Estimating direction of arrival with one-dimensional spectral analysis

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.

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.

In this paper, we investigate the problem of two-dimensional (2-D) direction of arrival (DOA) estimation in a distributed L-shaped array (LSA). The resolution of 2-D DOA estimation in distributed uniform L-shaped array is low, the number of available sources is limited by array elements and the estimation accuracy is susceptible to SNR. In order to promote the 2-D DOA estimation performance under distributed L-shaped array, this paper proposes a new L-shaped array geometry for 2-D DOA estimation based on the conjugate augmented property of signal second-order statistics. The proposed array structure is distributed augmented nested L-shaped array which every subarray is one-dimensional (1-D) distributed augmented nested array placed along y-axis and z-axis. By using Khatri-Rao product processing, the newly formed array possesses higher degree-of-freedom and number of virtual array apertures are more extended. Then, utilize spatial information and temporal information to construct a conjugate augmented spatial–temporal auto-correlation matrix for each orthogonal distributed subarray. With the redundancy removal and spatial smoothing, the rank of each covariance matrix is restored. Through analysis, each portion of the new formed virtual array can be used separately for 1-D azimuth and elevation angle estimation. Additionally, virtual cross-correlation matrix of two subarrays can accomplish angle-pairing procedure. Simulation results verify the effectivity of the proposed method in 2D-DOA estimation.

Direction of arrival (DOA) estimation is a classic problem in array processing. It has wide applications in wireless communications, radar, acoustics, and smart antennas, to name just a few. In this paper, we present a novel comparative study of six array geometries and their impact on mutual coupling and DOA estimation performance. Two scenarios are presented: with and without mutual coupling. A numerical software package was used to simulate the array geometries with dipole antennas. The mutual coupling matrix was calculated from the S‐parameters of the simulated arrays at the operating frequency based on specific sensor locations. The MUSIC algorithm was used to resolve the source location using the difference coarray technique. A well‐known smoothing technique was used to improve the rank of the covariance matrix, allowing MUSIC to compute the DOA using the sparse arrays. Several properties of each array are described, such as the physical sensor location, difference coarray, weight function, and coupling matrix. The sparse array HFCA and UACA achieved an RMSE below 2 degrees (for both 9 and 16 sources and the whole SNR range) and 0.5 degrees (for both 9 and 16 sources and SNR equals to 30 dB), respectively. The performance of the DOA estimation was compared using RMSE as a metric, considering the environment configuration with different number of sources and SNR conditions.

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.

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.

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.

FOMP algorithm for Direction of Arrival estimation

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.

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.

For direction of arrival (DoA) estimation, the data-driven deep-learning method has an advantage over the model-based methods since it is more robust against model imperfections. Conventionally, networks are based singly on regression or classification and may lead to unstable training and limited resolution. Alternatively, this paper proposes a two-branch neural network (TB-Net) that combines classification and regression in parallel. The grid-based classification branch is optimized by binary cross-entropy (BCE) loss and provides a mask that indicates the existence of the DoAs at predefined grids. The regression branch refines the DoA estimates by predicting the deviations from the grids. At the output layer, the outputs of the two branches are combined to obtain final DoA estimates. To achieve a lightweight model, only convolutional layers are used in the proposed TB-Net. The simulation results demonstrated that compared with the model-based and existing deep-learning methods, the proposed method can achieve higher DoA estimation accuracy in the presence of model imperfections and only has a size of 1.8 MB.

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.

The direction of arrival (DOA) estimation is a key issue in array signal processing, and there are many well-known methods, e.g., Capon, MUSIC, Root-MUSIC and some other DOA estimation algorithms in the literature. Nevertheless, the effective DOA estimation for closely spaced multiple sources with large power differences is still a difficult problem due to the deteriorated resolution for the low power sources. In this paper, a novel DOA estimation method called Capon-MUSIC algorithm is proposed, which has a much higher resolution for closely spaced multiple sources with obvious power differences. Finally, some numerical experiments are provided to demonstrate the effectiveness of the proposed method.

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.

This work investigates communication signal detection and direction of arrival (DOA) estimation for an integrated sensing and communications (ISAC) system with multiple hardware imperfections, including power amplifier nonlinearity, in-phase and quadrature phase imbalance, and phase-gain error (PGE). Conventional signal processing techniques struggle with the complex nonlinearities arising from these imperfections. Recently, deep neural networks (DNNs) have been employed to mitigate hardware impairments; however, they require a substantial number of pilot signals for training, leading to significant overhead, making them impractical in many applications. In this work, we design a signal flow inspired neural network (NN) to characterize the nonlinear ISAC system. Then, we propose a Bayesian method to jointly estimate the parameters of the PGE, the communication signals, and the DOAs by developing a message-passing inference algorithm based on the NN. Extensive simulation results demonstrate that the proposed method provides efficient and robust signal detection and DOA estimation performance under PGE, and significantly outperforms state-of-the-art ones.