Conventional Direction Of Arrival Research Articles

Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources.

In this paper, we propose a novel simultaneous Correlative Interferometer (CI) technique that elaborately estimates the Direction of Arrival (DOA) of multiple source signals incident on an antenna array. The basic idea of the proposed technique is that the antenna-array-based receiver compares the phase of the received signal with one of the candidates at each time sample and jointly exploits these multiple time samples to estimate the DOAs of multiple signal sources. The proposed simultaneous CI-based DOA estimation technique collectively utilizes multiple time-domain samples and can be regarded as a generalized version of the conventional CI algorithm for the case of multiple time-domain samples. We first thoroughly review the conventional CI algorithm to comprehensively explain the procedure of the direction-finding algorithm that adopts the phase information of received signals. We also discuss several technical issues of conventional CI-based DOA estimation techniques that are originally proposed for the case of a single time-domain sample. Then, we propose a simultaneous CI-based DOA estimation technique with multi-sample diversity as a novel solution for the case of multiple time-domain samples. We clearly compare the proposed simultaneous CI technique with the conventional CI technique and we compare the existing Multiple Signal Classification (MUSIC)-based DOA estimation technique with the conventional CI-based technique by using the DOA spectrum as well. To the best of our knowledge, the simultaneous CI-based DOA estimation technique that effectively utilizes the characteristics of multiple signal sources over multiple time-domain samples has not been reported in the literature. Through extensive computer simulations, we show that the proposed simultaneous CI technique significantly outperforms both the conventional CI technique in terms of DOA estimation even in harsh environments and with various antenna array structures. It is worth noting that the proposed simultaneous CI technique results in much better performance than the classical MUSIC algorithm, which is one of the most representative subspace-based DOA estimation techniques.

A Novel Nested Array Structure for DOA Based on CCM of Subarrays

An innovative nested array structure that can notably increase the DOF and the linear arrays’ direction of arrival (DOA) estimated performance is proposed. For the conventional nested array, we vectorize the ACM’s output of the whole array and then remove the repeated rows to get a virtual array’s output. In contrast with classical nested arrays, the superiority of the new nested array is that it utilizes the combination of reverse ordering and conjugation of the inner uniform linear array (ULA) for one of the two subarrays and the sparse outer ULA for another to increase the array aperture. This means the outer sparse ULA’s sensor spacing is approximately the length of the entire inner ULA in the classical nested array structure. Yet, it is about twice the length in the new nested array structure. We generate one lengthy consecutive virtual uniform array excluding any redundant virtual sensors by vectorizing the two subarrays’ cross-correlation matrix (CCM), which is mentioned above. With the export signal of the virtual array and its conjugate form of it, an equivalent covariance matrix of full rank is constructed, which is called the Toeplitz matrix, to compensate for the rank lack of the virtual array’s ACM. For the sake of obtaining the DOA of input signals, the conventional DOA estimation method will be implemented on the ACM. The increase in outer sparse ULA’s sensor spacing ensures an increase in virtual array aperture in principle, which means it is capable of increasing the number of DOA estimations, which is called DOF, and optimizing the DOA estimated performance in contrast with the ULA and classical nested arrays. Results from trials certify the preponderance of the proposed structure in the aspect of DOF and the accuracy of DOA estimation.

DOA estimation based on smoothed sparse reconstruction with time-modulated linear arrays

A novel direction of arrival (DOA) estimation method based on smoothed sparse reconstruction with time-modulated linear arrays (TMLA) is proposed in this paper. With the analysis of the noise variation after time modulation, a closed-form expression for the noise covariance under the optimized unidirectional phase center motion time sequence scheme is derived. Then a reweighted continuous function is designed for the smooth approximation to ℓ0-norm based on the orthogonality between the signal subspace and the noise subspace. Simulation results demonstrate that, compared with conventional DOA estimation method with time-modulated arrays, the proposed method possesses higher estimation accuracy and lower computational complexity, especially for the scenario with small snapshot and low signal-to-noise ratio.

