Two-dimensional Direction Of Arrival Research Articles

Robust Sparse Bayesian Two-Dimensional Direction-of-Arrival Estimation with Gain-Phase Errors

To reduce the influence of gain-phase errors and improve the performance of direction-of-arrival (DOA) estimation, a robust sparse Bayesian two-dimensional (2D) DOA estimation method with gain-phase errors is proposed for L-shaped sensor arrays. The proposed method introduces an auxiliary angle to transform the 2D DOA estimation problem into two 1D angle estimation problems. A sparse representation model with gain-phase errors is constructed using the diagonal element vector of the cross-correlation covariance matrix of two submatrices of the L-shaped sensor array. The expectation maximization algorithm derives unknown parameter expression, which is used for iterative operations to obtain off-grid and signal precision. Using these parameters, a new spatial spectral function is constructed to estimate the auxiliary angle. The obtained auxiliary angle is substituted into a sparse representation model with gain and phase errors, and then the sparse Bayesian learning method is used to estimate the elevation angle of the incident signal. Finally, according to the relationship of the three angles, the azimuth angle can be estimated. The simulation results show that the proposed method can effectively realize the automatic matching of the azimuth and elevation angles of the incident signal, and improves the accuracy of DOA estimation and angular resolution.

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.

A 2D-DOA Sparse Estimation Method with Total Variation Regularization for Spatially Extended Sources

In this paper, a novel two-dimensional direction of arrival (2D-DOA) estimation method with total variation regularization is proposed to deal with the problem of sparse DOA estimation for spatially extended sources. In a general sparse framework, the sparse 2D-DOA estimation problem is formulated with the regularization of extended source characteristics including spatial position grouping, acoustic signal block sparse, and correlation features. An extended sources acoustic model, two-dimensional array manifold and its complete representation, total variation regularization penalty term, and the regularization equation are built, and are utilized to seek the solutions where the non-zero coefficients are grouped together with optimum sparseness. A total variation sparse 2D-DOA estimation model is constructed by combining total variation regularization with LASSO. The model can be easily solved by the convex optimization algorithm, and the solving process can promote the sparsity of the solution on the spatial derivatives and the solution itself. The theoretical analysis results show that the steps of decorrelation processing and angle matching of traditional 2D-DOA estimation methods could be avoided when adopting the proposed method. The proposed method has better robustness to noise, better sparsity, and faster estimation speed with higher resolution than traditional methods. It is promising to provide a coherent sources sparse representation of a non-strictly sparse field.

An L-Shaped Three-Level and Single Common Element Sparse Sensor Array for 2-D DOA Estimation.

The degree of freedom (DOF) is an important performance metric for evaluating the design of a sparse array structure. Designing novel sparse arrays with higher degrees of freedom, while ensuring that the array structure can be mathematically represented, is a crucial research direction in the field of direction of arrival (DOA) estimation. In this paper, we propose a novel L-shaped sparse sensor array by adjusting the physical placement of the sensors in the sparse array. The proposed L-shaped sparse array consists of two sets of three-level and single-element sparse arrays (TSESAs), which estimate the azimuth and elevation angles, respectively, through one-dimensional (1-D) spatial spectrum search. Each TSESA is composed of a uniform linear subarray and two sparse subarrays, with one single common element in the two sparse subarrays. Compared to existing L-shaped sparse arrays, the proposed array achieves higher degrees of freedom, up to 4Q1Q2+8Q1-5, when estimating DOA using the received signal covariance. To facilitate the correct matching of azimuth and elevation angles, the cross-covariance between the two TSESA arrays is utilized for estimation. By comparing and analyzing performance parameters with commonly used L-shaped and other sparse arrays, it is found that the proposed L-shaped TSESA has higher degrees of freedom and array aperture, leading to improved two-dimensional (2-D) DOA estimation results. Finally, simulation experiments validate the excellent performance of the L-shaped TSESA in 2-D DOA estimation.

