Conventional Adaptive Beamforming Research Articles

Ultrasonic adaptive plane wave high-resolution imaging based on convolutional neural network

Components with complex surfaces can pose a challenge for achieving phased array ultrasonic testing. Although coupling issues can be addressed by immersing or adding plexiglass wedges, obtaining high-quality images in a short time remains difficult under such conditions. This paper proposes an adaptive plane wave imaging scheme to address these challenges. First, the interface is reconstructed using a plane wave priority echo estimation method. Then, a beamforming algorithm adapted to the irregular interface is used to generate low-resolution (LR) images, which are then reconstructed into high-resolution (HR) images in a short time with convolutional neural network (CNN). The CNN is trained with simulation data, and the defects of test blocks and wheel rim are tested. Experimental results show that the reconstruction method combined with CNN significantly improves imaging quality and speed compared to the conventional adaptive plane wave beamforming algorithm based on the time-domain physical model.

Robust adaptive Bayesian beamforming against stationary and nonstationary interferences

In this work, we aim to enhance the robustness of conventional adaptive beamforming schemes against both signal steering vector uncertainties and interference nonstationarity here. For this purpose, a random model with Watson prior distribution is applied to the steering vector of interest, and cluster structured prior belief about the interferer motion is incorporated into the statistical analysis. However, the difficulty in handling the normalization factor of the Watson distribution makes the Bayesian inference of this probabilistic model prohibitive. Towards this end, an efficient algorithm using variational Bayesian expectation-maximization is proposed, by iteratively majorizing a lower bound on the variational free energy to refine the latent parameters and circumvent intractable moment computation. A specific beamformer encompasses a trade-off among accuracy, speed and ease of implementation is thus obtained. Further, an extension of the algorithm to the case of moving interferences is presented by assigning a Dirichlet process prior to the hidden parametric space. By doing so, the underlying time-aware clusters embedded in the interference-plus-noise vectors can be automatically revealed. Both simulated and experimental results validate the superiority of the algorithms over the existing algorithms.

Fast Wideband Beamforming Using Convolutional Neural Network

With the wideband beamforming approaches, the synthetic aperture radar (SAR) could achieve high azimuth resolution and wide swath. However, the performance of conventional adaptive wideband time-domain beamforming is severely affected as the received signal snapshots are insufficient for adaptive approaches. In this paper, a wideband beamformer using convolutional neural network (CNN) method, namely, frequency constraint wideband beamforming prediction network (WBPNet), is proposed to obtain a satisfactory performance in the circumstances of scanty snapshots. The proposed WBPNet successfully estimates the direction of arrival of interference with scanty snapshots and obtains the optimal weights with effectively null for the interference by utilizing the uniqueness of CNN to extract potential nonlinear features of input information. Meanwhile, the novel beamformer has an undistorted response to the wideband signal of interest. Compared with the conventional time-domain wideband beamforming algorithm, the proposed method can fast obtain adaptive weights because of using few snapshots. Moreover, the proposed WBPNet has a satisfactory performance on wideband beamforming with low computational complexity because it avoids the inverse operation of covariance matrix. Simulation results show the meliority and feasibility of the proposed approach.

URGLQ: An Efficient Covariance Matrix Reconstruction Method for Robust Adaptive Beamforming

The computational complexity of the conventional adaptive beamformer is relatively large, and the performance degrades significantly due to both the model mismatch errors and the unwanted signals in received data. In this paper, an efficient unwanted signal removal and Gauss-Legendre quadra-ture (URGLQ)-based covariance matrix reconstruction method is proposed. Different from the prior covariance matrix recon-struction methods, a projection matrix is constructed to remove the unwanted signal from the received data, which improves the reconstruction accuracy of the covariance matrix. Considering that the computational complexity of most matrix reconstruction algorithms are relatively large due to the integral operation, we proposed a Gauss-Legendre quadrature-based method to approximate the integral operation while maintaining the accu-racy. Moreover, to improve the robustness of the beamformer, the mismatch in the desired steering vector is corrected by maximizing the output power of the beamformer under a constraint that the corrected steering vector cannot converge to any interference steering vector. Simulation results and prototype experiment demonstrate that the performance of the proposed beamformer outperforms the compared methods and is much closer to the optimal beamformer in different scenarios.

