DOA Estimation Accuracy Research Articles

Two-Dimensional Minimum Sensor Array: A New Perspective to Array Design

In this article, we design/propose a new class of planar arrays sparsely located on a two dimensional lattice to achieve the highest Degrees Of Freedom for a given number of sensors. We formulate an optimization problem to search for a hole free 2D sparse array with the fewest possible sensors. We convert this problem into a nonlinear binary problem by changing the variables, then into a binary linear programming problem and solve it efficiently by employing Branch and Bound programming. Our results show that this optimal array outperforms alternative state-of-the-art 2D array geometries in terms of target resolution and DOA estimation accuracy given the number of sensors. Moreover, the proposed array outperforms other geometries in terms of the resolution probability of close targets and in presence of mutual coupling.

Parameter Estimation of Frequency-Hopping Signal in UCA Based on Deep Learning and Spatial Time–Frequency Distribution

The parameter estimation and sorting of frequency-hopping (FH) signals are of great importance in both civilian and military applications. In this article, the estimation of hopping time, hopping period, hopping frequency, instantaneous bandwidth, and 2-D direction of arrival (2-D-DOA) of multiple FH signals in the uniform circular array (UCA) is studied. First, a novel lightweight model based on You Only Look Once (YOLO), named FH-GYOLO, is proposed to detect FH signals and estimate their time–frequency (TF) parameters. The proposed FH-GYOLO takes advantage of the ghost module, which can significantly reduce the computational cost and, simultaneously, achieve an efficient detection with high performance. Then, the 2-D-DOA estimation method of FH signals in UCA is proposed with the spatial TF distribution (STFD). In the proposed method, the steering vector of UCA and the STFD matrix are transformed into beamspace by beamspace transformation, and the closed-form solution is derived for the estimation of autopaired elevation and azimuth angles without the computationally expensive spatial–spectral search. Furthermore, in the proposed method, an iterative compensation process is developed, which can greatly improve the accuracy of DOA estimation without significantly increasing the computational complexity. Extensive simulation results and analysis demonstrated that the proposed algorithms exhibit better or similar performance than the other benchmark methods, and most importantly, the computational cost is substantially reduced.

CRB Weighted Source Localization Method Based on Deep Neural Networks in Multi-UAV Network

With the advent of the Internet of Things (IoT) era, the multi-unmanned aerial vehicle (UAV) networks have attracted great attention in the fields of source detection and localization. However, as a real-time signal processing performance of the UAV is limited by the computing speed and accuracy of the embedded hardware, the effectiveness of source localization is greatly reduced. Aiming at improving the accuracy and computational efficiency of source localization, a Cramer-Rao bound (CRB) weighted multi-UAV network source localization method is proposed based on the deep neural networks (DNN) and spatial spectrum fitting (SSF). The proposed source localization system is composed of UAVs equipped with a radar array. The source location can be achieved using the DOA of the sources signals of UAVs, but the accuracy and real-time performance of the conventional DOA estimation algorithms are not satisfactory, and the data fusion strategy of the conventional cross-location framework needs further improvement. In the proposed method, a DNN-based SSF denoted as the deep SSF (DeepSSF), is designed to achieve accurate DOA estimation. In the DeepSSF, the DOA estimation performance is guaranteed by the DNN’s strong nonlinear fitting ability and highly parallel structure. In addition, based on the obtained DOA information, the source is located once by every two UAVs. Finally, the source localization is realized based on the weighted CRB according to the principle that the more the DOA distribution deviates from zero, the lower the estimation accuracy. The simulation results verify the efficiency of the proposed method.

