Off-Grid Error Calibration for Single Snapshot DOA Estimation Based on Sparse Bayesian Learning

Collaborative Direction of Arrival estimation by using Alternating Direction Method of Multipliers in distributed sensor array networks employing Sparse Bayesian Learning framework

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.

Iterative reweighted proximal projection based DOA estimation algorithm for monostatic MIMO radar

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.

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.

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.

The advanced radar detection method which combines Tx beamforming and Rx array processing with highresolution direction of arrival (DOA) estimation is proposed. The proposed method associates DOA estimation direction with Tx beamforming direction (TxD-DOA) for a high accuracy detection for multiple targets in millimeter-wave radar system. Computer simulation and experiment evaluation verify the improvement effects of the TxD-DOA method. We have confirmed that the suppression of multiple radar reflection waves by the transmission beam scanning brings the better DOA estimation accuracy and higher angular resolution of the TxD-DOA for multiple human targets.

The problem of multiple incident signals’ direction of arrival (DOA) estimation for spatially separated polarisation sensitive array (SS‐PSA) is studied. The proposed SS‐PSA is a sparse uniform array with orthogonally oriented and spatially separated dipole‐triads. The proposed array can reduce the array mutual coupling by using the spatially separated polarised antenna instead of conventional spatially collocated polarised antenna. Moreover, the DOA estimation accuracy can be improved greatly due to the extended aperture offered by sparse array. Computer simulation results verify the effectiveness of the proposed algorithm.

Subspace-based high-resolution direction of arrival (DOA) estimation significantly deteriorates under array manifold perturbation and rank deficiency of the covariance matrix due to mutual coupling and multipath propagation, respectively. In this correspondence, the unknown mutual coupling can be circumvented by the proposed method without any passive or active calibration process, and the DOA of the coherent signals can be accurately estimated accordingly. With a newly constructed matrix, the deficient rank can be restored, and the effective array aperture can be extended compared with conventional spatial smoothing. The proposed method achieves a good robustness and DOA estimation accuracy with unknown mutual coupling. The simulation results demonstrate the validity and efficiency of the proposed method.

An algorithm to improve direction of arrival (DOA) estimation accuracy with an extended sensor array in the presence of multiple coherent signal sources is proposed. The algorithm uses virtual element theory to extend the sensor array, estimates virtual element information via linear prediction and expands the array aperture in practical sense; the sparsity of the target orientation in angle space is exploited to establish an over-complete dictionary and a reception model for the array signal in sparse space; the received array data is preprocessed using singular value decomposition (SVD) method and target DOA estimation is realized by calculating the best atoms. The algorithm improves DOA estimation accuracy by extended array and uses SVD to control computational complexity effectively, which ensures the accuracy and efficiency. Computer simulation shows that the proposed algorithm is able to accurately estimate the DOA for both single-target and closely spaced multi-target cases in low signal-to-noise ratio environments, and also has excellent DOA estimation performance in the presence of multiple coherent signal sources.

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.

Sparse Bayesian learning (SBL) is applied to the coprime array for underdetermined wideband direction of arrival (DOA) estimation. Using the augmented covariance matrix, the coprime array can achieve a higher number of degrees of freedom (DOFs) to resolve more sources than the number of physical sensors. The sparse-based DOA estimation can deteriorate the detection and estimation performance because the sources may be off the search grid no matter how fine the grid is. This dictionary mismatch problem can be well resolved by the SBL using fixed point updates. The SBL can automatically choose sparsity and approximately resolve the non-convex optimizaton problem. Numerical simulations are conducted to validate the effectiveness of the underdetermined wideband DOA estimation via SBL based on coprime array. It is clear that SBL can obtain good performance in detection and estimation compared to least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS) , simultaneous orthogonal matching pursuit total least squares (SOMP-TLS) and off-grid sparse Bayesian inference (OGSBI).

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.

In order to solve the problem that the channel gain-phase mismatch would deteriorate the performance of direction of arrival (DOA) estimation in actual direction finding (DF) system, a novel efficient gain-phase calibration algorithm based on the self-checking signal is proposed in this paper. By injecting a self-checking signal into the actual DF system, the whole calibration process could divide into the off-line pre-calibration and the auto-calibration part. Thus, it could realize the real-time auto-calibration efficiently during the DOA estimation process. Moreover, in order to verify the effectiveness of the proposed method, a practical DF signal processor based on the FPGA and DSP is implemented in this paper, and the experiments are carried out in the anechoic chamber. The experiment result shows that the proposed method could calibrate the gain-phase mismatch in real-time and have higher DOA estimation accuracy.