Direction Of Arrival Estimation Problem Research Articles

Direction of arrival estimation under Class A modelled noise in shallow water using variational Bayesian inference method

The shallow water noise shows obvious impulsive property, which greatly degrades the direction of arrival (DOA) performance due to the conventional design concept based on the Gaussian assumption. In this paper, DOA estimator in presence of impulsive noise utilising variational Bayesian inference is proposed. The Middleton's Class A noise model is considered as a typical underwater noise model to analyse the performance of DOA estimation. The DOA estimation problem is modelled as the sparse signal recovery problem, and the hierarchical Bayesian learning framework is formulated by considering the common sparsity of signal and the element-wise sparsity of the impulsive noise. The variational Bayesian inference realises the posterior estimation of signal and impulsive noise components. To mitigate the basis mismatches, the root sparse Bayesian learning method is applied to refine the steering vectors. Simulations verify the advantages of the proposed DOA method in terms of spatial resolution, root mean square error, accuracy, and robustness compared with the state-of-the-art benchmarks in the presence of Middleton's Class A noise.

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.

Communication-Efficient Decentralized Subspace Estimation

Machine learning techniques have been widely used in communication systems because of their superior performance. Among them, the classical machine learning algorithm Principal Component Analysis (PCA) aims to estimate the principal subspace of the received signals, and thus is also known as subspace estimation. It is often used in Direction of Arrival (DoA) tasks. Recently, the widespread deployment of networks has motivated researchers to solve the problem of subspace estimation in decentralized settings. An important concern in the design of decentralized algorithms is the communication complexity, because communication consumes much energy, while the sensors in the network are generally energy-limited. Specifically, communication complexity refers to the minimum amount of transmitted variables to obtain an estimate with an error smaller than <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula>. For existing algorithms, this complexity is <inline-formula><tex-math notation="LaTeX">$O(\log ^{2}(1/\varepsilon))$</tex-math></inline-formula>. In this paper, we improve this complexity to be <inline-formula><tex-math notation="LaTeX">$O(\log (1/\varepsilon))$</tex-math></inline-formula> by designing a new algorithm named Decentralized Subspace Estimation (DSE). Such improvement is achieved by using the gradient tracking technique. We theoretically analyze the influence of the network connectivity and the eigen-gap of the data on communication complexity. In addition, we use DSE to solve the DoA estimation problem. Experiments verify the effectiveness of the algorithm and the correctness of the theoretical result.

Super-Resolution DOA Estimation for Wideband Signals Using Non-Uniform Linear Arrays With No Focusing Matrix

We focus on developing an effective Direction Of Arrival (DOA) estimation method for wideband sources based on the super-resolution concept. In this letter, we represent the data model of a wideband DOA estimation problem in a new form. Then, using this model, we propose an atomic norm minimization problem that leads to an accurate wideband DOA estimation method with no need for any focusing matrices. Moreover, this method requires no initial estimate and can be implemented by non-uniform linear arrays. Numerical simulations show that in comparison to some well-known techniques, the proposed method generates outstanding accuracy and higher robustness to noise. The effectiveness of the method is also verified in presence of close adjacent sources.

Robust sparse reconstruction of signals with gapped missing samples from multi-sensor recordings

Reconstructing missing samples in multi-sensor recordings is important in many applications including blind source separation, signal detection and direction of arrival estimation problem. This study proposes a method of reconstructing missing samples from multi-sensor recordings of non-stationary amplitude-modulation frequency-modulated signals using a two step procedure. In the first step the instantaneous frequency of a given multi-sensor signal is estimated using a robust and efficient method. Then the instantaneous frequency information is exploited to jointly recover the instantaneous amplitudes of multi-sensor signals. For recovering instantaneous amplitudes, the Fourier series approximation of the instantaneous amplitude is exploited. Experimental results indicate that the proposed method achieves better performance than the existing method including time-frequency filtering method, gradient descent and orthogonal matching pursuit algorithms.