Modeling and numerical analysis of volume array radiation pattern impact on2D‐DOAestimation accuracy considering arrays' aperture angle

AbstractThis paper tries to obtain the maximum estimation accuracy of 2‐dimensional Direction of Arrival (2D‐DOA) from the spatial signal resource in the angle approaching the horizon by using the volume arrays pattern synthesizing. For this purpose, the well‐known Multiple Signal Classification (MUSIC) and the algorithm Root Mean Square Deviation (RMSD) are used to investigate 2D‐DOA estimation accuracy. For accurate design of array structure, the antenna elements' radiation pattern have been considered based on the full‐wave simulations along with the mutual coupling and shadow effects. The results show that the volume array structure presented with 13 radiative elements and the two side angles of 30 and 45 degrees has a much better DOA estimation accuracy in all angles especially in angles close to the horizon, compared to the planar array with the same number of radiative elements. Also, at the angle ±90° from broadside the presented volume aperture provides a maximum gain of up to 15.4 dBi, which is much more than the produced gain of planar aperture under the same conditions.

DOA Estimation Method Based on Improved Deep Convolutional Neural Network.

For the multi-target DOA estimation problem of uniform linear arrays, this paper proposes a DOA estimation method based on the deep convolution neural network. The algorithm adopts the deep convolutional neural network, and the DOA estimation problem of the array signal is transformed into the inverse mapping problem of the array output covariance matrix to a binary sequence in which “1” indicates that there is a target incident in the corresponding angular direction at that position. The upper triangular array of the discrete covariance matrix is used as the data input to realize the DOA estimation of multiple sources. The simulation results show that the DOA estimation accuracy of the proposed algorithm is significantly better than that of the typical super-resolution estimation algorithm under the conditions of low SNR and small snapshot. Under the conditions of high SNR and large snapshot, the estimation accuracy of the proposed algorithm is basically the same as those of the MUSIC algorithm, ESPRIT algorithm, and ML algorithm, which are better than that of the deep fully connected neural network. The analysis of the simulation results shows that the algorithm is effective, and the time and space complexity can be further reduced by replacing the square array with the upper triangular array as the input.

Non-circular signal DOA estimation based on coprime array MIMO radar

Aiming at the problems of low degree of freedom, small array aperture, and phase ambiguity in traditional coprime array direction-of-arrival estimation methods, a non-circular signal DOA estimation method based on expanded coprime array MIMO radar is proposed. Firstly, this method combines the coprime array and the MIMO radar to form transmitter and receiver array. Secondly, the array is expanded using the non-circular signal characteristics to reconstruct the received signal matrix. Then the dimensionality reduction is performed. The two-dimensional spectral peak search is converted into an optimization problem, and the optimization of the two-dimensional MUSIC algorithm is reconstructed using constraints, and a cost function is constructed to solve the problem. In addition, use the power series of the noise eigenvalues to correct the noise subspace to further improve the accuracy of the algorithm. Finally, the problem of no phase ambiguity in the method in this article is derived. Simulation experiments show that the method in this article can effectively avoid phase ambiguity, greatly improve the degree of freedom, and expand the array aperture. Compared with the traditional MUSIC algorithm and the mutual prime array MUSIC algorithm, it has better resolution and DOA estimation accuracy.

Fast DOA Estimation Based on the Transform Domain Weighted Noise Subspace Fitting Algorithm for Generalized Sparse Array

Compared with uniform arrays, a generalized sparse array (GSA) can obtain larger array aperture because of its larger element spacing, which improves the accuracy of DOA estimation. At present, most DOA estimation algorithms are only suitable for the uniform arrays, while a few DOA estimate algorithms that can be applied to the GSA are unsatisfactory in terms of computational speed and accuracy. To compensate this deficiency, an improved DOA estimation algorithm which can be applied to the GSA is proposed in this paper. First, the received signal model of the GSA is established. Then, a fast DOA estimation method is derived by combining the weighted noise subspace algorithm (WNSF) with the concept of “transform domain” (TD). Theoretical analysis and simulation results show that compared with the traditional multiple signal classification (MUSIC) algorithm and the traditional WNSF algorithm, the proposed algorithm has higher accuracy and lower computational complexity.

