Direction Of Arrival Estimation Method Research Articles

YOLO-DoA: A New Data-Driven Method of DoA Estimation Based on YOLO Neural Network Framework

Direction-of-arrival (DoA) estimation is one of the most promising technologies in array signal processing. Existing data-driven methods for DoA estimation are usually implemented by classification networks, which suffer from insufficient utilization about features of sources and require spectral peak-search stage. In this letter, we reframe DoA estimation as a target detection problem and propose a novel DoA estimation approach on the basis of the you only look once v3 (YOLOv3) framework, namely YOLO-DoA. DoAs of sources with confidence scores are directly predicted from the spectrum proxy with YOLO-DoA and an end-to-end estimation is realized. By combining squeeze-and-excitation operation, cross stage partial connections, and an improved loss function for bounding box regression, the performance of YOLO-DoA is enhanced. Simulation results demonstrate that the proposed approach outperforms several state-of-the-art methods in terms of network size, computational cost, prediction time, and accuracy of DoA estimation.

An ADMM-qSPICE-Based Sparse DOA Estimation Method for MIMO Radar

In recent years, sparse direction-of-arrival (DOA) estimation for multiple-input multiple-output (MIMO) radar has attracted extensive attention and been extensively studied, especially the method based on the classic least absolute shrinkage and selection operator (LASSO) estimator. The alternating-direction method of multipliers (ADMM) is an effective method for solving this problem at the cost of introducing an additional user parameter. To avoid introducing an additional user parameter, this paper adopts an equivalent transformation in the form of the generalized SParse Iterative Covariance-based Estimation (qSPICE) cost function to obtain a mean squared minimized form of the cost function. Then, the problem is transformed into a sparse optimization problem in the form of a weighted LASSO. Next, this unconstrained optimization problem is decomposed into three subproblems, which are solved separately to reduce the dimension of each problem and thus reduce the overall computational complexity based on ADMM. Simulation results and measured data indicate that the proposed method significantly outperforms the traditional super-resolution DOA estimation method and ADMM-LASSO method and slightly outperforms qSPICE in terms of resolution and sidelobe suppression capability. In addition, the proposed method has a much lower computational complexity and substantially fewer iterations than qSPICE.

A DOA Estimation Algorithm Based on Eigenvalues Ranking Problem

Although traditional subspace direction of arrival (DOA) algorithms enable super-resolution, the algorithm performance declines sharply when the number of sources is incorrectly estimated. This article proposes a new DOA estimation method as an optimization problem similar to the conventional minimum variance distortionless response (MVDR) that fully considers the eigenvalues ranking problem. After a mathematical derivation, a concise DOA estimation expression is given based on the mapping between eigenvalues. As the algorithm considers the relative ranking of eigenvalues, the number of sources is not required for DOA estimations. Therefore, the performance of the algorithm does not degrade due to incorrect estimations in the number of sources. To enhance the algorithm performance, this article analyzes the reasons for the formation of pseudo peaks based on the eigenvalues and gives the corresponding boundary conditions. Based on the analysis of white noise, in order to overcome the influence of color noise, this article gives a way to deal with color noise. Finally, the theory of the proposed algorithm is verified through simulation experiments, and its performance is demonstrated through comparative experiments with MUSIC under white and color noise.

A Novel DOA Estimation for Low-Elevation Target Method Based on Multiscattering Center Equivalent Model

The multipath in very high-frequency (VHF)radar will reduce the direction-of-arrival (DOA) estimation accuracy for the low-angle target following. Since the target and multipath signals have strong coherence in the spatial domain, it is challenging to distinguish them accurately. Especially in some terrain complex regions, various scattering media cause the multipath echo exhibit the multi-channel and nonuniform energy distribution features. Therefore, the single multipath DOA estimation methods will mismatch the actual signal, resulting in inaccurate DOA estimation. The current letter presents a new DOA estimation approach using a multiple scattering center model in complex terrain to solve the mentioned issue. In the presented method, multiple multipath is analogous to a single one based on the multipath signal’s spatial coherence. The equivalent model represents the DOA estimation problem with a parametric optimization problem, and the accurate estimation results can be attained using the Newton optimization approach. Compared with the conventional sparse reconstruction method, the presented method is not restricted by the Restricted Isometry Property (RIP), and employs a robust parameter estimation method to solve the angle super-resolution problem under the low signal-to-noise ratio (SNR). The experimental results reflect that the presented model and approach can efficiently promote the DOA estimation precision and calculational performance compared to conventional DOA estimation approaches.

