Direction Of Arrival Estimation Performance Research Articles

DOA Estimation for Coherent Signals With Improved Sparse Representation in the Presence of Unknown Spatially Correlated Gaussian Noise

In this paper, a new method is proposed for direction-of-arrival (DOA) estimation of coherent signals with improved sparse representation in unknown spatially correlated Gaussian noise. To be specific, leveraging a symmetric uniform linear array, the entries of the signal covariance matrix is firstly recasted to eliminate the spatially correlated noise. Subsequently, it is shown that an equivalent source vector can be obtained by squaring any row of the noise-free signal covariance matrix, irrespective of the coherency between the signals. Finally, an improved sparse representation, which enhances signal sparsity via utilizing a designed weight vector, is derived to determine the DOAs of the signals. Numerical examples are provided to demonstrate its superiority of DOA estimation performance in low signal-to-noise ratio (SNR) environments. Besides, it is computationally efficient, which is critical for large array and/or real-time data processing systems.

A Priori-Based Subarray Selection Algorithm for DOA Estimation.

A finer direction-of-arrival (DOA) estimation result needs a large and dense array; it may, however, encounter the mutual coupling effect, which degrades the performance of DOA estimation. There is a new approach to mitigating this effect by using a nonuniform array to achieve DOA estimation. In this paper, we consider a priori DOA estimation, which is easily obtained from tracking results. The a priori DOA requires us to pay close attention to the high possibility of where the DOA will appear; then, a weight according to the prior probability distribution of DOA is added to each direction, which leads the sensing matrix of DOA estimation to be near low-rank. Thus, according to the low-rank matrix approximation theory, an optimal low-rank approximate matrix is obtained and an algorithm is proposed to select the elements of the original array according to right singular vectors of the approximate matrix. After that, the impacts of different weights are analyzed, and a mixed weight is presented which has flexibility for common use. Finally, a number of numerical simulations are carried out, and the results verify the effectiveness of the proposed methods.

Subspace and sparse reconstruction based near-field sources localization in uniform linear array

This work studies the near-field localization problem using a symmetry uniform linear array (ULA). To decouple the range and direction of arrival (DOA), by exploiting the symmetry property of the array, two spatial correlation sequences are constructed, where each sequence only corresponds to one parameter, i.e., DOA or range. After decoupling, an attractive property is that the resulting sequences still share the similar ULA spatial structure. To perform DOA estimation, two approaches have been developed. The first one is based on the power of R (POR) method, which obtains the noise subspace without the eigendecomposition and prior information of the number of sources. The second one is developed using atomic norm minimization, which eliminates the off-grid issue. For range estimation, since the constructed sequence that corresponds to the range parameter shares the same spatial structure with the DOA sequence, the developed approaches are readily applied to obtain the range estimates. The proposed approach is also studied under one-bit measurement to show its robustness. The numerical studies including simulation and real-world data demonstrate the performance of the proposed method.

Closed expression of source signal's DOA information in sensor array

In this study, a novel closed expression of direction of arrival (DOA) information (DI) in a single-source scenario is proposed, which is more convenient than the theoretical expression to evaluate the performance of DOA estimation. Firstly, the authors give a uniform linear array system model, where the DI is expressed as the mutual information between the source and the received signal with complex additive white Gaussian noise. Then the posterior probability density function of DOA is deduced. Moreover, by dividing the integral interval into a signal part and a noise part, a novel closed approximate expression of DI is derived. It contains the posteriori entropy in low and high signal-to-noise ratio (SNR) cases and the normalised probability. The normalised probability is obtained through a normalisation procedure on the basis of the correlation functions. As special cases, the closed expression of DI in low and high SNR cases is given and some interesting relationships between physical quantities are revealed. Finally, numerical results are presented to verify the effectiveness of the proposed approximate closed expression.