Cramer-Rao bound investigation of a novel virtually extended nested arc array for 2D DOA estimation

This paper exploits a sparse array representation, a novel nested arc array, to generate a virtual non-uniform circular arrays that have been presented and investigated. To increase the array aperture, the virtual array has been developed using higher-order statistics, namely, the Forth-Order Cumulants (FOC). The extended array contains a combination of physical as well as virtual sensors. The increased degrees of freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. The Cramer-Rao bound (CRB) and the (DOA) estimation for such an array are developed and investigated for various arrays. The proposed array performance is superior to that of the uniform one. Further, the offered array is suitable for two-dimensional (2D) DOA estimation problems.

DOA estimation for uniform circular array without the source number based on beamspace transform and higher-order cumulant

Fourth-order cumulant is one of most widely used high-order cumulant for direction of arrival (DOA) estimation due to its ability of expanding the virtual array aperture as well as suppressing Gaussian noise. To address the two-dimensional (2D) DOA estimation problem, we propose a modified MUSIC scheme for uniform circular array (UCA) in this paper. Firstly, the fourth-order cumulant of UCA is considered to construct a new propagator, resulting in the elimination of a priori knowledge of the number of signals. Secondly, the UCA is transformed by beamspace transformation, reducing the time computational complexity of the algorithm since the two-dimensional grid search and singular value decomposition are avoided. And finally a low-rank recovery algorithm is adopted to improve the accuracy regarding the limited snapshots scenario. The numerical simulations validate the superiority of the proposed method.

Compressive Sampling Framework for 2D-DOA and Polarization Estimation in mmWave Polarized Massive MIMO Systems

The polarized massive multiple-input multiple-output (MIMO) technique has been regarded as a promising solution to millimeter wave (mmWave) communication systems, because it experiences more degrees-of-freedom than the scalar configuration, and it represents a significant opportunity for secure communication. To deliver smart service to terminals, it is essential to provide base stations (BS) with the capability of terminal’s direction-of-arrival (DOA) awareness. In this paper, a compressive sampling (CS) framework is proposed for two-dimensional (2D) DOA and polarization estimation in mmWave polarized massive MIMO systems. The proposed approach first reduces the data volume via a reduced-dimension matrix. Then it computes the signal subspace via the eigendecomposition of the compressed array measurement. Thereafter, the rotational invariance characteristic is utilized to form a normalized polarization steering vector. Finally, 2D-DOA and polarization are estimated by incorporating the Poynting vector and the least squares (LS) techniques. The proposed architecture is computationally much more economical than existing algorithms. Besides, it allows a mmWave BS to provide comparable estimation performance with arbitrary sensor geometry, which is more flexible than most of the existing architectures. Furthermore, it is robust to the sensor position error. Numerical simulations verify the advantages of the proposed framework.

Multitarget 2-D DOA Estimation Using Wideband LFMCW Signal and Triangle Array Composed of Three Receiver Antennas

Direction of arrival (DOA) estimation has been a primary focus of research for many years. Research on DOA estimation continues to be immensely popular in the fields of the internet of things, radar, and smart driving. In this paper, a simple new two-dimensional DOA framework is proposed in which a triangular array is used to receive wideband linear frequency modulated continuous wave signals. The mixed echo signals from various targets are separated into a series of single-tone signals. The unwrapping algorithm is applied to the phase difference function of the single-tone signals. By using the least-squares method to fit the unwrapped phase difference function, the DOA information of each target is obtained. Theoretical analysis and simulation demonstrate that the framework has the following advantages. Unlike traditional phase goniometry, the framework can resolve the trade-off between antenna spacing and goniometric accuracy. The number of detected targets is not limited by the number of antennas. Moreover, the framework can obtain highly accurate DOA estimation results.