CAE-CNN-Based DOA Estimation Method for Low-Elevation-Angle Target

For the DOA (direction of arrival) estimation of a low-elevation-angle target under the influence of a multipath effect, this paper proposes a DOA estimation method based on CAE (convolutional autoencoder) and CNN (convolutional neural network). The algorithm firstly inputs the signal covariance matrix of the array of the low-elevation target containing direct and reflected waves into the convolutional autoencoder to realize the de-multipath, and uses the spatial features extracted by the convolutional autoencoder as the input of the extreme learning machine to realize the DOA preclassification of direct waves; based on the preclassification results, one branch of the three parallel convolutional neural nets is selected, and the output of the convolutional autoencoder is used as the input of this branch to realize DOA estimation. The simulation results show that the algorithm has better estimation accuracy and efficiency than the conventional algorithms, especially when the DOA of the target is in the lower range. The analysis of the simulation results shows that the algorithm is effective, in which the convolutional autoencoder can effectively realize the de-multipath, and the use of parallel convolutional neural networks can avoid overfitting and underfitting and realize DOA estimation more accurately.

DOA Estimation Method in Echo-localization Ability for Human-beings

The principle of echo-localization processing of human beings is quite similar with animals like bats and dolphins, which has been widely applied in sonar. Direction of Arrival (DOA) methods plays an important role in estimating the radar, sonar and many other echo-localization communication fields. Typical methods in resolving echo-localization problems including classical (Multiple Signal Classification) MUSIC, (Estimation of Signal Parameter via Rotational Invariance Technique), ESPRIT and compressed sensing. The echo-localization methods and the resolving ambiguity methods via uniform array are systematically introduced in this paper. On this basis, the fast and accurate algorithms for human-being echo-localization in parameter (azimuth angle, elevation angle and range) estimation of signal are further introduced from time domain and frequency domain. The accuracy of the angle and distance estimation of the algorithm calculated by computer simulation experiment is over 99.9% and 97% respectively. The effectiveness of DOA method was verified according to MUSIC algorithm, which provides a rapid and accuracy information in echo-localization ability of human being.

A Comprehensive Analysis of the Impact of System Parameters on Subspace-based DoA Estimation Performance

This work provides an explanatory analysis of the influence of input parameters on the performance of subspace-based Direction of Arrival (DoA) estimation algorithms. The objective of this work is twofold. First, to drive a Steering Vector (SV) that works for arbitrary array configuration rather than just Uniform Linear Array (ULA) geometry. Second, to identify how the performance of the subspace-based algorithms is affected by tuning the input parameters. The later objective is crucial as it allows optimizing the algorithm through selecting optimum parameters to set an appropriate tradeoff between complexity and performance based on the intended applications. Toward that end, we firstly drive an SV for arbitrary array configuration followed by revealing the working principle of subspace based DoA techniques. Secondly, we evaluate the impact of several parameters namely Signal to Noise Ratio (SNR), number of snapshots, number of array elements, separation between array elements, number of available sources, and dependency between sources to conduct our analysis. Numerical simulations over a wide range of scenarios along with intensive Monte Carlo simulations are conducted to show the influence of these parameters on the resolution, accuracy, and complexity of the subspace based DoA estimation algorithm. As demonstrated by the obtained results, the performance of this class of DoA estimation method is determined mostly by the values of the input parameters. Furthermore, the simulation results show that tradeoff between performance and computational complexity needs to be considered when the system parameters are chosen for DoA estimation algorithms.

Performance analysis of deep neural networks for direction of arrival estimation of multiple sources

AbstractRecently, popular machine learning algorithms have successfully been applied to the direction of arrival (DOA) estimation. An implementation of determination of DOA estimation is presented based on deep neural networks (DNNs) to reduce the computational complexity of traditional superresolution DOA estimation methods. The classical DOA estimation algorithms have limitations due to unforeseen effects, such as array perturbations. Instead of computing an inverse mapping based on the incomplete forward mapping that relates the signal directions to the array outputs, the DOA problem is approached as a mapping, which can be approximated using a suitable DNN trained with input output pairs. The neural network architecture is based on a multilayer perception and a group of parallel DNNs to perform detection and DOA estimation, respectively. Simulation results are performed to investigate the effect of network parameters on estimation accuracy so that they can be roughly determined in the case of one signal scenario. Based on a set of simulations and experimental measurements, the performance of the optimum network is also assessed and compared to that of the classical DOA estimation methods for multiple signals. It has been shown that the proposed method can not only achieve reasonably high DOA estimation accuracy, but also dramatically reduce the computational complexity and the memory space.