An Iterative Lq-norm Based Optimization Algorithm for Generalized SPICE

A novel approach of the direction of arrival (DOA) estimation is proposed to improve the sparse iterative covariance-based estimator (SPICE) for the formulation, which chooses different norm constraints of signal and noise in the data covariance model. For a given norm, the problem of DOA estimation is solved by differentiating the objective function with respect to signal and noise parameters separately, without considering some model constraints. The iterative formulas of signal and noise components are derived for both single-snapshot and multiple-snapshot cases. Inspired by the derivation of the approach, a weighted version of generalized SPICE (WEQ-SPICE), is also considered from the gradient approach for the same estimation problem. The performances of the new optimization algorithm and the weighted version are both preferable to the generalized SPICE method. Especially in the case of the low signal-to-noise (SNR) ratio, the weighted version can effectively find the correct support of signals. The results of Monte Carlo simulations show the efficiency and advantages.

A Low Computational Cost Lightning Mapping Algorithm With a Nonuniform L-Shaped Array: Principle and Verification

Recently, 2-D multiple signal classification (MUSIC) algorithm was applied to map lighting propagation with improved quality. However, the quality is improved at the cost of increasing the calculation load. To improve the efficiency, this article proposes an improved MUSIC-based lightning mapping algorithm, which transforms the 2-D direction of arrival (DOA) estimation problem for an L-shaped array into 1-D DOA estimation problem for the two arms of the array. Additionally, the lightning mapping array is arranged in a nonuniform way to reduce the risk of trivial ambiguity problem. The performance of the developed lightning mapping system is verified with numerical Monte Carlo simulation and further with real lightning observation results. The simulation results show that the nonuniform array outperforms the uniform array in terms of detection accuracy, spatial resolution, and antiambiguity. The observation results show that the MUSIC-based methods produce better lightning mapping quality compared with the interferometry method (15 777 sources mapped), due to better robustness for low signal-to-noise ratio (SNR) lightning very high-frequency (VHF) signals. Compared with the 2-D MUSIC method (34 620 sources mapped), the proposed low computational cost method (30 461 sources mapped) is proven to produce fairly similar path of lightning leader with significant lower computational cost. Specifically, the proposed method saves about 84.91% of calculation time compared with the 2-D MUSIC method in practice.

Maximum likelihood DOA estimation based on improved invasive weed optimization algorithm and application of MEMS vector hydrophone array

&lt;abstract&gt;&lt;p&gt;Direction of arrival (DOA) estimation based on Maximum Likelihood is a common method in array signal processing, with many practical applications, but the huge amount of calculation limits the practical application. To deal with such an Maximum Likelihood (ML) DOA estimation problem, firstly, the DOA estimation model with ML for acoustic vector sensor array is developed, where the optimization standard in various cases can be unified by converting the maximum of objective function to the minimum. Secondly, based on the Invasive Weed Optimization (IWO) method which is a novel biological evolutionary algorithm, a new Improved IWO (IIWO) algorithm for DOA estimation of the acoustic vector sensor array is proposed by using ML estimation. This algorithm simulates weed invasion process for DOA estimation by adjusting the non-linear harmonic exponent of IWO algorithm adaptively. The DOA estimation accuracy has been improved, and the computation of multidimensional nonlinear optimization for the ML method has been greatly reduced in the IIWO algorithm. Finally, compared with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE) method and Tuna Swarm Optimization(TSO) algorithm, numerical simulations show that the proposed algorithm has faster convergence rate, improved accuracy in terms of Root Mean Square Error (RMSE), lower computational complexity and more robust estimation performance for ML DOA estimation. The experiment with tracking the orientation of the motorboat by Microelectronic mechanical systems (MEMS) vector hydrophone array shows the superior performance of proposed IIWO algorithm in engineering application. Therefore, the proposed ML-DOA estimation with IIWO algorithm can take into account both resolution and computation. which can meet the requirements of real-time calculation and estimation accuracy in the actual environment.&lt;/p&gt;&lt;/abstract&gt;

DOA Estimation for Heterogeneous Wideband Sources Based on Adaptive Space-Frequency Joint Processing