Sparse Billboard and T-Shaped Arrays for Two-Dimensional Direction of Arrival Estimation

In two-dimensional direction of arrival (2D-DOA) estimation, planar arrays can estimate the elevation and azimuth angles simultaneously. However, many planar array topologies such as billboard, L-shaped, T-shaped, and 2D nested arrays suffer from mutual coupling that results from the small separation between the physical sensors (antennas), which limits the estimation capability of the sensor array. In an attempt to reduce mutual coupling between sensors, this article proposes sparse billboard and T-shaped arrays in which the number of closely separated sensors is significantly reduced. In addition to extending the CRB for fourth order coarray, this article also derives closed-form expressions for the sensor locations and the number of consecutive lags or the uniform degrees of freedom (uDOF), in the fourth-order difference coarray (FODC). Simulation results demonstrate the robustness of the proposed sparse arrays against mutual coupling.

Coarray Tensor Completion for DOA Estimation

Sparse array direction-of-arrival (DOA) estimation using tensor model has been developed to handle multi-dimensional sub-Nyquist sampled signals. Furthermore, augmented virtual arrays can be derived for Nyquist-matched coarray tensor processing. However, the partially augmentable sparse array corresponds to a discontinuous virtual array, whereas the existing methods can only utilize its continuous part. Conventional virtual linear array interpolation techniques complete coarray covariance matrices with dispersed missing elements, but fail to complete the coarray tensor with whole missing slices. In this paper, we propose a coarray tensor completion algorithm for two-dimensional DOA estimation, where the coarray tensor statistics can be entirely exploited. In particular, in order to impose an effective low-rank regularization on the slice-missing coarray tensor, we propose shift dimensional augmenting and coarray tensor reshaping approaches to reformulate a structured coarray tensor with sufficiently dispersed missing elements. Furthermore, the shape of the reformulated coarray tensor is optimized by maximizing the dispersion-to-percentage ratio of missing elements. As such, a coarray tensor nuclear norm minimization problem can be designed to optimize the completed coarray tensor corresponding to a filled virtual array, based on which the closed-form DOA estimation is achieved. Meanwhile, the global convergence of the coarray tensor completion is theoretically proved. Simulation results demonstrate the effectiveness of the proposed algorithm compared to other matrix-based and tensor-based methods.

Novel cooperative localization method of over-the-horizon shortwave emitters based on direction-of-arrival and time-difference-of-arrival measurements

The location of long-distance shortwave radiation sources is practically significant in national defense security. Shortwave multistation-positioning systems mainly include direction-of-arrival (DOA) and time-difference-of-arrival (TDOA) intersection locations. These two systems have their advantages and disadvantages in terms of performance. To combine the advantages of these two positioning technologies, this study focuses on the cooperative positioning problem based on DOA and TDOA measurements. First, the two-dimensional DOA and TDOA observation models are established for the over-the-horizon propagation scenario. Subsequently, the Cramér-Rao lower bound (CRLB) of positioning accuracy is derived in the presence of measurement errors in virtual ionosphere height. Aiming at the strong nonlinear characteristics of the observation equations, a new DOA/TDOA cooperative localization method is proposed. Finally, the asymptotic efficiency of the new estimator is proved using the first-order error analysis theory. The new method comprises two stages. In the first stage, the shortwave DOA observation equation is transformed into a pseudo-linear observation equation by introducing an auxiliary variable, as well as solving a quadratic equation with one unknown. Next, an optimization model with two quadratic equality constraints is constructed, and an iterative optimization algorithm based on matrix $~\bf{QR}$ decomposition is proposed to obtain an intermediate estimate of the emitter position. The second stage transforms the shortwave TDOA observation equation into a pseudo-linear observation equation by combining the intermediate estimates given in the first phase. Also, an iterative-constrained weighted-least-squares estimator based on the matrix decomposition is proposed again to localize the emitter. Simulation results show that the new cooperative localization method has good global convergence, the localization performance can reach the CRLB, and the obtained cooperative gain is quite high.

