2D Direction Of Arrival Estimation Research Articles

2-D DOA Estimation of Coherent Signals Using the Dual-Size Spreading Array

Abstract We introduce a novel approach for high-precision estimation of two-dimensional (2-D) Direction-of-Arrival (DOA) under conditions of coherent interference. This study innovatively devises an antenna configuration, termed the Dual-Size Spreading Array, specifically tailored to estimate DOAs in such environments. The method involves integrating a subarray with the primary array to create a Dual-Size Extended Array structure. This integration allows for a transformation of the covariance matrix into a new form, where its rank solely depends on the number of impinging waves. Both the subarray and primary array must have a scale no less than the number of incoming wavefronts. This proposed technique not only amplifies the effective aperture but also significantly reduces the computational intricacy associated with DOA estimation procedures. The efficacy of our methodology has been substantiated through simulation results, which demonstrate that it outperforms the conventional spatial smoothing techniques. Moreover, we provide several practical guidelines designed to enhance estimation accuracy while concurrently minimizing computational demands. In summary, this research presents an advanced solution that effectively addresses challenges in 2D DOA estimation under coherent scenarios, achieving improved performance and computational efficiency compared to existing methods.

High-accuracy 2D DOA estimation with three parallel sparse nested array

To improve the performance for two-dimensional (2D) direction of arrival (DOA) estimation in the presence of limited antennas in practice, we propose a novel three parallel sparse nested array with extended aperture and reduced mutual coupling. The proposed array consists of three subarrays where locations of antennas have closed-form expressions, to efficiently achieve increased degrees of freedom in difference coarray domain. The unit inter-antenna spacings and the displacements among subarrays are all expanded by D1, D2 or D3 fold for aperture extension and mutual coupling reduction in physical array domain. By exploiting the configuration, the two methods, i.e., BOMP-based and CMT-BCS-based methods, are further explored for high-precision but ambiguous angle estimation, and then the coprime-ness between the displacements is utilized to solve the angle ambiguities. Simulation results demonstrate the superiority of the proposed array and methods for 2D DOA estimation over the existing technologies.

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

Parallel Complementary Virtual Arrays Algorithm for Direction of Arrival (DOA) Estimation

This Paper discusses the challenges faced by previous method 2D Direction of Arrival (DOA) systems, such as low degrees of freedom, poor resolution, and significant estimation errors in scenarios with small snapshots. In response to these issues, the present method proposes a low-complexity 2D Direction of Arrival (DOA) estimation algorithm based on a parallel complementary virtual array.
 The algorithm utilizes two mutually parallel complementary linear arrays to generate a virtual array, addressing the limitations of traditional parallel arrays. It constructs an extended matrix with enhanced 2D angular degrees of freedom using covariance and cross-covariance matrices. The final step involves obtaining automatic matching 2D angle estimates through Singular Value Decomposition (SVD) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT).
 In comparison to traditional 2D DOA estimation methods, the proposed algorithm better exploits the information from the array's received data. It can identify more incoming signals, offering high resolution without the need for 2D linear search or angle parameter matching. Importantly, it demonstrates effective estimation even in scenarios with low Signal-to-Noise Ratio (SNR) and small snapshots. Experimental simulation results validate the effectiveness and reliability of the proposed algorithm.

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.

Polarization Direction of Arrival Estimation for Vector Array of Unmanned Aerial Vehicle Swarm

Aiming at the problem of the excessive error of direction of arrival (DOA) estimation caused by the position disturbance of a UAV swarm during flight, a robust polarization-DOA estimation method based on sparse Bayesian learning (SBL) is proposed. First, the algorithm decomposes the covariance matrix of the received data of the UAV swarm vector array and then constructs the determination matrix of the UAV position coordinates by exploiting the orthogonality of the eigenvalues and eigenvectors. Then, the optimal solution of the semi-positive definite programming (SDP) problem is solved using the constrained global least square method, and the exact self-positioning coordinates of UAVs are obtained. Second, we construct a spatially discrete grid to model the received data of the UAV group vector array. The SBL theory is then applied to obtain the posterior probability distribution of the sparse signal matrix. The sparsity of the signal matrix is controlled with a hyperparameter, and the estimation of the DOA is conducted using a fixed-point iteration to obtain the maximum posterior estimate of the signal matrix. Finally, according to the estimated DOA, the polarization parameter is obtained from the constructed objective function of the polarization parameter estimation. The simulation results show that the proposed algorithm achieves higher accuracy and robustness than the traditional 2D DOA estimation algorithm in the direction-finding system for UAV swarm vector arrays.