An Improved Toeplitz Approximation Method for Coherent DOA Estimation in Impulsive Noise Environments.

Direction of arrival (DOA) estimation is an important research topic in array signal processing and widely applied in practical engineering. However, when signal sources are highly correlated or coherent, conventional subspace-based DOA estimation algorithms will perform poorly due to the rank deficiency in the received data covariance matrix. Moreover, conventional DOA estimation algorithms are usually developed under Gaussian-distributed background noise, which will deteriorate significantly in impulsive noise environments. In this paper, a novel method is presented to estimate the DOA of coherent signals in impulsive noise environments. A novel correntropy-based generalized covariance (CEGC) operator is defined and proof of boundedness is given to ensure the effectiveness of the proposed method in impulsive noise environments. Furthermore, an improved Toeplitz approximation method combined CEGC operator is proposed to estimate the DOA of coherent sources. Compared to other existing algorithms, the proposed method can avoid array aperture loss and perform more effectively, even in cases of intense impulsive noise and low snapshot numbers. Finally, comprehensive Monte-Carlo simulations are performed to verify the superiority of the proposed method under various impulsive noise conditions.

Two Rapid Power Iterative DOA Estimators for UAV Emitter Using Massive/Ultra-Massive Receive Array

To provide rapid direction finding (DF) for unmanned aerial vehicle (UAV) emitters in future wireless networks, a low-complexity direction of arrival (DOA) estimation architecture for massive multiple-input multiple-output (MIMO) receiver arrays is constructed. In this paper, we propose two strategies to address the extremely high complexity caused by eigenvalue decomposition of the received signal covariance matrix. Firstly, a rapid power iterative rotational invariance (RPI-RI) method is proposed, which adopts the signal subspace generated by power iteration to obtain the final direction estimation through rotational invariance between subarrays. RPI-RI causes a significant complexity reduction at the cost of a substantial performance loss. In order to further reduce the complexity and provide good directional measurement results, the rapid power iterative polynomial rooting (RPI-PR) method is proposed, which utilizes the noise subspace combined with the polynomial solution method to obtain the optimal direction estimation. In addition, the influence of initial vector selection on convergence in the power iteration is analyzed, especially when the initial vector is orthogonal to the incident wave. Simulation results show that the two proposed methods outperform the conventional DOA estimation methods in terms of computational complexity. In particular, the RPI-PR method achieves more than two orders of magnitude lower complexity than conventional methods and achieves performance close to the Cramér–Rao Lower Bound (CRLB). Moreover, it is verified that the initial vector and the relative error have a significant impact on the performance with respect to the computational complexity.

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.

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).

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.

The DOA Estimation Method for Low-Altitude Targets under the Background of Impulse Noise.

Due to the discontinuity of ocean waves and mountains, there are often multipath propagation effects and obvious pulse characteristics in low-altitude detection. If the conventional direction of arrival (DOA) estimation method is directly used for direction finding, it will lead to a large error. In view of serious misalignment in the DOA estimation of multipath signals under the background of impulse noise, a DOA estimation method based on spatial difference and a modified projection subspace algorithm is proposed in this paper. Firstly, the covariance matrix of the received data vector is used for spatial difference to eliminate the multipath effects of low-altitude targets. Secondly, the modified projection matrix is constructed using the signal source estimated with the least squares criterion and then used for modifying the covariance matrix, thus eliminating the cross-covariance matrices that affect the estimation accuracy. Finally, the modified covariance matrix is used for the DOA estimation of targets. Simulations show that the proposed algorithm achieves a higher accuracy in the DOA estimation of low-altitude targets than conventional algorithms under two common impulse noise models, without requiring prior knowledge of impulse noise.