A Robust Algorithm for DOA Estimation of Coherent Sources with UCA

Direction of arrival (DOA) estimation of coherent sources with a uniform circular array (UCA) is an intractable problem. The method-of-direction-estimation (MODE) algorithm has strong superiority in handling coherent sources compared with the classical MUSIC, and ESPRIT algorithms. However, MODE is sensitive to source numbers and does not work well in the UCA scenario. In order to improve the performance of MODE, a robust DOA estimation method named UCA-PUMA (principal-eigenvector-utilization-for-modal-analysis) is proposed. The complicated non-Vandermonde structured steering vector of UCA is transformed into a virtual Vandermonde structured steering vector in mode space. The proposed method gives a closed-form solution compared with the original UCA-MODE algorithm. The performance of the UCA-PUMA method is evaluated by simulations. Simulation results demonstrate that the UCA-PUMA is more robust to source numbers than the UCA-MODE, and coherent sources can be handled without spatial smoothing. In addition, the UCA-PUMA fully takes advantage of the UCA, which is able to discriminate sources coming from a 360o azimuthal field of view.

Direction of Arrival Estimation and Phase-Correction for Noncoherent Subarrays: A Convex Optimization Approach

Estimating the direction of arrival (DOA) of sources is an important problem in aerospace and vehicular communication, localization, and radar. In this article, we consider a challenging multisource DOA estimation task, where the receiving antenna array is composed of noncoherent subarrays, i.e., subarrays that observe different unknown phase shifts at every snapshot (e.g., due to waiving the demanding synchronization of local oscillators across the entire array). We formulate this problem as the reconstruction of joint sparse and low-rank matrices and solve the problem’s convex relaxation. To scale the optimization complexity with the number of snapshots better than general-purpose solvers, we design an optimization scheme, based on integrating the alternating direction method of multipliers and the accelerated proximal gradient techniques, which exploits the structure of the problem. While the DOAs can be estimated from the solution of the aforementioned convex problem, we further show how an improvement is obtained if, instead, one estimates from this solution only the subarrays’ phase shifts. This is done using another, computationally light, convex relaxation that is practically tight. Using the estimated phase shifts, “phase-corrected” observations are created and a final plain (“coherent”) DOA estimation method can be applied. Numerical experiments show the performance advantages of the proposed strategies over existing methods.

Small Size Array Underwater Acoustic DOA Estimation Based on Direction-Dependent Transmission Response

It has been recognized that the performance of the traditional direction of arrival (DOA) estimation algorithms is highly dependent on array geometry parameters, especially the array size and element number. Unfortunately, significant performance degradation may be caused under unideal array geometry such as small size array onboard small underwater vehicle. Among all the possible directions, the presence of underwater target at a certain direction constitutes a type of spatial sparsity. Thus, spatial sparse recovery provides a potential way to address this challenging problem. As each DOA will correspond to a different transmission response pattern with respect to each array element, thus constitutes a direction-dependent transmission response (DDTR) that can be explored. However, random contribution of underwater acoustic (UWA) channel contained in DDTR makes it extremely difficult to directly construct dictionary matrix with DDTR. In this paper, a novel DDTR based small size array DOA estimation method is proposed. First, DDTRs are decomposed into time delay (TD) term and random channel response (RCR) term to decouple the adverse impact of UWA channel. Second, TD is conveniently constructed as dictionary matrix in terms of geometry relationship. Then, by accumulating the constructed DOA at frequency bins selected with energy or correlation coefficient, a selective frequency accumulation compressed sensing reconstruction (SFA-CS) algorithm is designed to mitigate the negative effect of UWA channel. Compared with the conventional DOA estimation algorithms, simulation results demonstrate that the proposed method can achieve small array DOA estimation with a lower root mean squared error (RMSE) and higher success rate (SR).

Unambiguous broadband direction of arrival estimation based on improved extended frequency-difference method.

In this paper, we consider the problem of bearing ambiguity in the direction of arrival (DOA) estimation due to spatial aliasing when the minimum wavelength of the processing broadband signal is less than the element spacing of a uniform linear array (ULA). First, an extended frequency-difference (FD) method is presented. Unlike the existing FD methods, the extended FD signal is constructed by conjugate multiplying a diagonal matrix consisting of steering vectors at high frequency and pre-processing direction with the array sampled signal matrix at low frequency. Then, this paper establishes a decision criterion for distinguishing the aliasing component that varies linearly with frequency in the extended FD space. Finally, an unambiguous broadband DOA estimation method is achieved by suppressing spatial aliasing in the extended FD space. The simulation results show the effectiveness of the proposed method in low signal-to-noise ratio, low signal-to-interference ratio, and multi-interference conditions. The unambiguous processing ability of the proposed method is further verified in the South China Sea using ship signals in the frequency band of 200 to 700 Hz and a 10-element ULA with a 6.25 m spacing deployed on the seabed.

