Robust Adaptive Beamforming Research Articles

Robust adaptive beamforming for cylindrical uniform conformal arrays based on low-rank covariance matrix reconstruction

Recently, conformal arrays have attracted considerable interest because such arrays can provide reduced radar cross-section and increased angle coverage. In this article, we devise a robust adaptive beamforming (RAB) approach using cylindrical uniform conformal array (CUCA). Firstly, we derive the minimum variance distortionless response (MVDR) beamformer for the CUCA by utilizing the noise subspace of interference covariance matrix (ICM) and steering vector (SV) of the signal-of-interest (SOI). Subsequently, the ICM is reconstructed by estimating the noise-free covariance matrix of the CUCA outputs and the interference projection matrix. Specifically, the noise-free covariance matrix can be regarded as multiple low-rank covariance matrices, and each low-rank matrix is reconstructed by formulating a nuclear norm minimization (NNM) problem. With the reconstructed covariance matrix, the 2-D DOAs of sources are determined by employing 2-D MUSIC spectrum to form the interference projection matrix. In addition, the SOI SV is estimated by solving a quadratically constrained quadratic programming (QCQP) problem. Numerical results demonstrate that the proposed approach is obviously superior to the existing RAB techniques.

CAWE-ACNN Algorithm for Coprime Sensor Array Adaptive Beamforming.

This paper presents a robust adaptive beamforming algorithm based on an attention convolutional neural network (ACNN) for coprime sensor arrays, named the CAWE-ACNN algorithm. In the proposed algorithm, via a spatial and channel attention unit, an ACNN model is constructed to enhance the features contributing to beamforming weight vector estimation and to improve the signal-to-interference-plus-noise ratio (SINR) performance, respectively. Then, an interference-plus-noise covariance matrix reconstruction algorithm is used to obtain an appropriate label for the proposed ACNN model. By the calculated label and the sample signals received from the coprime sensor arrays, the ACNN is well-trained and capable of accurately and efficiently outputting the beamforming weight vector. The simulation results verify that the proposed algorithm achieves excellent SINR performance and high computation efficiency.

Efficient and Robust Adaptive Beamforming Based on Coprime Array Interpolation

Unlike uniform linear arrays (ULAs), coprime arrays require fewer physical sensors yet provide higher degrees of freedom (DOF) and larger array apertures. However, due to the existence of “holes” in the differential co-array, the target detection performance deteriorates, especially in adaptive beamforming. To address these challenges, this paper proposes an efficient and robust adaptive beamforming algorithm leveraging coprime array interpolation. The algorithm eliminates unwanted signals and uses the Gauss–Legendre quadrature method to reconstruct an Interference-plus-Noise Covariance Matrix (INCM), thereby obtaining the beamforming coefficients. Unlike previous techniques, we utilize a virtual interpolated ULA to expand the aperture, enabling the acquisition of a high-dimensional covariance matrix. Additionally, a projection matrix is constructed to eliminate unwanted signals from the received data, greatly enhancing the accuracy of INCM reconstruction. To address the high computational complexity of integral operations used in most INCM reconstruction algorithms, we propose an approximation based on the Gauss–Legendre quadrature, which reduces the computational load while maintaining accuracy. This algorithm avoids the array aperture loss caused by using only the ULA segment in the difference co-array and improves the accuracy of INCM reconstruction. Simulation and experimental results show that the performance of the proposed algorithm is superior to the compared beamformers and is closer to the optimal beamformer in various scenarios.

Robust adaptive beamforming with partly calibrated arrays in the presence of gain-phase errors

The performance of the beamformer, especially the beamformer based on the interference plus noise covariance matrix (INCM) reconstruction which needs accurate array manifold knowledge, will degrade dramatically in the presence of gain-phase errors. To solve this problem, we propose a robust adaptive beamforming method based on partly calibrated arrays (PCA). The main idea of this method is to estimate the gain-phase errors more accurately using the higher signal-to-noise ratio (SNR) signal sources and the PCA. After that, we calibrate the interference signal steering vector (SV) and reconstruct the more accurate INCM based on the estimation results. Finally, the SV of the desired signal is estimated by the intersection of two special subspaces. On the basis of the above research, the optimal weight vector is obtained. Numerical simulation results demonstrate the superior performance of the proposed beamformer relative to other existing beamformers in the presence of gain-phase errors.