Tensor‐based direction of arrival estimation with array virtual translation technique

The tensor-based spatial smoothing is a good algorithm for the direction of arrival (DOA) estimation, but it cannot make good use of the physical aperture of the array, so the paper proposes a tensor-based array virtual translation DOA estimation algorithm to solve the problem. Under the framework of tensor-based DOA estimation algorithm, the factor matrix obtained by tensor decomposition is extended to a signal subspace with Vandermonde structure by using array virtual translation technology. In addition, the algorithm expands the available array aperture, breaks through the limitation of physical array aperture on multi-target estimation ability, and further improves the estimation accuracy. Since the processing technique proposed in this paper has nothing to do with the construction of tensors, this technique is suitable for conventional DOA estimation algorithms based on tensors. Theoretical analysis and simulation experiments verify the effectiveness of the algorithm proposed in this paper.

Machine–learning-enabled metasurface for direction of arrival estimation

Abstract Metasurfaces, interacted with artificial intelligence, have now been motivating many contemporary research studies to revisit established fields, e.g., direction of arrival (DOA) estimation. Conventional DOA estimation techniques typically necessitate bulky-sized beam-scanning equipment for signal acquisition or complicated reconstruction algorithms for data postprocessing, making them ineffective for in-situ detection. In this article, we propose a machine-learning-enabled metasurface for DOA estimation. For certain incident signals, a tunable metasurface is controlled in sequence, generating a series of field intensities at the single receiving probe. The perceived data are subsequently processed by a pretrained random forest model to access the incident angle. As an illustrative example, we experimentally demonstrate a high-accuracy intelligent DOA estimation approach for a wide range of incident angles and achieve more than 95% accuracy with an error of less than 0.5 ° $0.5{}^{\circ}$ . The reported strategy opens a feasible route for intelligent DOA detection in full space and wide band. Moreover, it will provide breakthrough inspiration for traditional applications incorporating time-saving and equipment-simplified majorization.

Efficient DOA Estimation Method for Reconfigurable Intelligent Surfaces Aided UAV Swarm

The conventional direction of arrival (DOA) estimation methods are performed with multiple receiving channels. In this paper, a changeling DOA estimation problem is addressed in a different scenario with only one full-functional receiving channel. A new unmanned aerial vehicle (UAV) swarm system using multiple lifted reconfigurable intelligent surface (RIS) is proposed for the DOA estimation. The UAV movement degrades the DOA estimation performance significantly, and the existing atomic norm minimization (ANM) methods cannot be used in the scenario with array perturbation. Specifically, considering the position perturbation of UAVs, a new atomic norm-based DOA estimation method is proposed, where an atomic norm is defined with the parameter of the position perturbation. Then, a customized semi-definite programming (SDP) method is derived to solve the atomic norm-based method, where different from the traditional SDP method, an additional transforming matrix is formulated. Moreover, a gradient descent method is applied to refine the estimated DOA and the position perturbation further. Simulation results show that the proposed method achieves much better DOA estimation performance in the RIS-aided UAV swarm system with only one receiving channel than various benchmark schemes.

Wireless Localization Method Using the Distributed Iterative Stochastic-Resonance-Based Signal Spectral Combination

In this study, a kind of nonlinear stochastic-resonance (SR) signal enhancement technique combined with the distributed receiving array signal power spectrum combination approach is proposed. By utilizing the signal spectral power improvement technique, the fitness of the distributed SR system with the array structure, and the information combination of the receiving power spectra, the corresponding objective of wireless localization can be realized successfully. An iterative nonlinear SR-based processing structure and corresponding algorithm are also proposed, which guarantee the applicability of the proposed approach. Computer simulations give the better performances of the proposed method compared with the conventional direction of arrival (DoA) estimation approaches and corresponding wireless localization estimation results.