Two-dimensional Off-Grid DOA Estimation with Improved Three-Parallel Coprime Arrays on Moving Platform

In this paper, two-dimensional (2-D) direction-of-arrival (DOA) estimation issue is investigated by constructing array model on moving platform. Based on the moving array model, we propose two improved three-parallel coprime arrays (TPCPAs), which utilize the redundancy in the physical structure of moving TPCPA (MTPCPA) and are able to generate the same virtual array as MTPCPA using much fewer sensors. Accordingly, higher sensor utilization is achieved by the proposed arrays, which can contribute to the increase in the number of degrees of freedom. Besides, with the proposed arrays, we also present a 2-D off-grid DOA estimation algorithm, in which the estimated 2-D angles are automatically paired without extra pairing procedure. Particularly, by utilizing the $${\ell }_{p}(0<p<1)$$ norm and majorization–minimization method jointly, the proposed algorithm solves the grid mismatch problem effectively and accordingly enhances the 2-D DOA estimation performance. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed arrays and 2-D off-grid DOA estimation algorithm.

Max-MUSIC: A Low-Complexity High-Resolution Direction Finding Method for Sparse MIMO Radars

In this paper, we propose a low-complexity high-resolution direction-of-arrival (DoA) method (max-MUSIC) by exploiting multiple subarrays of a sparse multiple-input multiple-output (MIMO) radar. In this method, specific subarrays for different MIMO configurations are selected according to a proposed selection criterion for generating diverse MUSIC spatial spectrums. Subsequently, we design a new spatial spectrum function that can perform high DoA estimation accuracy and resolution without spatial aliasing, by leveraging the advantages of the diverse spatial spectrums. With a given number of antenna elements, enhancements in array aperture size can improve estimation accuracy while causing severe aliasing, which cannot be mitigated. To define a legitimate MIMO configuration for aliasing suppression, a criterion that offers an optimal compromise between DoA estimation performance and anti-aliasing ability is provided. Simulations are provided to verify the effectiveness of the proposed method.

Direction of arrival estimation for the uniform or non‐uniform noise with adaptive expectation maximisation algorithm

The authors consider the problem of direction-of-arrival (DOA) estimation for the uniform noise (UN) or non-UN (NUN) in a passive radar. The radar waveform to be estimated is modelled as a deterministic and unknown process. Under this condition, the well-known expectation maximisation (EM) algorithm can be utilised for the estimation. In the conventional EM algorithm, the DOA is updated in every iteration, whereas the noise power ratio for each signal component is kept constant. Hence, they have to specify the noise power ratio before implementing the EM algorithm. Clearly, the DOA estimation performance of the conventional EM algorithm is sensitive to this initial noise power ratio. To deal with this problem, they propose the adaptive EM (AEM) algorithms for the UN and NUN, respectively. In the authors’ proposed AEM algorithm, the noise power and DOA are jointly estimated and updated in each iteration, which indicates that the noise power ratio for each signal component would be adaptively changed. Therefore, the DOA performance of their proposed AEM algorithm is less sensitive to the initial noise power ratio, thereby achieving better estimation results. Finally, extensive experiments are carried out to validate the effectiveness of their proposed AEM algorithm.

Gridless Underdetermined DOA Estimation of Wideband LFM Signals With Unknown Amplitude Distortion Based on Fractional Fourier Transform

In this article, a wideband Direction-of-Arrival (DOA) estimation method for underdetermined scenarios is proposed, which effectively solves the basis mismatch problem. Based on the fractional Fourier transform (FRFT), the wideband received signal model with a coprime array is first derived by exploiting the aggregation characteristic of wideband linear frequency modulated (LFM) signals in the fractional Fourier (FRF) domain. Then, in order to increase the degree of freedom, an extended uniform linear array is built, and the covariance matrix of the signal is reconstructed by employing the penalized atomic norm minimization with the consecutive spatial dictionary. Meanwhile, without the knowledge of the noise level, the noise variance is estimated from the noisy incomplete data, which is utilized to improve the covariance matrix reconstruction performance. Additionally, for the unconditional model, the Cramér-Rao bound for the wideband DOA estimation based on a coprime array is derived. Different from the existing methods, the proposed method not only can estimate more DOAs of wideband signals than the number of physical sensors in the presence of unknown amplitude distortion but also can obtain more accurate DOA estimation performance without basis mismatch. The effectiveness of the proposed method is verified by our numerical results.