A Two-Dimensional DOA Estimation Method Based on Virtual Extension of Sparse Array

The interelement spacing of a coprime array breaks through the half-wavelength limitation, so that a larger array aperture can be obtained with a fixed number of array elements. In this paper, the symmetry of the noncircular signal is used to virtually expand the L-shaped array into an orthogonal cross array. Furthermore, the virtual received signal of the augmented array is obtained by the second-order statistic of the received data. Decoupling and dimension reduction of elevation and azimuth are realized by a z-axis subarray and y-axis subarray. Finally, the sparse reconstruction of the signal is realized by the minimum absolute convergence and selection operator method. This method can enlarge the aperture and freedom of array and has higher accuracy and resolution of DOA estimation. It has the advantages of automatic parameter pairing without additional pairing operation and is effective for coherent and incoherent signals. The final numerical simulation results prove the effectiveness of the method in this paper.

Lightweight CNNs-Based Interleaved Sparse Array Design of Phased-MIMO Radar

Conventional transmit subarray partitioning schemes of phased-MIMO radar will cause several problems, the reduction of array aperture, the increase of feeding network complexity and optimization algorithms time cost. Focus on the problems above, this paper proposes a deep learning-based interleaved sparse transmit subarray partitioning method. Firstly, the training data is generated by phased-MIMO array manifold matrix. Secondly, a dimensionality reduction method for radar data is introduced to reduce the dimensionality of the sample data while minimizing information loss. Then, a lightweight convolutional neural network is constructed for training and the optimal array structures is selected by classification. Finally, linear and plane arrays experiment results show that our proposed method can achieve 97.95% classification accuracy, better than other conventional dimensionality reduction methods and neural networks; compared with the traditional SCP partitioning method, our proposed method has similar beampattern sidelobe level and DOA estimation accuracy, but the time cost is greatly reduced.

Improved resolving capabilities of linear array using 2 q th order non‐circular statistics

Resolving more sources than sensors is always of interest to researchers. For this purpose, generation of the virtual array from the non-uniform linear array has recently gathered a lot of attention. The covariance/cumulant lags of the array output define virtual sensors and thereby virtual array. The aperture of the designed virtual array is much more than the aperture of physical array. This large aperture provides highest degrees of freedom to solve the underdetermined system. In the case of non-circular signals, pseudo-covariances/cumulants are significant, and this additional information can further be used to increase the virtual array aperture. Herein, a framework is proposed to extend the virtual array aperture by additionally using pseudo-/non-circular cumulants along with the circular cumulants of the array output for non-circular signals. The suggested framework not only increases the resolvability but also improves the DoA estimation accuracy. With fourth-order statistics, the virtual array aperture becomes almost double, and the increment is much more with further higher order statistics. Numerical simulations demonstrate the efficacy of the claims.

Use of “virtual” antenna array methods for reduction of DO A estimation systematic error caused by the scattering of waves on mobile carrier body

Article shows that “virtual” antenna arrays can be used to effectively improve the DOA estimation accuracy of mobile direction finders. “Virtual” antenna arrays are the samples of the spatial field distribution calculated by approximation of the field near a three-dimensional scattering body that supports physical (“real”) antenna system. Signals from the outputs of the “real” array are used as input data for the approximation process. Information on the geometry and material properties of the medium is not required. This procedure can be based on the main provisions of electrodynamics (Kirchhoff-Huygens principle, the Lorenz lemma, method of equivalent currents and fields) or on the use of quasi-static approximation of the field based on the apparatus of the theory of analytic functions of a complex variable (the Cauchy integral and Laurent series). “Virtual” arrays can reduce the error caused by the carrier body without costly and labour-intensive calibration procedures.

A Two-Dimensional Direction Finding Method Based on Non-Uniform Array

In this paper, an aperture expanding direction finding algorithm using L-shaped non-uniform sparse array is proposed. Firstly, the virtual array is expanded by vectorizing, de-redundant and sorting of received data covariance matrix. Secondly, the full rank matrix is got by smoothing the virtual array data, and the signal subspace is obtained by matrix block processing. Finally, the elevation angle and azimuth angle are acquired by using the rotation invariant relation. The algorithm does not need to decompose the covariance matrix of the data, nor does it need to search the two-dimensional spectral peaks. It can greatly reduce the computational complexity when there are many array elements and large number of snapshots. The simulation results show that the sparse array arrangement can enlarge the array aperture, improve the parameter resolution and the accuracy of DOA estimation, and verify the effectiveness of the proposed algorithm.