Vehicle Positioning With Deep-Learning-Based Direction-of-Arrival Estimation of Incoherently Distributed Sources

In this article, a novel vehicle positioning system architecture based on direction-of-arrival (DOA) estimation of incoherently distributed (ID) sources is proposed employing massive multiple-input–multiple-output (MIMO) arrays. Such an architecture with the associated signal model is more consistent with the actual array application and multipath transmission scenarios. First, an end-to-end two-dimensional (2-D) DOA estimation of ID sources utilizing a dual one-dimensional (1-D) convolutional neural network (D1D-CNN) under the deep learning (DL) framework is performed, where the normalized covariance matrix data is used for both offline training and online estimation. Then, the received SNR information is exploited to select a set of DOA estimates provided by multiple collaborative BSs for positioning. Moreover, transfer learning and an attention mechanism are employed to promote its generalization ability and achieve robustness against array perturbations. Simulation results are provided to show that the proposed method outperforms the state-of-the-art methods in terms of computational complexity, positioning accuracy, and robustness against array perturbations.

Off-grid sparse based two-dimensional direction of arrival estimation of acoustic vector sensor array in impulse noise

In order to estimate the direction of arrival (DOA) of acoustic vector sensor, the phased fractional low-order moment (PFLOM) is used to suppress impulse noise. First, based on PFLOM, an off-gird sparse based two-dimensional (2D) DOA estimation model for acoustic vector sensor array is proposed. Then, a three-step alternating iterative Orthogonal Matching Pursuit (OMP) algorithm is introduced to realize the off-grid 2D DOA estimation, and the self-pairing of azimuth and elevation is achieved. Finally, the effectiveness and accuracy of the proposed algorithm under impulse noise and small snapshots are verified by simulation.

A low-complexity two-dimensional DOA estimation algorithm based on an L-shaped sensor array

In this paper, a derivative-based MUSIC (multiple signal classification) algorithm for a mixture of circular and noncircular signals (DB-MUSIC-M) is proposed for two-dimensional (2D) direction of arrival (DOA) estimation employing an L-shaped uniform array. The DB-MUSIC-M transforms the 2D DOA estimation problem into a single one-dimensional (1D) estimation by finding the derivative of the objective function of the 2D improved MUSIC (I-MUSIC) algorithm, which greatly reduces its computational complexity. As it utilizes both the pseudo covariance matrix and the covariance matrix of the array data, the maximum number of signals that can be estimated is much higher than the total number of sensors. As a special case, the derivative-based MUSIC (DB-MUSIC) for circular signals is also proposed. There is no need for angle pairing for the proposed algorithms and they can handle the angle ambiguity problem effectively. As shown by simulation results, the proposed DB-MUSIC-M algorithm outperforms existing algorithms, with significantly reduced complexity compared to a direct 2D search method. Moreover, the proposed approach can be applied to some other array structures such as the uniform planar array.

2-D DOA Estimation of Incoherently Distributed Sources Considering Gain-Phase Perturbations in Massive MIMO Systems

In massive multiple-input multiple-output (MIMO) systems, accurate direction-of-arrival (DOA) estimation is important for the base station (BS) to perform effective downlink beamforming. So far, there have been few reports on DOA estimation considering gain-phase perturbations in massive MIMO systems. However, gain-phase perturbations indeed exist in practical applications and cannot be ignored. In this paper, an efficient method for two-dimensional (2-D) DOA estimation of incoherently distributed (ID) sources considering array gain-phase perturbations is proposed for massive MIMO systems. Firstly, a shift invariance structure is established in the subspace framework, and a constrained optimization problem is formulated to estimate the nominal azimuth and elevation DOAs as well as gain-phase perturbations with closed-form expressions, under the assumption that some of the BS antennas are well calibrated; secondly, the corresponding angular spreads are obtained with the aid of the estimated gain-phase perturbations. Theoretical analysis and an approximate Cramér-Rao bound are also provided. An improved estimation performance is achieved by the proposed method as demonstrated by numerical simulations.