Robust widely linear beamforming method for non-circular signals

Widely linear beamforming is known to outperform the conventional adaptive beamforming by fully employing the non-circularity of non-circular signals. In this paper, a robust widely linear beamformer (WLB) is proposed to achieve satisfactory output and robustness in low computational complexity. The augmented signal-of-interest (SOI) covariance matrix is built by performing integration over SOI angular sector. The principal eigenvector of the augmented SOI covariance matrix is taken as the SOI extended steering vector. The received signal vector is projected into the interference-plus-noise subspace to remove the SOI component and derive the augmented interference covariance matrix. The augmented noise covariance matrix is added to the derived augmented interference covariance matrix so that the augmented interference-plus-noise covariance matrix can be reconstructed. The proposed WLB possesses lower computational complexity than the state-of-the-art WLBs due to the avoidance of convex optimization programming. Numerical simulations illustrate the effectiveness of the proposed WLB.

Adaptive broadband frequency invariant beamforming using nulling-broadening and frequency constraints

The performance of conventional adaptive broadband beamforming algorithms is degraded because of rapidly moving interferences and look-direction errors. In this paper, a number of techniques are proposed to overcome this issue. By proposing an adaptive frequency invariant beamformer (FIB) that uses frequency constraints, we can obtain undistorted responses to broadband signal of interests (SOIs) and constant beamwidths over an entire frequency band without pre-steering delays. And the influence of look-direction errors can also be receded. Furthermore, a singular value decomposition of the frequency constraints is added to the proposed algorithm in view of releasing numerous degrees of freedom (DOFs), as this approach can simultaneously maintain the enhanced anti-interference performance and hold the undistorted response to SOIs. Finally, the nulling-broadening method involving the use of virtual interferences is adopted to construct a taper matrix and ensure robust performance versus rapidly moving interferences. This robust response to rapidly moving interferences and look-direction errors allows the proposed algorithm to achieve satisfactory broadband beamforming performance. Simulation results highlight the correctness and effectiveness of the proposed methods.

Image Quality Enhancement Using a Deep Neural Network for Plane Wave Medical Ultrasound Imaging.

Plane wave imaging (PWI), a typical ultrafast medical ultrasound imaging mode, adopts single plane wave emission without focusing to achieve a high frame rate. However, the imaging quality is severely degraded in comparison with the commonly used focused line scan mode. Conventional adaptive beamformers can improve imaging quality at the cost of additional computation. In this article, we propose to use a deep neural network (DNN) to enhance the performance of PWI while maintaining a high frame rate. In particular, the PWI response from a single point target is used as the network input, while the focused scan response from the same point serves as the desired output, which is the main contribution of this method. To evaluate the performance of the proposed method, simulations, phantom experiments and in vivo studies are conducted. The delay-and-sum (DAS), the coherence factor (CF), a previously proposed deep learning-based method and the DAS with focused scan are used for comparison. Numerical metrics, including the contrast ratio (CR), the contrast-to-noise ratio (CNR), and the speckle signal-to-noise ratio (sSNR), are used to quantify the performance. The results indicate that the proposed method can achieve superior resolution and contrast performance. Specifically, the proposed method performs better than the DAS in all metrics. Although the CF provides a higher CR, its CNR and sSNR are much lower than those of the proposed method. The overall performance is also better than that of the previous deep learning method and at the same level with focused scan performance. Additionally, in comparison with the DAS, the proposed method requires little additional computation, which ensures high temporal resolution. These results validate that the proposed method can achieve a high imaging quality while maintaining the high frame rate associated with PWI.

Maximum Likelihood Optimization of Adaptive Asynchronous Interference Mitigation Beamformer

In asynchronous (intermittent) interference scenarios, the content of co-channel interference sources over the data interval may be different from the interferers content over the training interval, typically with extra interference sources presented over the data interval. Under such conditions, conventional adaptive beamformer designed over the training interval may lose its efficiency when applied to the data interval. In this paper, we address the problem by 1) formulating a family of the second order statistics adaptive beamformers regularized by the covariance matrix estimated over the data interval; 2) proposing a maximum likelihood methodology for optimization of the combined (mixed) covariance matrix based on maximization of a product of a likelihood ratio that checks the accuracy of the recovered training signals and a likelihood ratio on equality of the eigenvalues in complementary to the signal subspace defined over the data interval; 3) demonstrating efficiency and robustness of the proposed solution as a linear adaptive beamformer and as an initialization for iterative beamformer with projections to the finite alphabet in different asynchronous interference scenarios comparing with the basic training and data based interference rejection combining receivers.

