Antenna without Phase Center for DOA Estimation in Compressive Array Processing

Recently, there are a lot of study of direction of arrival (DoA) estimation using compressive sensing (CS). As CS is a new paradigm in signal processing, there are many aspects of this method that can be investigated. In the case of DoA estimation in noisy measurement, it is important to correctly determine a correct threshold of CS reconstruction, particularly when CS reconstruction is implemented using L 1 -norm minimization. Too small threshold value will make the correct DoA does not lies in CS reconstruction searching area, while too large threshold value will burden CS iteration to select a solution from a large number of possible solutions. In this paper, we derived an optimal threshold value for CS reconstruction for DoA estimation mathematically and verified the result using computer simulation. Using Gaussian noise model, we obtain the chi-square distribution of euclidean distance of noisy and noiseless received vector. We introduce the thresholding index κ to scale the standard deviation of chi-square distribution to determine the CS reconstruction threshold and simulate this value for various SNR. We find that the optimal κ value 0.5 to 1 for high noise environment, and optimal κ value 1 to 2 in low noise environment.

Based on the extended noise subspace, the case of weak signal direction of arrival (DOA) estimation in presence of strong jamming is studied, and a novel approach is given in this paper. Under the condition knowing the number of strong interferences, first, the method forms the extended noise subspace, then, uses the conventional multiple signal classification (MUSIC) algorithm to constrain the strong interferences effectively and estimates weak signals' DOA information accurately based on the extended noise subspace. The method does not require the angle information of strong interferences and it has the same computation burden as conventional MUSIC. Theoretic analysis and computer simulation demonstrate the method is effective and feasible.

In automotive millimeter-wave (MMW) radar systems, achieving high-precision direction of arrival (DOA) estimation with a limited number of array elements is a crucial research focus. Compressive sensing (CS) techniques have been demonstrated to offer superior performance in DOA estimation compared to spectral estimation methods. However, traditional CS methods suffer from an off-grid effect, which causes their reconstruction results to deviate from the actual positions of the signal sources, thereby reducing the accuracy. Currently, as a gridless method, atomic norm minimization (ANM) has shown effectiveness in DOA estimation for uniform linear arrays (ULAs). However, the performance of ANM is suboptimal in non-uniform linear arrays (NULAs), and their computational efficiency is not satisfactory. In this paper, we propose a novel algorithm for DOA estimation in NULA, drawing inspiration from the alternating descent conditional gradient algorithm framework. First, we construct an atomic set based on the observation scene and select the atoms with the highest correlation to the residuals as potential signal sources for global estimation. Then, we construct a mapping function for the signal sources in the continuous domain and perform conditional gradient descent in the neighborhood of each signal source, addressing the bias introduced by the off-grid effect. We compared the proposed algorithm with ANM, Iterative Shrinkage Thresholding (IST), and Multiple Signal Classification (MUSIC) algorithms. Simulation experiments validate that the proposed algorithm effectively addresses the off-grid effect and is applicable to DOA estimation in coprime and random arrays. Furthermore, real data experiments confirm the effectiveness of the proposed algorithm.

In this paper, the issue of direction of arrival (DOA) estimation is discussed, and a partial angular sparse representation (SR)-based method using a sparse separate nested acoustic vector sensor (SSN-AVS) array is developed. Traditional AVS array is improved by separating the pressure sensor array and velocity sensor array into two different sparse array geometries with nested relationship. This improved array geometry can achieve large degrees of freedom (DOF) after the extended vectorization of the cross-covariance matrix, and only partial SR of the angle is required by exploiting the cyclic phase ambiguity caused by the large inter-element spacing of the virtual array. Joint sparse recovery is developed to amend the grid offset and unitary transformation is utilized to transform the complex atoms into real-valued ones. After sparse recovery, the sparse vector can simultaneously provide high-resolution but ambiguous angle estimation and unambiguous reference angle estimation embedded in the AVS array, and they are combined to obtain unique and high-resolution DOA estimation. Compared to other state-of-the-art DOA estimation methods using the AVS array, the proposed algorithm can provide better DOA estimation performance while requiring lower complexity. Multiple simulation results verify the effectiveness of the approach.

