DOA estimation of multiple sources in sparse space with an extended array technique

Shipborne high-frequency surface wave radar (HFSWR) plays an important role in vessel target surveillance. However, additional modulation on the echo signal introduced by the platform motion, including the forward movement and six-degree-of-freedom (6-DOF) motion may further aggravate the inaccuracy of target direction of arrival (DOA) estimation and severely limits its detection ability. This paper aims to establish the platform-motion model and mathematically analyze the influence of platform motion on target DOA estimation. Considering the forward movement, 6-DOF motion, and the installed irregular radar array, the formula affecting the target azimuth is derived and the new time-varying steering vector is determined. Simulation results validate the theoretical analysis and the derived formula. In addition, forward movement and yaw motion have the most crucial effect on DOA estimation because these two motions change the platform location and detection area.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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 this work, the grid mismatch problem for direction of arrival (DOA) estimation of array is studied. To solve the grid mismatch impact on the DOA estimation accuracy, a novel off-grid model for DOA estimation using sinc interpolation is proposed in this paper. Specifically, the off-grid error is represented as parameter to be estimated in the observation model. Under the framework of sparse Bayesian learning (SBL), the off-grid error is estimated via the variational Bayesian expectation maximization (VBEM) and eliminated by updating the grids with sinc interpolation. The simulation results demonstrate superior performance of the proposed method over state-of-the-art methods are reported, as well.