A Fast Adaptive Beamforming Technique for Efficient Direction-of-Arrival Estimation

A plethora of problems related to signal estimation and direction can be effectively solved by using a sensor array. To this end, uniform estimation for all direction-of-arrivals (DOAs) with low computational complexity is an indispensable step for numerous applications. In this article, we present the DOA estimation method exploiting the recently proposed fast variable step size least mean square (FVSSLMS) method (Jalal et al., 2020). In most of the DOA estimation works, a uniform linear array (ULA) was used. Nonetheless, a ULA does not perform well for the DOA estimation when the signal sources are impinging close to the array endfire. To circumvent this issue, we modify the structure of ULA by displacing its four sensors to the top and bottom of the first and the last sensor. Computer simulations demonstrate that the proposed method provides uniform estimation performance for all DOAs with reduced computation complexity.

Direction-of-arrival method based on randomize-then-optimize approach

The direction-of-arrival (DOA) estimation problem can be solved by the methods based on sparse Bayesian learning (SBL). To assure the accuracy, SBL needs massive amounts of snapshots which may lead to a huge computational workload. In order to reduce the snapshot number and computational complexity, a randomize-then-optimize (RTO) algorithm based DOA estimation method is proposed. The “learning” process for updating hyperparameters in SBL can be avoided by using the optimization and Metropolis-Hastings process in the RTO algorithm. To apply the RTO algorithm for a Laplace prior, a prior transformation technique is induced. To demonstrate the effectiveness of the proposed method, several simulations are proceeded, which verifies that the proposed method has better accuracy with 1 snapshot and shorter processing time than conventional compressive sensing (CS) based DOA methods.

High-precision DOA estimation for underwater acoustic signals based on sparsity adaptation

The direction of arrival (DOA) estimation technique is to obtain the direction information of the source when it reaches the array by processing and analyzing the received signal. In recent years, the DOA estimation of an array signal has been a research hotspot. For application scenarios with a small number of snapshots and a low signal-to-noise ratio, the compressive sensing theory has been commonly used to estimate the DOA of an array signal to achieve better estimation performance. However, the DOA estimation methods based on compressive sensing theory require information on source sparsity. Moreover, the influence of a complex underwater acoustic environment limits the accuracy of estimation algorithms. To address this limitation, this study proposes a high-precision DOA estimation model for underwater acoustic signals based on sparsity adaptation. The proposed model includes mainly two parts. In the first part, a source sparsity adaptive model based on a causal convolutional neural network is proposed. The model is used to address the constraint that the source sparsity should be known a priori when compressed sensing is used for DOA estimation. In the second part, a differential combination matching pursuit (DCMP) algorithm is adopted. First, a differentiated path filtering strategy is employed to reduce algorithm complexity and avoid the problem of invalid filtering. In addition, the combined optimization strategy is used to improve the prediction accuracy of the algorithm, providing an efficient error correction idea for the compressed sensing application to DOA estimation. The results of simulations conducted under seven different signal-to-noise ratios and using three different array types show that the proposed source sparsity adaptive model can reach an average prediction accuracy of 89.6%. In addition, compared with the other reconstruction algorithm accuracy, on the basis of ensuring low time complexity, the proposed DCMP algorithm can achieve an accuracy improvement of 9.99%–19.94% under seven different signal-to-noise ratio values. Moreover, the mean absolute error of the proposed DCMP algorithm is lower by approximately 0.05°–14° than those of the OMP and MMP algorithms.

Biquaternion-based DOA estimation of noncircular signals with time-modulated antenna arrays

A novel direction of arrival (DOA) estimation method of noncircular signals based on biquaternion with time-modulated antenna arrays is proposed in this paper. Time-modulated antenna arrays (TMAA) is introduced into the DOA estimation of noncircular signals for the first time, which makes the receiver only need a single RF processing channel, which effectively saves hardware resources. The noncircular features of the signal are fully exploited for virtual array expansion with the biquaternion framework. Aiming at the problem of nonuniform noise in the array output after time modulation, the nonuniform noise correction is realized by using the theoretical analysis of the time sequence scheme. The simulation illustrates that the proposed method has superior performance than conventional DOA estimation method with TMAA, in terms of resolution and numbers of localizable sources.

