2D Direction Of Arrival Estimation Research Articles

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.

2D DOA Estimation of Coherently Distributed Sources for Planar Arrays Based on Blind Signal Separation

A novel method is presented to estimate the direction-of-arrival (DOA) of coherently distributed (CD) sources for planar arrays. In the proposed method, the two-dimensional (2D) angular parameters are obtained by making use of the estimated generalized array manifold matrix, which is separated from the received observation data based on blind signal separation algorithm. The proposed method offers a number of advantages. First, the 2D central DOAs and angular spread variances can be estimated simultaneously. Second, the deterministic angular distributed functions (DADFs) of the CD sources do not need to know. Third, the special array geometries are not required, as the method is applicable to planar arrays. Computer simulations are shown to verify the efficacy of the proposed method.

Array manifold matching algorithm based on fourth-order cumulant for 2D DOA estimation with two parallel nested arrays

In this paper, a two-dimensional (2D) direction-of-arrival (DOA) estimation algorithm with two parallel nested arrays is developed. Firstly, a constructor method for fourth-order cumulant (FOC) matrices is given according to the distribution of sensors. Then a pre-existing DOA estimation technique is firstly used to estimate the elevation angles and an improved unilateral array manifold matching (AMM) algorithm is used to estimate the azimuth angles. Compared with some classical 2D DOA estimation algorithms, the proposed algorithm has much better estimation performance, particularly in the case of low SNR environment. Compared with some traditional FOC-based algorithms, the proposed algorithm has higher estimation precision. Simulation results can illustrate the validity of proposed algorithm.

Compressive-Sensing-Aided MIMO Radar Enabling Multi-Functional and Compact Sensors in Air Scenarios Using Optimized Antenna Arrays

We address the problem of direction-of-arrival (DoA) estimation for air targets using a compact, multi-functional radar sensor. In order to enhance the angular resolution of such sensors while exploiting the sparseness of typical air scenarios, we consider the combination of a multiple-input multiple-output (MIMO) radar approach with suitable compressive-sensing (CS) techniques. In particular, we investigate the combination of MIMO processing for two-dimensional (2D) antenna arrays with CS-based angular processing for three-dimensional (3D) target localization and 2D DoA estimation in azimuth and elevation. We analyze the benefits of randomized antenna element positions in one and two dimensions and devise optimized array geometries for practicable aperture sizes. In particular, we take physical side constraints into account, such as the smallest realizable/ desired element spacing as well as area restrictions for antenna placement within the overall aperture. The aperture area reserved by this means could be used to accommodate additional hardware components enabling a multi-functional sensor approach. Extensive computer simulation results for different 3D target scenarios illustrate the advantages of our CS-based compact MIMO radar approach with randomized antenna elements compared to fully randomized arrays, given the same number of physical antenna elements.

Sparse planar arrays for azimuth and elevation using experimental data.

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

Optimization of Non-uniform Planar Antenna Array Topology in Two-dimensional DOA Estimation

The paper deals with the optimization of the sparse planar antenna array for direction of arrival (DOA) estimation in two dimensions (azimuth and elevation). The optimization algorithm was proposed on the basis of the peak sidelobe level (SLL) and half-power beamwidth (HPBW) parameters. In empirical validation, we have set up a measurement system to test the efficiency of an optimized array configuration. The array was configured using the patch antennas with frequency band 2.4 GHz. In comparison with several popular array configurations, the experimental results show that the proposed antenna array was optimized, and it provided higher accuracy and resolution in two-dimensional (2D) DOA estimation.

2D DOA Estimation Exploiting Vertical Synthetic Planar Arrays

In this paper, vertical motions of sparse linear arrays (SLAs) are utilized to generate equivalent synthetic planar arrays for two-dimensional (2D) direction-of-arrival (DOA) estimation. The proposed array geometry named vertical synthetic planar array (VSPA) consists of an arbitrary SLA on the x-axis and a series of its time-shifted arrays in the vertical orientation. With the original linear array and the moving trail known, the difference coarray of VSPA can be easily obtained. By utilizing both the synthetic aperture processing and the coarray technique, VSPA has the ability to construct a synthetic planar array with only an SLA used. Compared with the traditional sparse planar arrays (SPAs), such as 2D nested array and 2D coprime array, VSPA can achieve higher degree-of-freedom and improved 2D DOA estimation performance with the same number of sensors. Moreover, as different original linear arrays and moving trails can be chosen for different applications, the construction of VSPA is of high flexibility. Numerical simulations are presented to verify the superiority of the proposed VSPA geometry over other typical SPAs.