Continuous Mapping of Broadband VHF Lightning Sources by Real-Valued MUSIC

To improve the mapping quality of lightning discharge processes at a reduced computational complexity, broadband implementation of the real-valued MUSIC (RV-MUSIC) direction of arrival (DOA) method is proposed and evaluated. A very high frequency (VHF) broadband high-speed continuous acquisition system consisting of three omnidirectional “L” shaped antennae array is implemented to acquire lightning radio emissions in a 20–80-MHz frequency band. The cost function of RV-MUSIC for the broadband lightning signal is derived. Monte-Carlo simulations are carried out to demonstrate functionality and to evaluate the robustness of the proposed method. Further, the proposed method is validated by generating lightning maps using observational data. Simulation and observational results are compared with the conventional incoherent MUSIC (IMUSIC) and interferometric DOA methods. The computational costs of all three methods are derived, and their respective estimated execution times are also presented. Results show that the proposed method can generate lightning maps of similar quality to that of IMUSIC at a significantly lower computational load.

Robust 2-D DOA Estimation in a Polarization Sensitive Single User Environment

Apart from the conventional parameters (such as signal-to-noise ratio (SNR), array geometry and size, and the number of samples), several other factors (e.g., alignment of the antenna elements, polarization parameters) influence the performance of direction of arrival (DOA) estimation algorithms. When all the antenna elements are aligned in the same direction, the polarization parameters uniformly affect the steering vectors, which is the underlying assumption of almost all conventional DOA algorithms. Unfortunately, in this case, for a given set of DOA angles, there exists a range of polarization parameters resulting in a very low SNR across all the antenna elements in the array and vice versa. To avoid this type of unwanted event, different antenna elements must be aligned differently. However, this fact will make almost all commonly used DOA estimation algorithms inoperable since the steering vectors are contaminated unevenly by the polarization parameters. To the best of our knowledge, no work in the literature handles this issue using simple hardware and signal processing techniques even for a single user environment. In this paper, that line of inquiry is pursued. We consider a circular array with the minimum number (i.e., 4) of short dipole antenna elements and propose an antenna alignment scheme. This ensures that at any given point no more than one element will suffer significantly from low SNR due to the contribution of polarization. A thresholding technique to isolate the antenna element after being seriously contaminated by the polarization parameters is developed and analyzed. Two algorithms that are suited for operating reliably in all possible DOA and polarization environments are addressed. The first algorithm follows the working principle of the popular MUSIC algorithm after cleaning the polarization contributions from the non-signal subspace. The other one, which is found as a byproduct of the process of cleaning the non-signal subspace, can estimate the DOA angles in a closed form manner. The implementations of the above algorithms for an arbitrary number of antenna elements greater than or equal to 4 are also presented. Finally, a thorough performance and complexity analysis are illustrated for those two algorithms considering various polarization and DOA scenarios.

DOA Estimation for Transmit Beamspace MIMO Radar via Tensor Decomposition With Vandermonde Factor Matrix

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general 4-order tensor model that enables computationally efficient DOA estimation is designed. Whereas other tensor decomposition-based methods treat all factor matrices as arbitrary, the essence of the proposed DOA estimation method is to fully exploit the Vandermonde structure of the factor matrices to take advantage of the shift-invariance between and within different subarrays. Specifically, the received signal of TB MIMO radar is expressed as a 4-order tensor. Depending on the target Doppler shifts, the constructed tensor is reshaped into two distinct 3-order tensors. A computationally efficient tensor decomposition method is proposed to decompose the Vandermonde factor matrices. The generators of the Vandermonde factor matrices are computed to estimate the phase rotations between subarrays, which can be utilized as a look-up table for finding target DOA. It is further shown that our proposed method can be used in a more general scenario where the subarray structures can be arbitrary but identical. The proposed DOA estimation method requires no prior information about the tensor rank and is guaranteed to achieve precise decomposition result. Simulation results illustrate the performance improvement of the proposed DOA estimation method as compared to conventional DOA estimation techniques for TB MIMO Radar.

Maximum Element Dichotomous Coordinate Descent Based Minimum Variance Distortionless Response DoA Estimator

In this paper, we devise an efficient approach for estimating the direction of arrival (DoA). The proposed DoA estimation approach is based on minimum variance distortionless response (MVDR) criteria within a recursive least squares (RLS) framework. The dichotomous coordinate descent algorithm is used to modify the calculation of the output power spectrum, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance. A numerical comparison confirms that the proposed DoA estimator outperforms the conventional RLS DoA estimator in terms of the computational complexity and DoA estimation error. Finally, the proposed theoretical DoA estimator is implemented on a field-programmable gate array (FPGA) board to verify the feasibility of the method. The numerical results of a fixed-point implementation demonstrate that the performance of the proposed method is very close to that of its floating-point counterpart.