Direction of arrival estimation in practical scenarios using moving standard deviation processing for localization and tracking with acoustic vector sensors

Typical direction of arrival (DOA) estimation is done with sensor arrays consisting of a great number of sensors. It is of interest to perform DOA estimation with few sensor locations. Acoustic vector sensors (AVS) provide one option for DOA estimation in applications where few sensor locations are required. The majority of AVS experiments have focused on stationary sources in laboratory environments where the source signature is known and controlled. Experiments in this paper have been conducted with in-air pressure-pressure (pp) AVS to track moving mechanical noise sources (ground vehicles) in real-world environments with various frequency content and signal to noise ratio. A moving standard deviation (MSD) algorithm has been used with AVS to estimate DOA at multiple sites. Azimuthal DOA accuracy has been shown to be dependent on ground-reflected paths for pp AVS with comparison to analytical models. Utilizing multiple AVS sites, in-air pp AVS are demonstrated to localize sources with complex signatures.

Improved De-Multipath Neural Network Models With Self-Paced Feature-to-Feature Learning for DOA Estimation in Multipath Environment

When the elevation of target is smaller than a beamwidth, the complex multipath signals will distort the feature of direct signal reflected from target. The elevation of target can hardly be estimated accurately. Hence, in this paper, we proposed three kinds of neural networks models including deep neural network (DNN), 1-D convolutional neural network (1-D CNN) and 2-D convolutional neural network (2-D CNN) and their optimization method to mitigate phase distortion caused by multipath signals and enhance the phase feature of direct signal. The direction of arrival (DOA) estimation accuracy of physics-driven methods including digital beamforming (DBF) and multiple signal classification (MUSIC) is effectively improved. Concretely, we analyze the origins of error of DOA estimation in multipath environment and discuss the importance of phase feature to DOA estimation. A complete framework of feature-to-feature phase enhancement is built for DOA estimation in radar systems. The results of experiments with real data collected from a very high frequency (VHF) radar demonstrate the superior DOA estimation performance of proposed feature-to-feature learning methods with respect to other state-of-the-art methods including physics-driven methods and existing data-driven methods.

DOA estimation method of electronically controlled beam‐scanning LWA based on ESPRIT algorithm

A novel direction-of-arrival (DOA) estimation method based on electronically controlled beam scanning leaky-wave antenna (LWA) combined with estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm is proposed. In order to implement this method, a virtual partial pattern synthesis method is presented to construct an array manifold of subarrays from LWA for the ESPRIT algorithm. Then, the multi-channel receiver model and signal subspace are established based on the beam scanning property of LWA. As the traditional array antenna is substituted by LWA, the rotation operator of the algorithm has to be changed. From this point, the preprocessing ESPRIT algorithm based on the Hadamard product is proposed to extract the directional matrix of LWA. Numerical simulations are conducted, and the DOA performance is demonstrated through estimation error, response rate, and compared with the Cramer-Rao bound. Simulation results show that the DOA method utilising LWA exhibits satisfactory estimation performance and fast response speed. In addition, the influence of antenna parameters on the estimation accuracy and the method to improve the performance of DOA estimation for LWA are discussed.