Padded Coprime Arrays for Improved DOA Estimation: Exploiting Hole Representation and Filling Strategies

As a generalized coprime array structure, the coprime array with displaced subarrays (CADiS) allows a large minimum inter-element spacing by introducing a specific displacement between two sparse subarrays. While this structure can effectively reduce mutual coupling, the holes in its difference co-array greatly decrease the achievable number of uniform degrees of freedom (DOFs). In this paper, we first provide a complete characterization for the hole locations in the difference co-array generated by a tailored CADiS (tCADiS) as the union of four subsets of locations related via simple symmetry properties. We then introduce two representation approaches for the hole locations, revealing that the latter can be generated from the differences between sensor locations in the subarray of tCADiS and a small uniform linear array, referred to as a padded subarray. Subsequently, we propose novel padded coprime arrays (PCAs) by incorporating the padded subarray into tCADiS to enlarge the consecutive segments in the difference co-array. This not only contributes to increase the number of available uniform DOFs, but also helps mitigating the mutual coupling by limiting the number of sensor pairs with small separations. Finally, numerical simulation results are provided to demonstrate the superiority of PCAs over existing sparse array configurations in terms of DOF, mutual coupling and DOA estimation accuracy.

Classification-Based One-Bit DOA Estimation for Sparse Arrays

Nowadays, high-resolution DOA estimation techniques have been widely used in many fields such as sonar, communication, radio astronomy and biomedicine etc. Unfortunately, conventional algorithms cannot achieve high precision due to the limitation of the array aperture, and usually suffer from high computational complexity. In this paper, we innovatively model the DOA estimation problem of incoherent signals as a binary classification problem and greatly reduce physical complexity by virtue of sparse arrays. We first propose a classification framework for DOA estimation by benefiting from one-bit quantification. In this framework, any classification algorithm can be exploited to estimate DOA, such as logistic regression used in this paper. And then, sparse array is considered to reduce the exceeding number of antennas. Moreover, an iterative grid refinement procedure is presented to achieve more accurate DOA estimation and further reduces the actual number of physical antennas. Simultaneously, we derive Cramer-Rao bound (CRB) for the proposed algorithm. Finally, simulations are conducted for correctness and validation and the results illustrate the significant performance and reduction of complexity in hardware and computation over the existing methods.

Determining Direction‐of‐Arrival Accuracy for Installed Antennas by Postprocessing of Far‐Field Data

AbstractDirection‐of‐arrival (DoA) estimation accuracy can be degraded due to installation effects, such as platform reflections, diffraction from metal edges, and reflections and refraction in the radome. To analyze these effects, this paper starts with a definition of the term installation error related to DoA estimation. Thereafter, we present a postprocessing method, which can be used to determine the DoA estimation accuracy for installed antennas. By computing synthetic signals from the installed far‐field data, it is possible to analyze the installation errors described above, in addition to analyzing array model errors. The method formulation is general, thus allowing generic array configurations, installation configurations, and direction‐finding algorithms to be studied. The use of the presented method is demonstrated by a case study of a wideband four‐quadrant array. In this case study, we investigate the installation errors due to a single‐shell radome. Thereafter, the effects of platform reflections are also analyzed, for an antenna placement in the tail of a fighter aircraft. Simulation results are presented for both the monopulse and the MUltiple SIgnal Classification direction‐finding algorithms.

A research on blind area of random layout units for localization

Acquisition distance information of the underwater target is very important to evaluate the target noise level, so it is necessary to do some research on the passive localization method for the underwater target. In this paper, the multi-hydrophone units model is used to passively achieve target localization information in the underwater environment; the accurate DOA estimation and ranging calculation method are presented. The localization blind area problem with different units models is discussed. The blind area problem caused by traditional passive localization model (three units) is solved by the method with four random units, which can locate the underwater unpredictable target in arbitrary direction.