Efficient sparse parameter estimation based methods for two‐dimensional DOA estimation of coherent signals

This study addresses the problem of direction-of-arrival (DOA) estimation of coherent signals via sparse parameter estimation. Since many sparse methods provide good performances regardless of signal correlations and array geometry, they can be considered as candidates for DOA estimation of coherent signals impinging on a sensor array with arbitrary geometry. However, their straightforward applications require high computational loads especially for two-dimensional (2D) DOA estimation. Two efficient methods based on sparse parameter estimation are herein presented; one is a combined approach of sparse estimation and the RELAX algorithm extended for 2D DOA estimation and the other relies on the adaptive 2D grid refinement and power update control. Numerical simulations are performed to demonstrate the efficiency of the proposed methods using a uniform circular array for both 1D and 2D DOA estimation cases. It is shown that sparse asymptotic minimum variance (SAMV)-RELAX, a combined approach of SAMV and RELAX, outperforms SAMV and multi-stage SAMV in 2D scenarios without suffering from plateau effects for off-grid signals and that its computational load is significantly lower than those of SAMV and multi-stage SAMV. In addition, SAMV-RELAX does not require the difficult selection of grid parameters for fine DOA estimation unlike the multi-stage approach.

Improved DFT Algorithm for 2D DOA Estimation Based on 1D Nested Array Motion

In this letter, two-dimensional (2D) direction of arrival (DOA) estimation using one-dimensional (1D) nested array motion is studied, and an improved Discrete Fourier transform (DFT) algorithm is proposed. Exploiting nested array to move vertically along its axis enables 2D DOA estimation with large-scale and hole-free difference co-array. DFT algorithm has lower complexity than multiple signal classifications(MUSIC) method, but traditional DFT algorithm still requires multiple extra searches to ensure estimation accuracy. We use DFT to obtain the initial angle estimations, and then compensate the estimation offsets via total least squares (TLS) constructed from Taylor expansion approximation. Compared with the traditional DFT search method, the proposed method has lower complexity and better performance. Multiple simulations are conducted to verify the effectiveness of our approach.

Optimal rotation of UAV for enhanced 2D direction of arrival estimation

Optimal rotation of an unmanned aerial vehicle (UAV) mounted with a cross array for enhanced two-dimensional (2D) direction estimation is discussed, and a novel method based on Cramer–Rao bound (CRB) minimisation is proposed. CRB serves as the lower bound for direction-of-arrival (DOA) estimation, which directly determines the localisation performance of jamming sources. Based on the fact that CRB differs while UAV's rotation angle changes, a theoretical closed-form solution for an optimal rotation in the 2D direction estimation is derived, and then the authors can acquire capability enhancement of DOA estimation after the optimal rotation. Rigorous analysis and multiple simulations demonstrate the feasibility and effectiveness of the proposed scheme.

Computationally Efficient Ambiguity-Free Two-Dimensional DOA Estimation Method for Coprime Planar Array: RD-Root-MUSIC Algorithm

While the two-dimensional (2D) spectral peak search suffers from expensive computational burden in direction of arrival (DOA) estimation, we propose a reduced-dimensional root-MUSIC (RD-Root-MUSIC) algorithm for 2D DOA estimation with coprime planar array (CPA), which is computationally efficient and ambiguity-free. Different from the conventional 2D DOA estimation algorithms based on subarray decomposition, we exploit the received data of the two subarrays jointly by mapping CPA to the full array of the CPA (FCPA), which contributes to the enhanced degrees of freedom (DOFs) and improved estimation performance. In addition, due to the ambiguity-free characteristic of the FCPA, the extra ambiguity elimination operation can be avoided. Furthermore, we convert the 2D spectral search process into 1D polynomial rooting via reduced-dimension transformation, which substantially reduces the computational complexity while preserving the estimation accuracy. Finally, numerical simulations demonstrate the superiority of the proposed algorithm.