Robust adaptive beamforming for cylindrical uniform conformal array

As we all know, conformal arrays can provide smaller radar cross-section (RCS) and greater angle coverage than conventional linear arrays and planar arrays. In this paper, we develop a robust adaptive beamforming (RAB) approach using the cylindrical uniform conformal array. Firstly, we reconstruct the interference-plus-noise covariance matrix (INCM) by estimating the steering vectors (SVs) and powers of all interferences. Specifically, we estimate the interference SVs by exploiting the MUSIC spectrum and corrected by solving a minimization problem based on the orthogonality between the interferences SVs and noise subspace, and the interferences powers are further estimated by utilizing the non-correlation between different signal SVs. With the reconstructed INCM, the SV of the signal-of-interest is estimated by solving a quadratically constrained quadratic programming problem. Numerical results demonstrate that the proposed approach is obviously superior to the existing RAB techniques.

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction with Gaussian Random Dimensionality Reduction

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction with Gaussian Random Dimensionality Reduction

Robust adaptive beamforming via quasi-signal subspace estimation for covariance matrix reconstruction

In this paper, a novel narrowband interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for robust adaptive beamforming (RAB). To enhance the effectiveness of the INCM reconstruction, we offer a prior selection of the dimension of a quasi-signal subspace (QSS) based on the signal subspace proximity employing two subsample covariance matrices (SSCMs). The QSS herein can provide estimations of all relevant factors of interference for the INCM. Moreover, by employing the eigenvectors of the SSCM, the noise power can be estimated precisely through a nonlinear regularization scheme. Finally, the signal-of-interest steering vector is corrected by an optimization problem exploiting the reconstructed INCM. The proposed RAB method can capitalize on the benefits of the QSS without prior knowledge of the number of sources. The results of the simulations demonstrate the effectiveness of the proposed method in terms of various mismatches.

Deep unfolding model‐based for hybrid robust wide band adaptive beamforming

AbstractThe design of arrays capable of receiving wideband signals differs from arrays that can only receive narrowband signals. These arrays must be able to receive signals with an instant bandwidth of several GHz across the entire operating frequency, such as High‐Resolution Radars or Terahertz in 6G communication systems. In these arrays, using a time delay line structure leads to an increase in beamformer coefficients, resulting in high computational complexity. This poses a challenge for beamforming in wideband systems. Additionally, classic Wideband beamformers face other factors, such as poor performance in the presence of input direction of arrival error, array calibration error, and requiring too many snapshots to reach the steady state of the beamformer. Therefore, the robustness of wideband adaptive beamforming using deep unfolding model‐based technique is focused on, which has not been discussed before. The advent of deep unfolding, an innovative technique, amalgamates iterative optimization approaches with elements of neural networks. The aim is to deftly maneuver through various tasks across disciplines such as machine learning, signal and image processing, and telecommunication systems. Also, the network training method is done to become more robust against the mentioned factors. In the proposed structure, the constraints of the previous methods have been evaluated. It is observed to have better performance compared to other classic algorithms. Also, with the investigations of the proposed method with other conventional deep learning methods, it was observed that in some cases the proposed structure performance is equal to the conventional deep learning method and sometimes better.

Low-Complexity Uncertainty-Set-Based Robust Adaptive Beamforming for Passive Sonar

Recent work has highlighted the potential benefits of exploiting ellipsoidal uncertainty-set-based robust Capon beamformer (RCB) techniques in passive sonar. Regrettably, the computational complexity required to form RCB weights is cubic in the number of adaptive degrees of freedom, which is often prohibitive in practice. For this reason, several low-complexity techniques for computing RCB weights, or equivalent worst case robust adaptive beamformer weights, have recently been developed. These techniques, whose complexities are only quadratic in the number of adaptive degrees of freedom, use gradient-based, reduced-dimension Krylov-subspace or Kalman-filtering methods. In this work, we review these techniques for passive sonar, analyzing their complexities and evaluating them initially on simulated data. The best performing methods are then evaluated on two in-water recorded passive sonar data sets. One set, containing a strong controlled acoustic source, demonstrates the ability of the algorithms to protect against signal cancellation when pointing at the source, and their ability to reject the source when pointing away from it. The other data set, recorded during a period when the boat was accelerating, demonstrates the ability of the algorithms to operate in the presence of speed-induced noises.