For direction-of-arrival (DOA) estimation of heterogeneous wideband sources, we propose a new adaptive space-frequency joint processing algorithm. The algorithm is implemented in the sparse Bayesian learning (SBL) DOA framework, which is named as ASF-SBL algorithm in this paper. The traditional SBL-based DOA methods suffer from the problem of erroneous DOA estimation due to the structural mismatch between the invariant prior and the sparse coefficients. To solve this problem, the ASF-SBL algorithm employs a new space-frequency correlation prior model that can be adaptively changed to fit heterogeneous DOA scenarios. Specifically, nine alternative space-frequency structural patterns are constructed to represent the joint space-frequency characteristics of spatial sparse signals. By evaluating the space-frequency correlation of the sparse coefficients updated in each iteration under SBL framework, a suitable pattern is selected from the nine choices to determine the adaptive prior of each coefficient. This adaptive method leads to accurate DOA estimation in different wideband sources scenarios. In addition, we introduce a distributed processing method to extend the ASF-SBL algorithm to two-dimensional DOA estimation. This extension is achieved by decoupling the DOA estimation into two one-dimensional estimations. The decoupling avoids the problems of a huge redundant dictionary and excessive computational complexity caused by the combination of azimuth and elevation angles. Numerical simulations show that the ASF-SBL algorithm is superior to existing algorithms in DOA estimation of heterogeneous sources.

Efficient DOA Estimation Method for Reconfigurable Intelligent Surfaces Aided UAV Swarm

The conventional direction of arrival (DOA) estimation methods are performed with multiple receiving channels. In this paper, a changeling DOA estimation problem is addressed in a different scenario with only one full-functional receiving channel. A new unmanned aerial vehicle (UAV) swarm system using multiple lifted reconfigurable intelligent surface (RIS) is proposed for the DOA estimation. The UAV movement degrades the DOA estimation performance significantly, and the existing atomic norm minimization (ANM) methods cannot be used in the scenario with array perturbation. Specifically, considering the position perturbation of UAVs, a new atomic norm-based DOA estimation method is proposed, where an atomic norm is defined with the parameter of the position perturbation. Then, a customized semi-definite programming (SDP) method is derived to solve the atomic norm-based method, where different from the traditional SDP method, an additional transforming matrix is formulated. Moreover, a gradient descent method is applied to refine the estimated DOA and the position perturbation further. Simulation results show that the proposed method achieves much better DOA estimation performance in the RIS-aided UAV swarm system with only one receiving channel than various benchmark schemes.

Direction-of-Arrival Estimation for Large Antenna Arrays With Hybrid Analog and Digital Architectures

The large antenna arrays with hybrid analog and digital (HAD) architectures can provide a large aperture with low cost and hardware complexity, resulting in enhanced direction-of-arrival (DOA) estimation and reduced power consumption. This paper investigates the trade-off between DOA estimation and power consumption in large antenna arrays with HAD architectures. Particularly, the DOA estimation problem of fully-connected, sub-connected (SC), and switches-based (SE) hybrid architectures is formulated into a unified expression, with the compression matrix in a time-varying form. Based on this model, we derive a dynamic maximum likelihood (D-ML) estimator that is suitable for both HAD and conventional fully digital (FD) structures, and the closed-form expression of Cramér-Rao bound (CRB) to evaluate the performance limit of the D-ML estimator for different HAD structures. The theoretical CRB analysis in the single-source case reveals that, the SC structure has the ability to achieve approximately the same performance as the FD structures at DOAs around zero, but suffers from the inherent angle ambiguity because of the antenna grouping. In addition, we propose a dynamic SC (D-SC) structure that is proved to eliminate the angle ambiguity with time-varying phase shifters, and a switch optimization (SWO) algorithm to minimize the CRB of SE structures. Finally, we introduce a new metric, DOA efficiency, to measure the trade-off between the DOA estimation performance and power consumption of different structures. Simulation results verify our theoretical analysis and the superiority of the proposed D-SC structure and the SWO algorithm.