Uniform linear array (ULA) geometry does not perform well for direction of arrival (DOA) estimation at directions close to the array endfires. Shirvani and Akbari solved this problem by displacing two elements from both ends of the ULA to the top and/or bottom of the array axis. Shirvani-Akbari array (SAA) presents a considerable improvement in the DOA estimation of narrowband sources arriving at endfire directions in terms of DOA estimation accuracy and angular resolution. In this paper, all new proposed SAA configurations are modelled and also examined, numerically. In this paper, two well-known DOA estimation algorithms, multiple signal classification (MUSIC) and minimum variance distortionless response (MVDR), are used to evaluate the effectiveness of proposed arrays using total root mean square error (RMSE) criterion. In addition, two new scenarios are proposed which divide angular search to two parts, directions close to array endfires as well as middle angles. For middle angles, which belong to (−70∘≤𝜃≤70∘), ULA is considered, and for endfire angles, the angles which belong to (−90∘≤𝜃≤−70∘) and (70∘≤𝜃≤90∘), SAA is considered. Simulation results of new proposed scenarios for DOA estimation of narrowband signals show the better performance with lower computational load.

We propose a Taylor expansion multiple signal classification (TE MUSIC) method for joint direction of departure (DOD) and direction of arrival (DOA) estimation in a bistatic multiple-input multiple-output (MIMO) array. First, using a Taylor expansion of the steering vector, a two-dimensional (2D) search in the conventional MUSIC method for MIMO arrays is reduced to a two-step one-dimensional (ID) search in the proposed TE MUSIC method. Second, DOAs of the targets can be achieved via Lagrange multiplier by a ID search. Finally, substituting the DOA estimates into the 2D MUSIC spectrum function, DODs of the targets are obtained by another ID search. Thus, the DOD and DOA estimates can be automatically paired. The performance of the proposed method is better than that of the MIMO ESPRIT method, and is similar to that of the 2D MUSIC method. Furthermore, due to the ID search, the TE MUSIC method avoids the high computational complexity of the 2D MUSIC method. Simulation results are presented to show the effectiveness of the proposed method.

Currently, the widely used methods for direction of arrival (DOA) estimation were constructed based on the subspace, such as Multiple Signal Classification (MUSIC) and Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT), which needed to know the number of sources in advance. In this paper, a new model based on the Generalized Reference Curve Model (GRCM) for the DOA estimation was proposed, which do not need to know the sources number in advance. And the comparison of the performance between the proposed model and the MUSIC model was given to demonstrate the effectiveness of our method. The algorithm of Multi-target Intermittent Particle Swarm Optimization (MIPSO) was adopted to solve the model proposed in this paper, and the performance of the MIPSO was analyzed through a simulation. The result shown that:(1) the GRCM was an effective model to solve the DOA estimation without prior knowledge of the sources number; (2) the MIPSO was an efficient algorithm to solve the DOA estimation with much shorter operation time and high precision.

In this paper we propose for comparative analysis of wideband direction of arrival (DOA) estimation methods with nested array. Previously developed methods, Incoherent method, Coherent signal subspace processing (CSSM) and Weighted average of signal subspace (WAVES) could not perform satisfactory DOA estimation due to the single dimensionality and associated with lesser degree of freedom. In nested array, DOA estimation is done on the same source that is Gaussian source with additive white Gaussian noise (AWGN). While, nested array performed DOA estimation by decomposing uniform linear array (ULA) into multidimensional array, by which algorithm gets improved performance compare to the conventional methods. In nested array, power spectrum is measured by using multiple signal classification (MUSIC) and performance index is evaluated using Monte Carlo simulation.

For two-dimensional (2D) direction of arrival (DOA) estimation in a uniform rectangular array (URA), the conventional method converts the 2D problem into a one-dimensional (1D) problem; however, the computational complexity is high, and the accuracy is limited by the grid interval. To address this issue, based on sparse representation theory and a separable observation model (SPM), this paper presents a novel off-grid-framework-based 2D DOA estimation approach by designing a modified 2D off-grid model and a solution for the multisnapshot case in the SPM. The proposed algorithm can be divided into two stages. In the first stage, we use a matching pursuit and focal underdetermined system solver (MFOCUSS) algorithm to quickly identify the candidate or potential areas where the true sources may exist. In the second stage, the candidate areas obtained in the first stage are regarded as the initialization. Then, for a specific source, we regard other sources as interference. By using an alternating descent method, we can obtain accurate DOAs. Moreover, based on the equivalence of time delay and spatial spacing, a 2D off-grid method for multisnapshot cases is proposed in this paper. Numerical simulations demonstrate the effectiveness and efficiency of the proposed algorithm.