A New Robust Adaptive Beamforming Algorithm Based on GSC

A New Robust Adaptive Beamforming Algorithm Based on GSC

Robust Adaptive Beamforming Based on Manifold Analysis for Flexible Conformal Array of Smart Morphing Wing Aircraft

Robust Adaptive Beamforming Based on Manifold Analysis for Flexible Conformal Array of Smart Morphing Wing Aircraft

Improved eigenspace-based method for robust adaptive beamforming with dimension search

The eigenspace-based technique, as a classic method for robust adaptive beamforming (RAB), can substantially mitigate the negative impact caused by model mismatch. However, the conventional eigenspace-based beamformer (CESB) undergoes severe performance degradation at low signal-to-noise ratio (SNR). This is because it firmly sets the dimension of the projection subspace (DOPS) to the source number. To alleviate this problem, an improved eigenspace-based approach is proposed in this communication, where the DOPS is auto-selected to adapt to different cases. We roughly analyze the rationality that the robustness of the eigenspace-based technique can be enhanced by simply adjusting the DOPS at low SNR. In addition, we concretely propose an automatic selection method for the DOPS derived from a minimum beamformer sensitivity estimation problem. The proposed method is advantageous in that it is parameter-free. Moreover, simulation experiments are performed to demonstrate the improvement of the CESB and its robustness against steering vector mismatch.

Robust adaptive beamforming via residual convolutional neural network

Abstract Aiming at the problem that the covariance matrix includes the desired signal and the signal steer vector mismatches will degrade the beamforming performance, an effective robust adaptive beamforming (RAB) approach is presented in this paper based on a residual convolutional neural network (RAB-RCNN). In the presented method, the RAB-RCNN model is designed by introducing a residual unit, which can extract the deeper features from the signal sample covariance matrix. Residual noise elimination and interferences power estimation are utilized to reconstruct the desired signal covariance matrix, and correct the mismatched steering vector (SV) by the eigenvalue decomposition of the reconstructed desired signal covariance matrix. The projection method is utilized to redesign the signal interference-plus-noise covariance matrix. Furthermore, the beamforming weight vector is calculated with the two parameters obtained before and used as the label of the RAB-RCNN model, The trained model can rapidly and precisely output the predicted beamforming weight vector without complex matrix operations, including the matrix inversion of the signal covariance matrix, so that the calculation time can be reduced for beamforming. Simulations demonstrate the robustness of the presented approach against SV mismatches due to the direction-of-arrival estimation error, sensor position error, and local scattering interference.

Robust Adaptive Beamforming for Interference Suppression Based on SNR

Robust adaptive beamforming (RAB) can be used to suppress interference signals while retaining the desired signals received by a sensor array. However, desired signal self-cancellation and model mismatch can affect RAB performance. In this paper, a novel interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for RAB to solve these problems. The proposed method divides the desired signal into two ranges according to the input signal-to-noise ratio (SNR), namely low SNR and high SNR. In the low SNR range, INCM reconstruction directly uses the same sample covariance matrix as the sample matrix inversion (SMI) beamformer to retain the advantages of the traditional SMI algorithm. In the high SNR range, the eigenvalues of the sample covariance matrix are used to estimate the interference power and noise power. The optimized interference steering vector (SV) is obtained by solving a quadratic convex optimization problem in an interference subspace. The INCM is reconstructed from the interference SVs, interference power, and noise power. The reconstructed INCM is then used to correct the desired signal SV via maximizing the beamformer output power. This is achieved by solving a quadratically constrained quadratic programming (QCQP) problem. Analysis and simulation results are presented which demonstrate that the proposed method performs well under a variety of mismatch conditions.

Robust Wideband Adaptive Beamforming With Adjustable Nulls in High Dynamic Scene

Robust Wideband Adaptive Beamforming With Adjustable Nulls in High Dynamic Scene

Robust Wideband Adaptive Beamforming by Convolutional Neural Network Structures in an Array System

The structure of arrays capable of receiving wideband signals differs from arrays which can only receive narrowband signals. These arrays should be capable of receiving several GHz instant bandwidth signals over the entire operating frequency, like High Resolution Radars or Terahertz in 6G communication systems. In these arrays, the number of beamformer coefficients increase due to using a time delay line structure, hence leading to a high computational complexity. This is one of the challenges of beamforming in wideband systems. Additionally, there are other factors in classic Wideband beamformers. These factors include poor performance against input DOA (direction of arrival) error, array calibration error, and too many snapshots to reach the steady state of the beamformer. Therefore, this paper focuses on the robustness of beamforming using deep learning technique, which has not been discussed before. The basis of network design is convolutional layers. Two different proposed approaches have been proposed to obtain optimal structure. In the first approach, appropriate values of hyperparameters are estimated, whereas the network model is selected in the second approach. Also, the network training method is done to become more robust against the mentioned factors. In the proposed structures, the constraints of the previous methods have been evaluated. The proposed structure is shown to have a superior performance when compared with other existing algorithms. In addition, the matrix of signal samples is replaced with the covariance matrix at the network's input, so the calculation time is significantly improved compared to the previous methods.