DOA tracking for seamless connectivity in beamformed IoT-based drones

In recent times, there has been a surge of interest around the usage of adaptive antenna arrays of Internet of Things (IoT) based Drones in the communication systems. Adaptive antenna arrays have the ability to form customized radiation patterns based on the changes in the environment by employing methods for estimating Direction of Arrival (DOA) and adaptive beamforming. Nevertheless, upon deploying adaptive antenna arrays in complex IoT platforms, the radiation patterns that result from the use of such adaptive algorithms may be adjusted to the preceding location of the node and not attuned to the current location. These issues that arise due to mobility can be resolved by continuously tracking the DOA of the intended target. As DOA is time varying in an IoT Drone environment, existing algorithms for estimating the DOA like MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) cannot be used to track the signal subspace recursively, as they are based on batch eigenvalue decomposition which is highly time consuming with a time complexity of O(n3). Furthermore, DOA estimation algorithms do not result in robust subspace estimates when the Signal to Noise Ratio (SNR) is low.The main novelty of the proposed work is a low computational complexity subspace tracking algorithm for tracking DOA in order to provide seamless connectivity. Simulation results show that the proposed DOA tracking takes lesser time for tracking the current location of the drone target as opposed to conventional DOA estimation methods. Furthermore,it is observed that the tracking process remains unaffected by SNR.

Low-complexity neural network based DOA estimation for wideband signals in massive MIMO systems

Massive multiple-input multiple-output (MIMO) has become one of the most promising technologies for wireless communication systems, in which the direction-of-arrival (DOA) plays an important role in interference cancellation and transmission reliability. However, the challenge of conventional wideband DOA estimation algorithms is that their high computational complexity brings great difficulties for their effective application in massive MIMO systems. In this paper, we propose a wideband low-complexity DOA estimation algorithm based on a principal component analysis (PCA) neural network for massive MIMO systems. First, a new criterion for constructing a focusing matrix is proposed to avoid complex angle pre-estimation. To further reduce the complexity of the eigenvalue decomposition (EVD), we propose a signal subspace estimation algorithm based on PCA, which uses only a limited amount of self-organizing learning to estimate the weights of the network and the signal subspace and does not require prior sample training. Moreover, to increase the estimation accuracy, we use the Akaike information criterion (AIC) to divide signal and noise subspaces accurately. The theoretical analysis and simulation results show that the computational complexity of the proposed algorithm is effectively reduced, and the angles of wideband sources can be accurately estimated in massive MIMO systems.

Crosscorrelation and DOA Estimation for L-Shaped Array via Decoupled Atomic Norm Minimization

A novel two-phase method for two-dimensional (2D) direction-of-arrival (DOA) estimation with L-shaped array based on decoupled atomic norm minimization (DANM) is proposed in this paper. In the first phase, given the sample crosscorrelation matrix, the gridless DANM technique considering the noise and finite snapshots effects is employed to exploit the structure and sparse properties of the crosscorrelation matrix. The resulting DANM-based algorithm not only enables the crosscorrelation matrix reconstruction (CCMR) but also reconstructs the covariance matrix of the L-shaped array. Hence, sequentially, in the second phase, the conventional 2D DOA estimators for the L-shaped array can be adopted for the angle estimation. With appropriate 2D DOA estimators, the resulting proposed algorithms can not only achieve better performance but also detect more source number, compared with conventional crosscorrelation-based DOA estimators. Moreover, the proposed method, termed CCMR-DANM, not only has blind characteristic that it does not require the prior information of source numbers but also is more efficient than the existing CCMR-based counterparts. Numerical simulations demonstrate the effectiveness and outperformance of the proposed method.