2D DOA estimation algorithm with increased degrees of freedom for two parallel linear arrays

In this paper, a two-dimensional (2D) direction-of-arrival (DOA) estimation algorithm with increased degrees of freedom for two parallel linear arrays is presented. Being different from the conventional two-parallel linear array, the proposed two-parallel linear array consists of two uniform linear arrays with non-equal inter-element spacing. Propagator method (PM) is used to obtain a special matrix which can be utilized to increase the virtual elements of one of uniform linear arrays. Then, the PM algorithm is used again to obtain automatically paired elevation and azimuth angles. The simulation results and complexity analysis show that the proposed method can increase the number of distinguishable signals and improve the estimation precision without increasing the computational complexity.

ESPRIT-Based DOA Estimation with Spatially Spread Long Dipoles and/or Large Loops

The radiation efficiency of short electric dipole and small magnetic loop is low. Therefore, the long electric dipole and large magnetic loop for direction of arrival (DOA) estimation are investigated in this study. A novel array composed of long electric dipole, large magnetic loop, or a hybrid long electric dipole and large magnetic loop is proposed. Then a corresponding algorithm based on ESPRIT is proposed to estimate the two-dimensional (2D) DOA. The proposed array has eight elements. The first four elements and other four elements construct the rotational invariant property. Then, the 2D direction cosine can be estimated accurately but with ambiguity. After that, the ambiguous value is instituted into the spatially spread vector sensor for spatial phase compensation. Then, the steering vector of the collocated orthogonal vector sensor is obtained to calculate a fake coarse DOA estimation. By comparing the above ambiguous fine estimation with the fake coarse estimation, the closest estimation is taken as the finally 2D DOA estimation. The computation of the proposed algorithm is small due to a lack of angle searching. Moreover, the long dipole has high radiation efficiency, and the spatially spread vector sensor has low mutual coupling. Simulation results demonstrate the effectiveness of the proposed algorithm.

Improved subspace‐based method for 2D DOA estimation with L‐shaped array

An improved subspace-based method for 2D direction of arrival (DOA) estimation of an L-shaped array is proposed in this Letter. Based on real-valued singular value decomposition (SVD), the signal subspaces corresponding to the 2D DOA are obtained from the left and right singular vectors, respectively. Then, the weighted least squares method is utilised to estimate the DOAs from the reconstructed complex-valued signal subspaces, which are automatically paired. Owing to the real-valued SVD, the complexity of the proposed algorithm is reduced and numerical results confirm the effectiveness and accuracy of the proposed approach.

Gridless Super-Resolution Direction-of-Arrival Estimation with Arbitrary Planar Sparse Array

AbstractTwo-dimensional (2D) direction-of-arrival (DOA) estimation with arbitrary planar sparse array has attracted more interest in massive multiple-input multiple-output application. The research on this issue recently has been advanced with the development of atomic norm technique, which provides super resolution methods for DOA estimation, when the number of snapshots is limited. In this paper, we study the problem of 2D DOA estimation from the sparse array with the sensors randomly selected from uniform rectangular array. In order to identify all azimuth and elevation angles of the incident sources jointly, the 2D atomic norm approach is proposed, which can be solved by semidefinite programming. However, the computational cost of 2D atomic norm is high. To address this issue, our work further reduces the computational complexity of the problem significantly by utilizing the atomic norm approximation method based on the concept of multiple measurement vectors. The numerical examples are provided to demonstrate the practical ability of the proposed method to reduce computational complexity and retain the estimation performance as compared to the competitors.

Joint 2D DOA and Doppler frequency estimation for L-shaped array using compressive sensing

A joint two-dimensional (2D) direction-of-arrival (DOA) and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing (CS) framework. Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix, three smaller scale matrices with independent azimuth, elevation and Doppler frequency are introduced adopting a separable observation model. Afterwards, the estimation is achieved by L 1 -norm minimization and the Bayesian CS algorithm. In addition, under the L-shaped array topology, the azimuth and elevation are separated yet coupled to the same radial Doppler frequency. Hence, the pair matching problem is solved with the aid of the radial Doppler frequency. Finally, numerical simulations corroborate the feasibility and validity of the proposed algorithm.