Virtual covariance matrix reconstruction-based adaptive beamforming for small aperture array.

Recently, many robust adaptive beamforming (RAB) algorithms have been proposed to improve beamforming performance when model mismatches occur. For a uniform linear array, a larger aperture array can obtain higher array gain for beamforming when the inter-sensor spacing is fixed. However, only the small aperture array can be used in the equipment limited by platform installation space, significantly weakening beamforming output performance. This paper proposes two beamforming methods for improving beamforming output in small aperture sensor arrays. The first method employs an integration algorithm that combines angular sector and gradient vector search to reconstruct the interference covariance matrix (ICM). Then, the interference-plus-noise covariance matrix (INCM) is reconstructed combined with the estimated noise power. The INCM and ICM are used to optimize the desired signal steering vector (SV) by solving a quadratically constrained quadratic programming (QCQP) problem. The second method proposes a beamforming algorithm based on a virtual extended array to increase the degree of freedom of the beamformer. First, the virtual conjugated array element is designed based on the structural characteristics of a uniform linear array, and received data at the virtual array element are obtained using a linear prediction method. Then, the extended INCM is reconstructed, and the desired signal SV is optimized using an algorithm similar to the actual array. The simulation results demonstrate the effectiveness of the proposed methods under different conditions.

Robust Adaptive Beamformer Based on Constant Modulus Penalty Criteria

In this study, a robust adaptive beamformer based on constant modulus (CM) criteria is developed to improve the robustness of the array beamforming, which is a reconstructing minimal optimization for solving the mismatch problem of weight vector caused by steering vector mismatch. In the global positioning system (GPS) L1 band, firstly, a GPS array signal is modelled by designing a dual-polarized antenna array. Secondly, the distortion problem of beamforming is formulated in the traditional minimum variance distortionless response (MVDR) beamformer. For repairing the weight vector mismatch problem, a novel beamformer based on the CM envelope response is proposed to reconstruct MVDR beamforming in the array processing. Besides, min-max penalty criteria are used to enable the beamformer to allocate more degrees of freedom (DOFs) when penalizing the MVDR beamformer responses. Finally, an auxiliary two-element real variable is designed to plan the proposed beamformer. But it is still a nonconvex quadratic programming problem, so an alternating direction method of multipliers (ADMM) is employed to transform the objective function into several subproblems. Illustrative numerical simulation results are provided for validating the effectiveness of the proposed beamformer by comparing it with other existing approaches.

A wavefront adaptive sensing beamformer for ocean acoustic waveguides.

This paper addresses robust adaptive beamforming for passive sonar in uncertain, shallow-water environments. Conventional beamforming is still common in passive sonar because adaptive beamformers suffer from signal mismatch in complex multipath environments. Existing approaches to robust adaptive beamforming try to model and account for the uncertainty in the beamformer's hypothesized signal subspace by using additional linear or quadratic constraints. Doing so, however, reduces the adaptivity of the beamformer and is prone to insufficiently suppressing interference. Instead, this paper uses blind source separation methods to adaptively estimate the complex spatial wavefronts of both targets and interference without requiring detailed physical modeling of the channel. By exploiting the different temporal spectra and/or frequency-selective multipath fading of targets and interference, this approach constructs a "signal-free" covariance matrix without imposing directional gain constraints. In doing so, the wavefront adaptive sensing (WAS) beamformer is able to separate targets from strong interference that is within the conventional beam width of the target. Simulation results in a realistic shallow-water channel are presented as well as results using the SWellEx96 S59 data with an injected target to show that the proposed WAS beamformer outperforms conventional and minimum variance adaptive beamformers in a shallow-water scenario.

New convex approaches to general MVDR robust adaptive beamforming problems

AbstractConsider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference‐plus‐noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction‐of‐arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double‐sided norm constraint, and a similarity constraint; as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution; otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal‐to‐interference‐plus‐noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only.