Robust adaptive beamforming with low sensitivity for mutual coupling based on auxiliary elements

The performance of the conventional adaptive beamformer undergoes degradation in the presence of the mutual coupling between the neighbouring elements. To eliminate the sensitivity for the MC, the dummy elements are fixed around the array. Here, the authors demonstrate the optimal layers of auxiliary elements for uniform rectangular array (URA) in the case of the specific MC model and give the concrete theoretical proof. The corresponding derivation proves that only one layer of auxiliary elements is needed to tackle with the MC effect, and the output SINR and beampattern are improved by means of the proposed method for URA. Finally, the simulation results have shown the effectiveness of authors’ method.

Low‐complexity robust adaptive beamforming method for MIMO radar based on covariance matrix estimation and steering vector mismatch correction

In this study, the authors consider a low-complexity robust adaptive beamforming problem in a collocated multiple-input multiple-output (MIMO) radar. This study is motivated by the fact that in practical applications, the conventional adaptive beamforming algorithm for MIMO radar requires a large computational complexity and suffers from a great performance degradation because of the finite number of training snapshots, the desired signal steering vector mismatch and the corruption of training data by the desired signal. Since the dimension of the virtual steering vector of the MIMO radar is relatively large, the proposed method can estimate the covariance matrix by using a low-complexity method to effectively improve the computational efficiency of the adaptive beamforming algorithm and the robustness of the beamformer against the covariance matrix uncertainty. Besides, based on the estimated covariance matrix, the proposed method can also correct the desired signal steering vector mismatch to efficiently prevent the desired signal cancellation phenomenon. Simulation results demonstrate that the performance of the proposed method is always close to that of the optimal processing in a wide range of signal-to-noise ratio or of the number of training snapshots.

A Robust Eigenanalysis Interference Canceler Using Sensitivity-Based Number of Sources Estimation

When the estimation of the number of sources is inaccurate and the expected signal is mixed in the training data, the conventional eigenanalysis interference canceler (EC) will result in the expected signal cancelation, which leads the performance of adaptive beamforming to be degraded significantly. In this paper, a robust eigenanalysis interference canceler (REC) algorithm is proposed to resolve this problem by using the minimum sensitivity-based number of sources estimation. In the proposed method, the number of sources is first pre-estimated by effectively using the minimum sensitivity function. Then, based on the eigenvalue decomposition of the array covariance matrix, the expected signal in the training data is determined and eliminated, so that the corresponding impact of the adaptive weight calculation can be avoided. Finally, the adaptive weight vector is obtained by orthogonally projecting the quiescent weight vector into the interference subspace. Simulation results show that the performance of the output signal-to-interference-plus-noise ratio (SINR) of the proposed algorithm has improved significantly when compared with the conventional adaptive beamforming methods.

Robust adaptive beamforming method for active sonar in single snapshot

Forming narrow beams is a useful way for active sonar to anti-reverberation when it works in the shallow water. High-resolution adaptive beamforming with the performance of narrow beamwidths and low sidelobe levels is a better and more efficient method, particularly in the scenario where the installation space for sonar array is limited, such as hull-mounted sonar. Due to the short duration of target echo signal in the complex and varying acoustic channel, conventional adaptive beamforming methods are invalid. Therefore, this paper proposes a robust adaptive beamforming method for active sonar in single snapshot, also called the steered dominant mode rejection (STDMR). Firstly, STDMR steered the sample covariance matrix (STCM) based on wide-band focusing, which the needed number of snapshots is greatly reduced. Secondly, by partial eigendecomposition, the large eigenvalues of the STCM which are greater than the noise energy and their eigenvectors are used for dominant mode rejection (DMR). DMR is a typical eigenspace-based algorithm which has small computational load and fast convergence speed. Finally, modified with the methods of diagonal loading of 3-5dB over the noise energy and signal mismatch protection, improved the robustness of this method. Simulation and experimental data analysis shows that the STDMR method achieves narrow beams and low-level sidelobes in single snapshot. Hence, the STDMR beamformer is an appropriate implementation to use for active sonar detection systems.

Regulated-Element Frost Beamformer for Vehicular Multimedia Sound Enhancement and Noise Reduction Applications

A key requirement of an adaptive sensor array involves the ability to deterministically adjust the directional response of the array to reduce noise and reverberations, null interferences, and enhance the gain and recognition of the desired signal. This paper presents a low-carbon adaptive broadband beamforming algorithm called the regulated-element Frost beamformer. It enhances the desired signal based on the noise conditions of the individual omnidirectional sensors deployed in a complex dynamic environment that is prone to steering errors. The investigation of this algorithm was carried out in an interference-dominant, noisy automobile environment characterized by diffuse noise conditions. An embedded system measurement of real-time signals was carried out using omnidirectional acoustic sensors mounted in a model convertible F-Type car driven at speed limits of 20 to 50 mph. The simulation results indicate an array gain enhancement of 2 dB higher than the conventional Frost beamformer and it requires less sensors and filter taps for real-time reconfigurable implementations. The experimental results reveal that the average array gain of the regulated-element beamformer is 2.9 dB higher than the conventional Frost beamformer response. The minimum floor array gain of the regulated-element beamformer is 5 dB, representing 70% noise reduction than the conventional adaptive beamformers.