Three-Dimensional Coprime Array for Massive MIMO: Array Configuration Design and 2D DOA Estimation

In massive multiple-input multiple-output (MIMO) systems, it is critical to obtain the accurate direction of arrival (DOA) estimation. Conventional three-dimensional array mainly focuses on the uniform array. Due to the dense arrangement of the sensors, the array aperture is limited and severe mutual coupling effects arise. In this paper, a coprime cubic array (CCA) configuration design is presented, which is composed of two uniform cubic subarrays and can extend the interelement spacing with a selection of three pairs of coprime integers. Compared with uniform cubic array (UCA), CCA achieves the larger array aperture and less MC effects. And the analytical expression of Cramer–Rao Bound (CRB) for CCA is derived which verifies that the proposed CCA geometry outperforms the conventional UCA in two-dimensional (2D) DOA estimation performance in massive MIMO systems. Meanwhile, we propose a computationally efficient 2D DOA estimation algorithm with high accuracy for CCA. Specifically, we utilize array mapping to extract two uniform arrays from the nonuniform array by exploiting the relation derived from the signal subspace and the two directional matrices. Then, we operate a reduced dimension process on the uniform arrays and convert the 2D spectrum peak searching (SPS) problem into one-dimensional (1D) one, which significantly reduces the computational complexity. In addition, we employ the polynomial root finding technique with a lower complexity instead of 1D SPS to further relieve the computational complexity. Simultaneously, with coprime property, the phase ambiguity problem is solved, which results from the large interelement spacing. Numerical simulation results demonstrate that the proposed algorithm is very computationally efficient without degradation of DOA estimation performance.

Two-Dimensional DOA Estimation via Deep Ensemble Learning

To achieve fast and accurate two-dimensional (2D) direction of arrival (DOA) estimation, a novel deep ensemble learning method is presented in this paper. First, a convolutional neural network (CNN) is employed to learn a mapping between the spatial covariance matrix of the received signals from the antenna elements and the directions of arrival. To avoid any explicit feature extraction step, the real and imaginary parts of the spatial covariance matrix are fed to the CNN. The output layer of the CNN uses three neurons, two of them are the sine and cosine values of the azimuth angle that are used to uniquely determine the azimuth angle, and the third neuron is a normalized value for representing the elevation angle. Second, to improve the prediction performance, since that a single CNN with limited training data has difficulties learning the highly complex and nonlinear mapping from the received signal to the angle of arrival, an ensemble learning method is proposed. Five different CNN networks are trained independently with different training conditions. The prediction results of each individual CNN are calculated as an average to obtain the final estimated results of the azimuth and elevation angles. Simulation results show that the processing time of the proposed deep ensemble learning method is dramatically reduced. In terms of the accuracy, it outperforms the neural network-based 2D DOA estimation and achieves performance comparable to the MUSIC algorithm.

Approach of 2D direction of arrival estimation of FMCW traffic radar by utilising 1D array

The frequency-modulated continuous wave (FMCW) radar will play a more important role in future intelligent traffic systems due to low cost and high adaptability to complex environments. Generally, a 2D array is utilised to measure range, speed and azimuth and elevation angles (4D) for multiple vehicles simultaneously. However, a traffic radar utilising a 2D array will enhance its system complexity; therefore, the increased cost would make it less superior to LiDAR. In this Letter, an azimuth and elevation angles estimation method of FMCW radar utilising only 1D array is proposed. Thus, it can provide 4D parameters to multiple vehicles simultaneously. The feasibility of the proposed approach is verified by on-road measurement data.

Two‐dimensional DOA estimation for noncoherent and coherent signals using subspace approach

AbstractThis paper focuses on the problem of two‐dimensional (2D) direction‐of‐arrival (DOA) estimation for a mixture of noncoherent and coherent signals impinging on two parallel uniform linear arrays. It adopts the principal‐eigenvector utilization for modal analysis (PUMA)–based algorithm. The algorithm offers a closed‐form solution for updating the 2D DOA estimation and pairs the estimated angles automatically as well as has mild computational complexity. Finally, simulation results confirm that our PUMA‐based algorithm has good performance in handling 2D DOA estimation even in the presence of coherent signals.