DOA Estimation Aided by Magnitude Measurements

This correspondence discusses the estimation of direction-of-arrival (DOA) in a magnitude-aided antenna array (MA-AA), where magnitude-only radio frequency (RF) chains are introduced into the classical AA to acquire magnitude measurements. DOAs are initially estimated by the multiple signal classification (MUSIC) algorithm based on the complex-valued measurements from the conventional antennas. After griding the neighborhoods of these initial DOAs, the DOA estimation problem with the hybrid observations in MA-AA is converted as the recovery problem of sparse signals, which can be resolved by generalized approximate message passing (GAMP). Due to the “spatial leakage” effect, non-zero clusters appear around true DOAs. Their positions (i.e., non-zero supports) provide DOAs estimations. Moreover, DOAs and supports remain unchanged in several snapshots, then common supports are shared. Therefore, the cluster-sparse property of sparse signals is exploited by modeling a hidden Markov-tree (HMT) in the shared supports, on which belief propagation (BP) is executed to recover the binary probabilities of supports. Some unknown hyper-parameters in GAMP and BP are learned by expectation-maximization (EM). In comparison to existing estimators, EM-BP-GAMP shows advantages on DOA estimation, computational complexity, and DOA resolution. With the EM-BP-GAMP estimator, MA-AA is more energy-efficient than the classical AA. These advantages are successfully validated by experimental results.

Neural network-aided sparse convex optimization algorithm for fast DOA estimation

In this paper, a fast sparse convex optimization algorithm based on a neural network is proposed to improve the direction of arrival estimation. First, a fast [Formula: see text]-sparse representation of the array covariance vector model based on the Hermitian Toeplitz structure of array covariance is established to reduce computational complexity in data dimension and variable number. Then, the estimation error upper bound problem is investigated, and a neural network-aided coefficient selection method is developed. The direction of arrival estimation problem is solved through spectral peak search. Finally, the algorithm is extended to the case of off-grid error. The algorithm’s advantages in accuracy, calculation speed and robustness is verified by the simulations.

On the Complementarity of Sparse L0 and CEL0 Regularized Loss Landscapes for DOA Estimation.

L0 sparse methods are not widespread in Direction-Of-Arrival (DOA) estimation yet, despite their potential superiority over classical methods in difficult scenarios. This comes from the difficulties encountered for global optimization on hill-climbing error surfaces. In this paper, we explore the loss landscapes of L0 and Continuous Exact L0 (CEL0) regularized problems in order to design a new optimization scheme. As expected, we observe that the recently introduced CEL0 penalty leads to an error surface with less local minima than the L0 one. This property explains the good behavior of the CEL0-regularized sparse DOA estimation problem for well-separated sources. Unfortunately, CEL0-regularized landscape enlarges L0-basins in the middle of close sources, and CEL0 methods are thus unable to resolve two close sources. Consequently, we propose to alternate between both error surfaces to increase the probability of reaching the global solution. Experiments show that the proposed approach offers better performance than existing ones, and particularly an enhanced resolution limit.

Direction-of-Arrival Estimation over Sea Surface from Radar Scattering Based on Convolutional Neural Network

Conventional direction-of-arrival (DOA) estimation methods are primarily used in point source scenarios and based on array signal processing. However, due to the local scattering caused by sea surface, signals observed from radar antenna cannot be regarded as a point source but rather as a spatially dispersed source. Besides, with the advantages of flexibility and comparably low cost, synthetic aperture radar (SAR) is the present and future trend of space-based systems. This paper proposes a novel DOA estimation approach for SAR systems using the simulated radar measurement of the sea surface at different operating frequencies and wind speeds. This article’s forward model is an advanced integral equation model (AIEM) to calculate the electromagnetic scattered from the sea surface. To solve the DOA estimation problem, we introduce a convolutional neural network (CNN) framework to estimate the transmitter’s incident angle and incident azimuth angle. Results demonstrate that the CNN can achieve a good performance in DOA estimation at a wide range of frequencies and sea wind speeds.