A novel DOA estimation method for an antenna array under strong interference

Strong interference will affect direction of arrival (DOA) estimation of weak desired signal and even cause DOA estimation failure. This paper investigates the weak signal DOA estimation for an antenna array under strong interference signals, and proposed a novel DOA estimation method for strong interference source suppression and weighted l1-norm sparse representation. A parallel adaptive beamforming algorithm based on power inversion is used to suppress strong interference and form new array data. To reduce spurious peaks in the spectrum under strong interference, a weighted matrix is determined by the optimized subspace algorithm for the subspace projection. Then, the DOA estimation, which is calculated by weighted l1-norm sparse representation, is formed by the weighted matrix and new array data. In this paper, the superiority of the proposed algorithm is illustrated by an example of unmanned aerial vehicle (UAV) video signal DOA estimation under strong interference signals. The simulated results of an orthogonal frequency division multiplexing signal indicate that the proposed algorithm shows merits of fewer snapshots, a sharper main lobe, a lower average noise spectrum value, higher DOA estimation accuracy and success rate. For validation, an outdoor experiment was conducted which demonstrated that the proposed algorithm is superior to other algorithms and can be used for DOA estimation of UAV video signals under strong WiFi interference. Both the simulations and experiments verify that the proposed algorithm can effectively suppress strong interference and achieve better DOA estimation performance for weak signals.

Deep learning-based DOA estimation using CRNN for underwater acoustic arrays

In the marine environment, estimating the direction of arrival (DOA) is challenging because of the multipath signals and low signal-to-noise ratio (SNR). In this paper, we propose a convolutional recurrent neural network (CRNN)-based method for underwater DOA estimation using an acoustic array. The proposed CRNN takes the phase component of the short-time Fourier transform of the array signals as the input feature. The convolutional part of the CRNN extracts high-level features, while the recurrent component captures the temporal dependencies of the features. Moreover, we introduce a residual connection to further improve the performance of DOA estimation. We train the CRNN with multipath signals generated by the BELLHOP model and a uniform line array. Experimental results show that the proposed CRNN yields high-accuracy DOA estimation at different SNR levels, significantly outperforming existing methods. The proposed CRNN also exhibits a relatively short processing time for DOA estimation, extending its applicability.

Synthetic sparse nested array with extended aperture and reduced mutual coupling for DOA estimation

To obtain a larger aperture for improving direction of arrival (DOA) estimation performance, we present a synthetic sparse nested array consisting of three subarrays with dual-polarization antennas, and then propose a cascade method composing of three steps for super-resolution angle estimation with range of 180 degree. There is a systematic procedure to determine the number and positions of antennas in each single-polarization subarray used for the synthetic sparse nested array, in order to efficiently reduce mutual coupling and obtain increased degrees of freedom and aperture for difference coarray with limited physical antennas. By exploiting the configuration and fully utilizing the aperture of the proposed array, two sparse uniform linear arrays are achieved in difference coarray domain, for giving coarse estimation and fine but ambiguous estimation in the first and second steps, respectively. Then an automatic pair matching based on pseudo ambiguous angles is provided to obtain unique DOA estimation in the third step. Theoretical analysis and simulation results are given to demonstrate the superiority of the proposed array and method for high-accuracy DOA estimation in the presence of mutual coupling.

Accurate Direction–of–Arrival Estimation Method Based on Space–Time Modulated Metasurface

A metasurface (MTS)-based direction of arrival (DoA) estimation method is presented. The method exploits the properties of space–time modulated reflective metasurfaces to estimate in real-time the impinging angle of an illuminating monochromatic plane wave. The approach makes use of the amplitude unbalance of the received fields at broadside at the frequencies of the two first-order harmonics generated by the interaction between the incident plane wave and the modulated metasurface. Here, we first describe analytically how to generate the desired higher order harmonics in the reflected spectrum and how to realize the breaking of the spatial symmetry of each order harmonic scattering pattern. Then, the 1-D omnidirectional incident angle can be analytically computed using +1st- and −1st-order harmonics. The approach is also extended to 2-D DoA estimation by using two orthogonally arranged 1-D DoA modulation arrays. The accuracy of 1-D DoA estimation is verified through full-wave numerical simulations. Compared to conventional DoA estimation methods, the proposed approach simplifies the computation and hardware complexity, ensuring at the same time estimation accuracy. The proposed method may have potential applications in wireless communications, target recognition, and identification.