White noise reduction for wideband linear array signal processing

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.

This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is based on the Expectation Maximization method where ESPRIT is used in the maximization step. The key idea is to iteratively interpolate the data to a virtual uniform linear array in order to apply ESPRIT to estimate the DOA. The iterative approach allows one to improve the interpolation using the previously estimated DOA. One of this method’s novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as Spectral MUSIC, EM-IQML and the method based on manifold separation technique. EM-ESPRIT is shown to be more robust to additive noise. Furthermore, EM-ESPRIT fully exploits the advantages of using a nonuniform array over a uniform array: simulations show that for the same aperture and with a smaller number of sensors, the nonuniform array presents almost identical performance as the equivalent uniform array.

The Direction of Arrival (DoA) estimation using linear sensor arrays is a critical task in array signal processing, with applications spanning SONAR, RADAR, and more. Traditional methods often struggle with the non-linear and high-dimensional nature of the data involved. This paper proposes a novel approach that leverages the strengths of both deep learning and machine learning classifiers. By combining an overcomplete Auto Encoder (AE) with a Support Vector Machine (SVM), the proposed method effectively extracts intricate features from the high-dimensional input signals, enabling accurate DoA estimation. The model was trained and evaluated using field data collected from the Indian Ocean. Sensor delays were introduced experimentally to the collected single-channel data by positioning acoustic sources at various angles within 0 to 180-degree relative to a linear microphone array with 16 channels. In DOA estimation, where experimental data are often noisy or missing features, the AE learns a detailed latent space representation that helps to smooth the data before it is classified. While AE + SVM is not new, its application to DoA estimation with noisy, incomplete, or sparse experimental data is novel. The overcomplete AE addresses the unique challenges of DoA estimation by improving feature quality and enabling more accurate, robust predictions. Experimental results demonstrate the efficacy of this unified model, achieving a remarkable 94.7% accuracy in DoA estimation tasks.

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.

A novel algorithm for the direction of arrival (DOA) estimation based on the fractional Fourier transform (FRFT) is proposed. Firstly, using the properties of FRFT and mask processing, Multi-component LFM sig-nals are filtered and demodulated into a number of stationary single frequency signals. Then the one-dimensional (1-D) direction estimation of LFM signals can be achieved by combining with the tradi-tional spectrum search method in the fractional Fourier (FRF) domain. As for the multi-component LFM signals, there is no cross-term interference, the mean square error (MSE) and Cramer-Rao bound (CRB) are also analyzed which perfects the method theoretically, simulation results are provided to show the validity of our method. The proposed algorithm is also extended to the uniform circular array (UCA), which realizes the two-dimensional (2-D) estimation. Using the characteristics of time-frequency rotation and demodulation of FRFT, the observed LFM signals are demodulated into a series of single frequency ones; secondly, operate the beam-space mapping to the single frequency signals in FRF domain, which UCA in array space is changed into the virtual uniform circular array (ULA) in mode space; finally, the DOA estimation can be realized by the traditional spectral estimation method. Compared with other method, the complex time-frequency cluster and the parameter matching computation are avoided; meanwhile enhances the esti-mation precision by a certain extent. The proposed algorithm can also be used in the multi-path and Doppler frequency shift complex channel, which expands its application scope. In a word, a demodulated DOA esti-mation algorithm is proposed and is applied to 1-D and 2-D angle estimation by dint of ULA and UCA re-spectively. The detailed theoretical analysis and adequate simulations are given to support our proposed al-gorithm, which enriches the theory of the FRFT.

A structured least square (LS) method for simultaneous estimation of the mutual coupling matrix (MCM) and directions of arrival (DOAs) of signal sources for uniform linear array (ULA) and uniform circular array (UCA) is presented. The DOAs and MCM can be simultaneously estimated by the proposed method when observations of at least two different DOAs are available. This method significantly simplifies the procedure of mutual coupling compensation and it can also be applied for the calibration of ULA and UCA. Simulation results demonstrate the efficiency and accuracy 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.

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.

This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method.

In this proposed work, a subspace based method of Direction of Arrival (DOA) estimation with Mutual Coupling (MC) compensation and wavelet denoising for Uniform Linear Array (ULA) is addressed. A preprocessing technique of denoising by Wavelet Transform (WT) is accomplished and followed by Mutual Coupling compensation algorithm to improve DOA estimation. A complex symmetric Toeplitz matrix is modeled and based on this matrix, mutual coupling between sensors is compensated. By denoising and mutual coupling compensation, this method accomplishes a satisfactory performance for weak signals in DOA estimation without array calibration. The effectiveness of the proposed method is studied through simulations.

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 the field of array signal processing, direction of arrival (DOA) estimation is a prime area of research. DOA estimation and adaptive beamforming (ABF) are the main issues in smart antennas, which dynamically find the direction of desired and interfering users and finds the optimum weights for beamforming. There are numerous spectral and eigen structure algorithms for estimating the direction of narrow band sources. However, in a complex multipath channel environment, received signals from different directions are fully or partially correlated, which prevents the applications of high resolution techniques to estimate the direction of incoming signals. Maximum likelihood (ML) is an efficient technique for DOA estimation in a low signal to noise ratio (SNR) and coherent channel environment. In this paper, we use particle swarm optimization (PSO) for estimating ML solution by optimizing complex non linear multimodal function over a high dimensional space in linear arrays. PSO-ML estimator has been compared with conventional DOA estimation techniques in uncorrelated, partially correlated and coherent channel environment. The performance of PSO-ML estimator and conventional algorithms are analyzed in varying partially correlated channel environment. The simulation results demonstrate that PSO based estimator gives superior statistical performance.

Distributed subarray antennas (DSAs), which are sparse arrays consisting of two or more far separated subarrays, have many advantages over uniform linear array, especially for direction of arrival (DOA) estimation. However, they are subject to manifold ambiguity, which has significant influence on DOA estimation. In order to solve the manifold ambiguity of uncorrelated sources for DSA, a novel method based on estimation of signal parameters via rotational invariance technique by utilizing optimal subarray partition is proposed in this paper. In the proposed method, an optimized reference estimation is obtained by the rotational invariance between the new subarrays with optimal partition of DSA. The high accuracy and unambiguous DOA estimations are then disambiguated easily according to the optimized reference estimation. In this way, the performance of disambiguated DOA estimation can be enhanced in cases of the low signal-to-noise ratio and the large spacing between the subarrays. Moreover, the ambiguity threshold effect of DOA estimation for DSA is analyzed by means of the maximum a posteriori estimator. Computer simulation results show good performance of the proposed method and the effectiveness of the ambiguity threshold for DSA.

Direction of arrival (DOA) estimation has emerged as a promising technology for many military and civilian applications, such as radio astronomy and wireless communications. However, it remains very challenging to estimate DOA for distributed sources within impulsive noise environments. As is widely known, the utilization of the subspace technology in array signal processing can enable high-resolution DOA estimation. In many instances, most of these algorithms assume that the noise is Gaussian. Considering the impulsive noise environments, the derivative of the error function is derived as the iteratively weighted factor in the objective function of low-rank decomposition. Two iterative algorithms are proposed to compute the signal subspace to implement DOA estimation for coherently distributed sources. To further improve the DOA estimation accuracy and increase the number of estimated sources, the virtual data samples are reconstructed from the extended co-prime array. Simulation results confirm that the two proposed impulsive noise suppression algorithms provide better performance than the existing algorithms. The virtual data samples that are reconstructed from the extended co-prime array can be utilized as the effective inputs for subspace-like algorithms.

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.