Covariance Matrix Reconstruction for Direction Finding with Nested Arrays Using Iterative Reweighted Nuclear Norm Minimization

In this paper, we address the direction finding problem in the background of unknown nonuniform noise with nested array. A novel gridless direction finding method is proposed via the low-rank covariance matrix approximation, which is based on a reweighted nuclear norm optimization. In the proposed method, we first eliminate the noise variance variable by linear transform and utilize the covariance fitting criteria to determine the regularization parameter for insuring robustness. And then we reconstruct the low-rank covariance matrix by iteratively reweighted nuclear norm optimization that imposes the nonconvex penalty. Finally, we exploit the search-free DoA estimation method to perform the parameter estimation. Numerical simulations are carried out to verify the effectiveness of the proposed method. Moreover, results indicate that the proposed method has more accurate DoA estimation in the nonuniform noise and off-grid cases compared with the state-of-the-art DoA estimation algorithm.

An optimizing nested MIMO array with hole-free difference coarray

According to the newly proposed nested MIMO (Multiple-Input Multiple-Input Multiple Output Multiple Array) array design method, we propose to replace the traditional nested array into an optimizing nested array, ie, to optimizing nested MIMO array design. It not only retains the original advantage of nested MIMO array design closed expression with array element position and degree of freedom(DOF), but also greatly improves the array aperture and DOF. Optimizing nested MIMO array firstly uses the optimizing nested array as the transmitting and receiving arrays, and then make the difference set processing for the coarray of MIMO array (coarray, CA). By properly designing the array spacing of the transmitting and receiving arrays, we can obtain a non-porous difference array. When the total number of array elements is given, by analyzing the characteristics of the array structure, the best array element number of the transmitting and receiving arrays can be obtained. Simulation experiments show that compared with the nested MIMO array design, the proposed method can effectively expand the array aperture, increase the DOF, and increase the DOA estimation accuracy of the MIMO radar without increasing the number of actual array elements.

Efficient sparse representation algorithm for accurate DOA estimation of multiple targets with single measurement vector

AbstractIn order to rapidly achieve accurate direction‐of‐arrival (DOA) estimation of multiple targets using a single measurement vector (i.e., array signal vector), we propose a new efficient sparse representation algorithm based on the orthogonal matching pursuit (OMP) using a step‐by‐step search approach. Regardless of the high mutual coherence of redundant dictionary (i.e., array manifold matrix), the optimal sparse solutions for DOAs of multiple targets can be yielded with a relatively low computational cost, as compared to the iterative local searching OMP method that is up‐to‐date. Several simulation and experimental results demonstrated that the proposed scheme is much more effective than the existing subspace‐based algorithms in a noisy environment and other sparse representation algorithms, even in actual measurement cases.

Low-complexity DOA estimation from short data snapshots for ULA systems using the annihilating filter technique

This paper addresses the problem of DOA estimation using uniform linear array (ULA) antenna configurations. We propose a new low-cost method of multiple DOA estimation from very short data snapshots. The new estimator is based on the annihilating filter (AF) technique. It is non-data-aided (NDA) and does not impinge therefore on the whole throughput of the system. The noise components are assumed temporally and spatially white across the receiving antenna elements. The transmitted signals are also temporally and spatially white across the transmitting sources. The new method is compared in performance to the Cramér-Rao lower bound (CRLB), the root-MUSIC algorithm, the deterministic maximum likelihood estimator and another Bayesian method developed precisely for the single snapshot case. Simulations show that the new estimator performs well over a wide SNR range. Prominently, the main advantage of the new AF-based method is that it succeeds in accurately estimating the DOAs from short data snapshots and even from a single snapshot outperforming by far the state-of-the-art techniques both in DOA estimation accuracy and computational cost.