propagates under water, this paper proposes a velocity-independent two-dimensional (2-D) direction-of-arrival (DOA) estimation algorithm with three parallel uniform linear arrays. Based on the double parallel linear arrays (DPLA), this algorithm adds another parallel linear array that is not in the same plane as DPLA, which is called three parallel linear arrays. By employing the matrix signal processing among those three arrays, the acoustic velocity variable can be removed from the expressions of elevation and azimuth. And the azimuth and elevation angles of the target are obtained by linear partitive operation, which does not need spectrum peak search or additional angle matching procedure. The simulation results demonstrate that the proposed algorithm performs better than the traditional 2-D DOA algorithms in the underwater environment of unknown acoustic velocity. Compared with the velocity-independent 2-D DOA algorithm, it has lower computational complexity.

Recurrent networks for direction-of-arrival identification of an acoustic source in a shallow water channel using a vector sensor.

Conventional direction-of-arrival (DOA) estimation algorithms for shallow water environments usually contain high amounts of error due to the presence of many acoustic reflective surfaces and scattering fields. Utilizing data from a single acoustic vector sensor, the magnitude and DOA of an acoustic signature can be estimated; as such, DOA algorithms are used to reduce the error in these estimations. Three experiments were conducted using a moving boat as an acoustic target in a waterway in Houghton, Michigan. The shallow and narrow waterway is a complex and non-linear environment for DOA estimation. This paper compares minimizing DOA errors using conventional and machine learning algorithms. The conventional algorithm uses frequency-masking averaging, and the machine learning algorithms incorporate two recurrent neural network architectures, one shallow and one deep network. Results show that the deep neural network models the shallow water environment better than the shallow neural network, and both networks are superior in performance to the frequency-masking average method.

ICAbasedDoAestimation with minimum input data

AbstractThis paper presents a method for locating electromagnetic sources with an optimized number of measurements by using Independent Component Analysis method. This method can detect the Direction of Arrival (DoA) of sources in special cases such as application of equal number of sensors and sources and detection of sources placed one behind another (overlapped). Simulations and measurements were performed to evaluate the performance of the presented method as well as the comparison to MUSIC and ESPRIT classical algorithms. The ICA method does not only estimate the number of sources, but also has the capability to correlate the DoA of the estimated signal to its source. The advantages and disadvantages of the three methods show the high potential application of the ICA as DoA algorithm.

A Study on Target Detection using Covariance Correlation Matrix of Spatial Adaptive Processing

In this paper, we study for direction of arrival estimation of the desired target in spatial adaptive processing system. The interference signal removed by using the optimal weight of the covariance correlation matrix in order to estimate desired target signal. The spatial adaptive processing system updates the weight of the direction of arrival algorithm to estimate the desired signal. The weight update use an adaptive algorithm such as MUSIC. The optimal weight is obtained by Lagrange multiplier and the covariance correlation matrix. The covariance correlation matrix applies signal phase matching and uses the output power spectrum of the direct of arrival algorithm to estimate the desired target direction. We compare the performance of the proposed method with the existing method by computer simulation. The existing method has poor resolution due to phase errors of 5o and -3o in the estimation of three targets [10o, 20o, 30o]. While, the method proposed in this study accurately estimated the desired three targets. This study proved that the proposed method is superior to the existing method as a result simulation result.

Geolocation of RFIs by Multiple Snapshot Difference Method for Synthetic Aperture Interferometric Radiometer

The presence of unauthorized radio frequency interference (RFI) sources seriously affects the retrieval of brightness temperature of a synthetic aperture interferometric radiometer (SAIR). Postobservation RFI geolocation is important for improving the RFI situation hereafter and mitigating the impact of the identified RFIs. Previous works have demonstrated the potential of using high-/super-resolution direction-of-arrival (DOA) estimation techniques to achieve accurate localization of RFI sources in SAIR imagery. In this article, a multiple snapshot difference method is proposed to further reduce the RFI source geolocation bias. The covariance matrices of the consecutive snapshots with power changed RFIs are picked out and subtracted to cancel out the background scene. A MUSIC-based DOA algorithm is developed. Numerical simulations validate the theoretical correctness and the practical effectiveness of the proposed method.

Time-Varying DOA Tracking Algorithm Based on Generalized Labeled Multi-Bernoulli

Direction of arrival (DOA) tracking for multi-sources is a hot issue in array signal processing. To deal with the problem that sources DOA and their number are time-varying, a DOA tracking algorithm based on Generalized Labeled Multi-Bernoulli (GLMB) filter is proposed. Since the measurement value has only one set of data, the measurement association mapping (MAM) does not match, which leads to deviations in the GLMB filter update step. In this regard, we used the estimated sources number of the previous time step as the measurement number of the current time step, and successfully achieved MAM matching. Subsequently, particle filtering is used to approximate the posterior distribution of DOA, where the particle likelihood function can be calculated by the multi-signal classification (MUSIC) spatial spectrum function. In addition, by exponentially weighting the likelihood function, the number of particles in the high likelihood region of the posterior distribution increases, which makes the GLMB filter pruning and merging operations more effective. Simulation results show that the method is better than the probability hypothesis density DOA (PHD-DOA) algorithm in tracking state sources and estimating the number of targets.

DOA estimation in the autocorrelation domain for coprime array

In this paper a new algorithm for direction of arrival (DOA) estimation in coprime arrays based on the autocorrelation domain (AD) method is proposed. The spatial autocorrelation sequence of the virtual uniform linear array (ULA) associated with the coprime array is built by averaging the diagonals of the spatially smoothed covariance matrix. The AD method estimates the DOAs by solving a generalized eigenvalue problem and refining the obtained solution. The main advantage of the introduced method is a spatial spectrum without false peaks. Simulation results indicate that the proposed approach is better than existing methods, especially for small number of snapshots.

A Novel Efficient Passive Spatial Orientation Detection Method of UMT Enabled by ISB

The passive detection and direction-of-arrival (DOA) estimation problem is of great importance in many underwater applications such as target reconnaissance and data collection. In this paper, an Efficient Correlation-based Orientation Detection (ECOD) method is proposed to achieve high efficiency. Without high computational complexity in any Transform Domain, the time consumption of ECOD is largely reduced, which is especially critical for underwater intrusion detection, territorial waters protection, and many other real-time underwater applications. To achieve good invisibility, we design an intelligent submerged buoy (ISB) structure, which consists of six embedded hydrophones and an in situ electronic control unit (IECU). As a supplement to solutions against complex underwater environments, a hybrid ECOD method is also developed by involving the cooperation from underwater distributed sensor networks. To be specific, when high SNR signals are not recorded by a single ISB node, other distributed sensors are scheduled to assist in cooperative sensing. Simulation experiments demonstrate the efficiency of the ECOD method in passive 3D spatial orientation of underwater acoustic target and show that the ECOD method has a better performance in time consumption compared with general DOA algorithms.