Structured Tensor Reconstruction for Coherent DOA Estimation

Existing tensor-based coherent direction-of-arrival (DOA) estimation methods adopting spatial smoothing to decorrelate the coherent tensor statistics usually lead to a poor decorrelation performance. In this letter, we propose a structured tensor reconstruction method for two-dimensional coherent DOA estimation, which then avoids the inefficient spatial smoothing. In particular, after investigating the structural property of the four-dimensional incoherent covariance tensor, we propose a tensorial Hermitian Toeplitz mapping rule to reconstruct a structured covariance tensor from the rank-deficient coherent covariance tensor statistics. It is theoretically proved that, the reconstructed covariance tensor admits a decorrelated canonical polyadic model with a tensorial Hermitian Toeplitz structure, whose decomposition ensures a closed-form coherent DOA estimation. The effectiveness of the proposed method is verified by simulations.

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.

Two-dimensional multi-snapshot Newtonized orthogonal matching pursuit for DOA estimation

Estimating the azimuth and elevation angles of targets is referred to as two-dimensional direction of arrival (2D-DOA) estimation problem, which is of vital importance in array signal processing and multiple input multiple output (MIMO) millimeter wave communication fields. Inspired by the Newtonized orthogonal matching pursuit (NOMP) for line spectrum estimation (LSE), this paper proposes the two-dimensional multi-snapshot NOMP (2D-MNOMP) to deal with the 2D-DOA estimation. Specifically, two-dimensional fast Fourier transform (FFT) is utilized to significantly reduce the computation complexity, and a Newton refinement step and feedback strategy are proposed to improve performance of DOA estimation. Based on the generalized likelihood ratio test (GLRT), the stopping criterion is established. The near-optimal performance of 2D-MNOMP is also demonstrated by comparing against other methods and the Cramér-Rao bound (CRB), both in terms of simulations and real data.

Two-dimensional DOA estimation method of acoustic vector sensor array based on sparse recovery

In order to solve the Direction of Arrival (DOA) estimation of fast-moving targets in a strong noisy environment, an auto-paired two-dimensional (2D) DOA estimation algorithm architecture based on the sparse recovery of acoustic vector sensor arrays is proposed. The structure of the array signal autocorrelation operator is similar to the 2D compressed sampling model. Based on the structure of the autocorrelation operator, a 2D DOA estimation sparse recovery model for the Uniform Line Array (ULA) of the acoustic vector sensors is proposed. Meanwhile, the modified Compressive Sampling Matching Pursuit (CoSaMP) algorithm is used to realize the auto-paired 2D DOA estimation. The simulation results show that the method proposed in this paper can effectively suppress noise, and can be used to realize 2D DOA estimation of acoustic vector sensor ULA under a low Signal-to-Noise Ratio (SNR) and small snapshots.

Multi-Maneuvering Sources DOA Tracking With Improved Interactive Multi-Model Multi-Bernoulli Filter for Acoustic Vector Sensor (AVS) Array

To solve the problem of the direction of arrival (DOA) maneuvering in acoustic vector sensor (AVS) array, we propose an interactive multi-model Multi-target Multi-Bernoulli (IMM-MeMBer) two-dimensional (2-D) DOA tracking algorithm. The idea of the IMM algorithm is employed to interactively estimate the predicted sampled particles at the expense of calculating the likelihood function of the predicted particles by pseudo-spectrum of multi-signal classification (MUSIC). The proposed method fully considers various possibilities of target motion, which makes the target state estimation more effective. Moreover, the de-noising and exponential weighting of MUSIC pseudo-spectrum improve the likelihood function of particles, thus enhancing the weight of particles in high likelihood region and making these particles more effective in the subsequent resampling process. Simulation results show that the IMM-MeMBer algorithm has better performance than projection approximation subspace tracking of deflation MUSIC (PASTD-MUSIC), MeMBer, particle filter (PF), and random finite set PF (RFS-PF) in the DOA tracking of maneuvering sources.