Exploration on 2D DOA estimation of linear array motion: Uniform linear motion

Generally, due to the limitation of the dimension of the array aperture, linear arrays cannot achieve two-dimensional (2D) direction of arrival (DOA) estimation. But the emergence of array motion provides a chance for that. In this paper, a generalized motion scheme and a novel method of 2D DOA estimation are proposed by exploring the linear array motion. To be specific, the linear arrays are controlled to move along an arbitrary direction at a constant velocity and snap per fixed time delay. All the received signals are processed to synthesize the comprehensive observation vector for an extended 2D virtual aperture. Subsequently, since most of 2D DOA estimation methods are not universal to our proposed motion scheme and the reduced-dimensional (RD) method fails to handle the case of the coupled parameters, a decoupled reduced-complexity multiple signals classification (DRC MUSIC) algorithm is designed specifically. Simulation results demonstrate that: a) our proposed scheme can achieve underdetermined 2D DOA estimation just by the linear arrays; b) our designed DRC MUSIC algorithm has the good properties of high accuracy and low complexity; c) our proposed motion scheme with the DRC method has better universality in the motion direction.

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.

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.

An Efficient 2D DOA Estimation Algorithm Based on OMP for Rectangular Array

Recently, orthogonal matching pursuit (OMP) has been widely used in direction of arrival (DOA) studies, which not only greatly improves the resolution of DOA, but can also be applied to single-snapshot and coherent source cases. When applying the OMP algorithm to the rectangular array DOA of the millimeter-wave radar, it is necessary to reshape the two-dimensional (2D) signal into a long one-dimensional (1D) signal. However, the long 1D signal will greatly increase the number and length of atoms in the complete dictionary of the OMP algorithm, which will greatly increase the amount of computation. Taking advantage of the sparsity of targets in the DOA space, an efficient 2D DOA estimation algorithm based on OMP for rectangular array is proposed. The main idea is to reduce the number of atoms in the complete dictionary of the OMP algorithm, thereby greatly reducing the amount of computation required. A simulation verifies that the efficiency of the proposed algorithm is much higher than the conventional algorithm with almost the same estimation accuracy.

Deep Unfolded Gridless DOA Estimation Networks Based on Atomic Norm Minimization

Deep unfolded networks have recently been regarded as an essential way to direction of arrival (DOA) estimation due to the fast convergence speed and high interpretability. However, few consider gridless DOA estimation. This paper proposes two deep unfolded gridless DOA estimation networks to resolve the above problem. We first consider the atomic norm-based 1D and decoupled atomic norm-based 2D gridless DOA models solved by the alternating iterative minimization of variables, respectively. Then, the corresponding deep networks are trained offline after constructing the corresponding complete training datasets. At last, the trained networks are applied to realize the 1D DOA and 2D estimation, respectively. Simulation results reveal that the proposed networks can secure higher 1D and 2D DOA estimation performances while maintaining a lower computational expenditure than typical methods.

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.

2D DOA estimation by a large-space T-shaped array

In this paper, a two-dimensional (2D) direction of arrival (DOA) estimation algorithm by a large-space T-shaped array is proposed. The used T-shaped array consists of a generalized unfolded co-prime array and a symmetrically unfolded co-prime array. The minimum element space (MES) of the proposed T-shaped array can exceed half-wavelength of received signals. The symmetry of the T-shaped array is used to construct an extended cross-covariance matrix, singular value decomposition (SVD) of which can obtain multiple signal subspaces. By combining the co-prime characteristic of element spacing with the rotational invariance of uniform linear array, three extended signal subspaces can be obtained without using virtual elements. Using the three extended signal subspaces, high-precision 2D DOA estimation can be got. The proposed T-shaped array has strong robustness to mutual coupling. The proposed method can eliminate angle ambiguity caused by large-space and has higher estimation precision than many similar 2D DOA estimation algorithms. Many simulation results can prove the performance of the proposed scheme.