A Super-Resolution DOA Estimation Method for Fast-Moving Targets in MIMO Radar

Direction of arrival (DOA) estimation is an essential problem in the radar systems. In this paper, the problem of DOA estimation is addressed in the multiple-input and multiple-output (MIMO) radar system for the fast-moving targets. A virtual aperture is provided by orthogonal waveforms in the MIMO radar to improve the DOA estimation performance. Different from the existing methods, we consider the DOA estimation method with only one snapshot for the fast-moving targets and achieve the super-resolution estimation from the snapshot. Based on a least absolute shrinkage and selection operator (LASSO), a denoise method is formulated to obtain a sparse approximation to the received signals, where the sparsity is measured by a new type of atomic norm for the MIMO radar system. However, the denoise problem cannot be solved efficiently. Then, by deriving the dual norm of the new atomic norm, a semidefinite matrix is constructed from the denoise problem to formulate a semidefinite problem with the dual optimization problem. Finally, the DOA is estimated by peak-searching the spatial spectrum. Simulation results show that the proposed method achieves better performance of the DOA estimation in the MIMO radar system with only one snapshot.

Ultrawideband Discharge Source DOA Estimation Method Using Multiple Baseline Wideband Time-Domain Interferometry with Hilbert Transform

The research interest of ultrawideband (UWB) discharge source location estimation has increased these years. In this paper, a direction of arrival (DOA) estimation method using multiple baseline wideband time-domain interferometry with Hilbert transform for UWB discharge source is proposed based on time-domain and frequency-domain characteristics of radiated RF electromagnetic pulses (EMPs) from discharge sources. Monte Carlo simulations are then carried out; the results indicate that, the proposed method provides a better performance in UWB discharge source DOA estimation than the traditional time-domain method, especially in low signal-to-noise ratio (SNR) conditions. Moreover, the influences of antenna array configurations and incident angles of radiated EMPs on the estimation precision are also studied. It has been shown that, the accuracy of both elevation angle and azimuth angle estimation improves with the increase of the antenna element number and baseline length. As for the influence of incident angles, the estimation accuracy of elevation angle enhances when real elevation angle increases, while that of azimuth angle tends to be opposite. Meanwhile, the real azimuth angle has little effect on the DOA estimation. Finally, an experimental setup for discharge source DOA estimation is introduced and the experiment results are illustrated.

Performance analysis and DOA estimation method over acoustic vector sensor array in the presence of polarity inconsistency

This paper investigates the direction of arrival (DOA) estimation performance in the presence of polarity inconsistency in uniform acoustic vector sensor (AVS) linear array. We analyze the influence of polarity bias on beampattern directivity of the AVS array. The analysis results show that the polarity bias leads to asymptotically biased estimation. Then, the analytical expression for the asymptotic bias based on classical beamforming is derived in the presence of polarity error. Moreover, to improve the DOA estimation performance in the presence of polarity inconsistency, a polarity calibration method is proposed. Numerical simulations reveal the effectiveness and superiority of the proposed calibration method when the polarity error satisfies with the uniform distribution and the normal distribution.

Computationally efficient DOA estimation for coprime linear array: a successive signal subspace fitting algorithm

ABSTRACT In this paper, direction of arrival (DOA) estimation of multiple signals with coprime array is investigated and signal subspace fitting (SSF) method is linked to the coprime array, which achieves a better DOA estimation performance than the traditional uniform array. While the SSF method requires expensive computational cost in the case of multiple signals due to the multidimensional global angular searching, we propose a successive SSF (S-SSF) algorithm from a computationally efficient perspective. In the proposed algorithm, we employ rotational invariance and coprime property to obtain the initial estimates. Then, via a successive scheme, we transform the traditional multidimensional global angular searching problem into one-dimensional partial angular searching one. Consequently, the computational complexity has been significantly reduced. Specifically, the proposed S-SSF algorithm can obtain almost the same DOA estimation performance as SSF but with remarkably lower complexity. Finally, Cramer-Rao Bound (CRB) is provided and numerical simulations demonstrate the effectiveness of the proposed algorithm.