Direction of arrival estimation in multipath environments using deep learning

SummaryThis article aims to present a novel direction of arrival (DOA) estimation strategy in multipath environments using deep learning. Eigen decomposition‐based algorithms, such as multiple signal classification (MUSIC), have high‐resolution DOA estimation performance, but they fail to work in the case of coherent signals. These algorithms require extensive computation and are difficult to implement in real time. Neural networks (multilayer perceptron [MLP] and radial basis function neural network [RBFNN]) are also applied to DOA estimation problem, and they are found to be faster than the conventional techniques, but they fail to ensure the desired accuracy in multipath environments when the training data set contains a huge number of samples and the number of incident signals was unknown. To enhance the DOA estimation performance, an efficient convolutional neural network (CNN)‐based smart antenna is proposed. This smart antenna is composed of a uniform linear array (ULA), an intelligent DOA estimator, and an efficient adaptive beamformer, and the space is decomposed into five space sectors. The intelligent DOA estimator contains six CNN networks. One network is used as a classifier to select one or more space sectors, and five networks are used to calculate the DOAs of unknown number of coherent or noncoherent incident signals that received in the selected space sectors. The simulation results demonstrate that the proposed DOA estimator enables reliable DOA estimation despite very challenging multipath environment, and the CNN substantially reduces the CPU time for the DOA estimation computations especially when the number of incident signals is large.

A Novel Modified Artificial Bee Colony for DOA Estimation

Aims: We consider the Direction of Arrival (DOA) estimation for code division multiple access (CDMA) signals. Background: Solving this problem requires non-linear optimization and thus the speed of convergence becomes crucial. Objective: A novel Modified Artificial Bee Colony (MABC) has been proposed. We use secondorder Taylor series expansion of the cost function to ameliorate the searchability of artificial bee colony (ABC) for finding the globally optimal solution. Methods: The main idea is to harness the exploration and exploitation features. The optimum point of second-order Taylor expansion of cost function is used as a velocity factor of the ABC algorithm. Results: The proposed technique is used for solving the DOA estimation problem of a CDMA system. Simulation results confirm the performance improvement of our proposed algorithm. Conclusion: The cost function of the DOA estimation usually leads to a non-linear optimization problem. Using evolutionary algorithms can improve convergence rate of such problems.

DoA Estimation Using Neural Tangent Kernel under Electromagnetic Mutual Coupling

Antenna element mutual coupling degrades the performance of Direction of Arrival (DoA) estimation significantly. In this paper, a novel machine learning-based method via Neural Tangent Kernel (NTK) is employed to address the DoA estimation problem under the effect of electromagnetic mutual coupling. NTK originates from Deep Neural Network (DNN) considerations, based on the limiting case of an infinite number of neurons in each layer, which ultimately leads to very efficient estimators. With the help of the Polynomial Root Finding (PRF) technique, an advanced method, NTK-PRF, is proposed. The method adapts well to multiple-signal scenarios when sources are far apart. Numerical simulations are carried out to demonstrate that this NTK-PRF approach can handle, accurately and very efficiently, multiple-signal DoA estimation problems with realistic mutual coupling.

Photonic direction-of-arrival estimation based on compressive sensing.

The optical approach to estimate the direction-of-arrival (DOA) estimation of microwave signals has attracted a lot of attention recently. Most of the existing methods are based on a one-sensor array system, which converts the DOA estimation problem into an optical power estimation problem. Their main disadvantage is that additional work is needed to represent the relationship between the phase shifts and the optical powers before estimation. The algorithm proposed in this paper is based on an N-sensor array (N>2), where the optical power vector is obtained first and then a compressive sensing-based approach is applied to directly estimate the phase shift. As demonstrated by simulation results, the proposed algorithm can achieve much better estimation accuracy and robustness than existing optical DOA estimation algorithms considered.

Atomic Network-Based DOA Estimation Using Low-Bit ADC

In the direction of arrival (DOA) estimation problem, when a low-bit analog to digital converter (ADC) is used, the estimation performance severely deteriorates. In this paper, the DOA estimation problem is considered in a low-cost direction finding system with low-bit ADC. To eliminate quantization noise, we propose a novel network ADCnet, which is a composition of fully connected layers and exponential linear unit (ELU) layers, and the input signals are the received signals using low-bit ADC. After the ADCnet, an AtomicNet is also proposed to estimate the DOA from the denoised signals, where atomic vectors are corresponding to the steer vectors. A loss function considering both the reconstruction performance and the sparsity is proposed in the AtomicNet. Different from the exiting atomic norm-based methods, the proposed method can avoid an optimization problem and estimate the DOA with lower computational complexity. Simulation results show that the proposed method outperforms the existing methods in the DOA estimation performance using low-bit ADC.