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.

A Computationally Efficient and Virtualization-Free Two-Dimensional DOA Estimation Method for Nested Planar Array: RD-Root-MUSIC Algorithm.

To address the problem of expensive computation in traditional two-dimensional (2D) direction of arrival (DOA) estimation, in this paper, we propose a 2D DOA estimation method based on a reduced dimension and root-finding MUSIC algorithm for nested planar arrays (NPAs). Specifically, the algorithm proposed in this paper transforms the problem based on 2D spectral peak search into two one-dimensional estimation problems by reducing the dimension, and then transforms the one-dimensional estimation problem into a problem of polynomial root finding. Finally the parameters are paired to realize the 2D DOA estimation. The proposed algorithm not only performs two root finding operations directly according to the 2D spectral function transformation, avoiding the performance degradation caused by intermediate operations, but can also fully exploit the enlarged array aperture offered by NPAs with reduced computational complexity and no need for virtualization. The superiorities of the proposed algorithm in terms of estimation accuracy and complexity are verified by simulations.

Low-Complexity 2D DOA Estimation and Self-Calibration for Uniform Rectangle Array with Gain-Phase Error

Most subspace-based algorithms need exact array manifold for direction of arrival (DOA) estimation, while, in practical applications, the gain-phases of different array elements are usually inconsistent, degrading their estimation performance. In this paper, a novel low-complexity 2D DOA and gain-phase error estimation algorithm is proposed by adding auxiliary array elements in a uniform rectangular array (URA). Firstly, the URA is modeled as the Kronecker product of two uniform linear arrays (ULAs) to decouple the 2D DOA estimation. Then, several well-calibrated auxiliary array elements are added in the two ULAs, based on which the rotation invariant factor of the URA destroyed by the gain-phase error is reconstructed by solving constrained optimization problems. Lastly, ESPRIT is used to estimate the 2-D DOA and the gain-phase error coefficients. The closed-form expressions of the estimation CRBs are also derived, providing insight into the impact of gain-phase error on DOA estimation. Simulation results are used to validate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.

Fast and Efficient Two-Dimensional DOA Estimation for Signals with Known Waveforms Using Uniform Circular Array

This paper addresses the two-dimensional (2D) direction-of-arrival (DOA) estimation issue for signals with known waveforms but unknown amplitudes using uniform circular array (UCA). Unlike maximum likelihood (ML) methods such as decoupled maximum likelihood (DEML), parallel decomposition (PADEC) and so forth, which estimate DOA by spectrum peak search, we propose an efficient interferometer-based method with known waveforms. The proposed method first estimates spatial signature matrix based on ML method whose each column contains 2D DOA information corresponding to a source. Then, an interferometer procedure is performed to obtain 2D DOA estimate of each source from a closed-form solution separately and in parallel. Several simulation results show that the proposed method can achieve a significantly improvement in performance that coincides with the ML method as well as Cramér-Rao Bound (CRB), especially under some poor conditions, such as low SNR, fewer sensors or small snapshots. In addition, the performance will not degrade as the number of sources increases if the source signals are uncorrelated with each other. Meanwhile, it reduces a great amount of computational complexity without loss of too much accuracy. Thus, the proposed method is quite suitable for 2D DOA estimation with known waveforms in practice.

A high-precision 2D DOA estimation algorithm by a large-space three-parallel array for reducing mutual coupling

In this paper, a high-precision two-dimensional (2D) direction of arrival (DOA) estimation algorithm by three parallel uniform linear arrays (ULAs) is proposed. Both the internal spacing of each sub-array and the spacing between two adjacent sub-arrays can exceed the half-wavelength of incident signal. An extended propagator method (PM) algorithm is introduced to obtain a multiple extended propagator matrix by processing the covariance matrix of received signals. Then, by using the extended propagator matrix, unambiguous and high-precision 2D DOA estimation can be obtained without extra pairing process. For the proposed array construction, mutual coupling effect can be ignored as long as the element interval is large enough. The extended PM algorithm based on the proposed array has far higher precision than the existing similar algorithms, which can be proved by some simulation experiments.