Enhanced beamspace MUSIC for cost‐effective FMCW automotive radar

As one important sensor for automotive applications, frequency modulated continuous wave (FMCW) radars working at millimetre wave frequency, e.g. 24 or 77 GHz, are drawing much attention in recent years. Compared with range and radial velocity measurement, direction of arrival (DOA) estimation is more challenging in FMCW automotive radars due to the space limitation and computational complexity constraint. The feature of the signal processing procedure further results in the problem of single snapshot and relatively low signal-to-noise ratio (SNR) level. In this study, the authors propose a low-complexity beamspace multiple signal classification (MUSIC) scheme to improve the DOA estimation performance, where (i) the prior information is exploited to improve beamformer design, (ii) a modified MUSIC estimator is formulated to alleviate the performance degradation due to low SNR, (iii) a joint sub-matrix averaging and Toeplitz structure recovery processing is utilised to compensate the sample covariance estimation error resulted from single snapshot, especially for closely located targets. Simulations are given to demonstrate the efficiency of the authors' proposed enhanced beamspace DOA estimation for cost-effective FMCW automotive radar.

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.

Diagonal Unloading Beamforming in the Spherical Harmonic Domain for Acoustic Source Localization in Reverberant Environments

Spherical microphone arrays allow the sound field analysis in three dimensions with the advantage of having the same resolution in all directions. By considering the frequency-independent character of the steering vectors in the spherical harmonic (SH) domain, we propose a very low-complexity SH diagonal unloading (DU) beamforming with a novel frequency smoothing power transform (FSPT) of the covariance matrices. We consider the direction of arrival (DOA) estimation problem of acoustic sources in reverberant conditions. The DU beamforming provides high resolution directional response since it exploits the subspace orthogonality property of the covariance matrix by the removal or the attenuation of the signal subspaces, obtained through the subtraction of an opportune diagonal matrix from the covariance matrix. The FSPT aims at smoothing the narrowband covariance matrices of the entire set of frequency domain components, and it pursues this goal by minimizing the narrowband error contributions due to reverberation in the broadband frequency smoothing covariance matrix. We analyze the DOA estimation performance using speech signals with simulations and real acoustic data in reverberant conditions. The results show that the proposed SH-DU-FSPT has a DOA estimation performance comparable to that of high resolution state-of-the-art methods with a significant reduction of the computational cost, since the steering directional responses are computed on the broadband frequency smoothing covariance matrix.

Joint DOD and DOA Estimation in Slow-Time MIMO Radar via PARAFAC Decomposition

We develop a new tensor model for slow-time multiple-input multiple-output (MIMO) radar, and apply it for joint direction-of-departure (DOD), and direction-of-arrival (DOA) estimation. This tensor model aims to exploit the independence of phase modulation matrix, and receive array in the received signal for slow-time MIMO radar. Such tensor can be decomposed into two tensors of different ranks, one of which has identical structure to that of the conventional tensor model for MIMO radar, and the other contains all phase modulation values used in the transmit array. We then develop a modification of the alternating least squares algorithm to enable parallel factor decomposition of tensors with extra constants. The Vandermonde structure of the transmit, and receive steering matrices (if both arrays are uniform, and linear) is then utilized to obtain angle estimates from factor matrices. The multi-linear structure of the received signal is maintained to take advantage of tensor-based angle estimation algorithms, while the shortage of samples in Doppler domain for slow-time MIMO radar is mitigated. As a result, the joint DOD, and DOA estimation performance is improved as compared to existing angle estimation techniques for slow-time MIMO radar. Simulation results verify the effectiveness of the proposed method.

2-D DOA Estimation in a Cuboid Array Based on Metaheuristic Algorithms and Maximum Likelihood

This paper proposes to apply the genetic algorithm and the firefly algorithm to enhance the estimation of the direction of arrival (DOA) angle of electromagnetic signals of a smart antenna array. This estimation is essential for beamforming, where the antenna array radiating pattern is steered to provide faster and reliable data transmission with increased coverage. This work proposes using metaheuristics to improve a maximum likelihood DOA estimator for an antenna array arranged in a uniform cuboidal geometry. The DOA estimation performance of the proposed algorithm was compared to that of MUSIC on different two dimensions scenarios. The metaheuristic algorithms present better performance than the well-known MUSIC algorithm.