gold-MUSIC based DOA estimation using ULA antenna of DS-CDMA sources with propagation delay diversity

DOA (Direction of Arrival) estimation is a major problem in array signal processing applications. Recently, compressive sensing algorithms, including convex relaxation algorithms and greedy algorithms, have been recognized as a kind of novel DOA estimation algorithm. However, the success of these algorithms is limited by the RIP (Restricted Isometry Property) condition or the mutual coherence of measurement matrix. In the DOA estimation problem, the columns of measurement matrix are steering vectors corresponding to different DOAs. Thus, it violates the mutual coherence condition. The situation gets worse when there are two sources from two adjacent DOAs. In this paper, an algorithm based on OMP (Orthogonal Matching Pursuit), called ILS-OMP (Iterative Local Searching-Orthogonal Matching Pursuit), is proposed to improve DOA resolution by Iterative Local Searching. Firstly, the conventional OMP algorithm is used to obtain initial estimated DOAs. Then, in each iteration, a local searching process for every estimated DOA is utilized to find a new DOA in a given DOA set to further decrease the residual. Additionally, the estimated DOAs are updated by substituting the initial DOA with the new one. The simulation results demonstrate the advantages of the proposed algorithm.

Direction of Arrival (DOA) estimation is one of the most fundamental problems in array signal processing, and it is widely used in many fields such as radar, sonar, and communications. This paper uses Compressed Sensing (CS) technology to focus on DOA estimation. Aiming at the problems caused by fewer snapshots in the practical application of DOA estimation, a Nonuniform Overcomplete Dictionary (NUOD) combining initialization space is proposed. In addition, the new DOA estimation algorithm of Orthogonal Match Pursuit (OMP) is improved by a Genetic Algorithm (GA). Furthermore, in order to improve the performance of DOA estimation of CS technology, the following three improvements are proposed. (1) Make full use of the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) to determine the initialization point and then determine the scope of the initialization space according to the Crame’r–Rao bound (CRB). (2) Aiming at a large amount of calculation, the algorithm can realize the nonuniform over-complete dictionary design of the popular array matrix according to the sparse representation of the partition of the initialization space. (3) To further improve the algorithm’s performance, the nonuniform over-complete dictionary design is combined with the processing flow of the GA improved OMP algorithm. The simulation results prove that the method in this paper has the advantages of less computing time, low estimation error, and wide application range.

Recently, 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.

This paper presents a brief overview of narrowband direction of arrival (DOA) estimation algorithms and techniques. A comprehensive study is carried out in this paper to investigate and evaluate the performance of variety of algorithms for DOA estimation. Two categories of DOA estimation algorithms are considered for discussion which are Classical methods and Subspace based techniques. Classical methods include Sum-and-Delay method and Capon’s Minimum Variance Distortionless Response (MVDR) while Subspace based techniques are multiple signal classification (MUSIC) and The Minimum Norm Technique. Also ESPIRIT technique is evaluated. Inefficiencies are pointed out and solutions are suggested to overcome these shortfalls. Simulation results shows that the MUSIC algorithm is able to better represent the DOAs of signals with more prominent peaks. The Min-Norm algorithm also identifies the DOAs of signals similar to the MUSIC algorithm, but produces spurious peaks at other locations. The MVDR method identifies the DOAs of signals, but the locations are not represented by sharp peaks, due to spectral leakage. The classical beamformer also produces several spurious peaks. MUSIC show higher accuracy and resolution than the other algorithms. It should be noted that MUSIC is more applicable because it can be used for different array geometries.

This paper addresses the source association (SA), direction of arrival (DOA), and fading coefficients (FCs) estimation problem in multipath environment. First, we establish a rank reduction property for a multipath signal model with the existence of multiple groups of coherent signals. Subsequently, based on this property, effective algorithms for SA, DOA, and FCs estimation have been developed. The proposed DOA and FCs estimation methods exploit the multipath structure information to achieve improved accuracy. The new DOA estimation methods work well even in the case that the DOAs of the multipath signals associated with different sources are (nearly) overlapped. Meanwhile, the new methods are applicable to arbitrary array geometry while without decreasing the effective array aperture. Then, the stochastic Cramér-Rao bound on DOA and FCs estimation of multipath model (MCRB) exploiting the multipath structure information is derived in closed form. Numerical simulations have been provided to demonstrate the effectiveness of the proposed methods.