Frequency diverse array and MIMO hybrid radar transmitter design via Cramér–Rao lower bound minimisation

Frequency diverse array (FDA) produces a range–angle-dependent transmit beampattern and offers a potential solution to localise targets in two dimensions with respect to slant range and azimuth angle. However, it is difficult to unambiguously estimate the target location information by a standard FDA radar via conventional adaptive beamforming due to its coupling range–angle response. In this study, the authors propose two FDA and multiple-input multiple-output (MIMO) hybrid radar transmitter design schemes by minimising the Cramer–Rao lower bound (CRLB) for range-dependent target localisation, namely, FDA–MIMO radar and transmit subarray FDA–MIMO (TS-FDA) radar. The former uses a small frequency increment across the MIMO antennas, whereas the latter divides the FDA elements into multiple subarrays using the same waveform within each subarray and orthogonal waveforms in distinct subarrays. The formulated CRLB minimisation problem is solved by convex optimisation. Furthermore, the targets are localised using the beamspace-based multiple signal classification algorithm. The designed FDA–MIMO and TS-FDA radars are evaluated by comparing their mean square error and cumulative distribution function performance.

Iterative Robust Capon Beamforming with Adaptively Updated Array Steering Vector Mismatch Levels.

The performance of the conventional adaptive beamformer is sensitive to the array steering vector (ASV) mismatch. And the output signal-to interference and noise ratio (SINR) suffers deterioration, especially in the presence of large direction of arrival (DOA) error. To improve the robustness of traditional approach, we propose a new approach to iteratively search the ASV of the desired signal based on the robust capon beamformer (RCB) with adaptively updated uncertainty levels, which are derived in the form of quadratically constrained quadratic programming (QCQP) problem based on the subspace projection theory. The estimated levels in this iterative beamformer present the trend of decreasing. Additionally, other array imperfections also degrade the performance of beamformer in practice. To cover several kinds of mismatches together, the adaptive flat ellipsoid models are introduced in our method as tight as possible. In the simulations, our beamformer is compared with other methods and its excellent performance is demonstrated via the numerical examples.

Wideband beamforming for multipath signals based on frequency invariant transformation

It is well known that the performance of conventional adaptive beamformers degrades severely due to the presence of coherent or correlated interferences (multipath propagation) and various techniques have been developed to improve the performance of the beamformer. However, most of the work in the past has been focused on the narrowband case. In this paper, the wideband beamforming problem in the presence of multipath signals is addressed, with a novel approach proposed by employing a pre-processing stage based on the frequency invariant beamforming (FIB) technique. In this approach, the received wideband array signals are first processed by an FIB network, and then a traditional narrowband adaptive beamformer or an appropriate instantaneous blind source separation (BSS) algorithm can be applied to the network outputs. It is shown that with the proposed structure, cancellation of the desired signal is reduced, leading to a significantly improved output signal to interference plus noise ratio (SINR).

Robust adaptive beamforming based on convex optimization

Adaptive beamforming is an efficient way of spatial filtering in the presence of interference and noise. However, the conventional adaptive beamforming, e.g., MVDR, may degrade significantly due to the poorly estimated covariance matrix or steering vector errors. Convex optimization has now emerged as a major signal processing tool and made a significant impact on numerous problems because of its foundational nature and potential ability in signal processing. Thus in this paper, several robust adaptive beamforming algorithms based on the convex optimization are presented and evaluated, where a novel mathematical tool called “Yalmip” is used to solve the second-order cone problem in these algorithms. Numerical simulations and comparison show that these robust adaptive beamforming algorithms still approach robust to the above-mentioned problems.

Robust Adaptive Microphone Array with Mainlobe and Response Ripple Control

Many existing adaptive beamformers possess robustness against arbitrary array steering vector (ASV) mismatches within presumed uncertainty set. However, when the array facing a large steering direction error, their performance degrade significantly since the uncertainty in steering direction generally gives rise to an outstanding mismatch in ASV. In the applications of microphone array, large steering direction error is often unavoidable because of the motion of target speaker. Meanwhile, in addition to conventional adaptive beamformers, microphone array also requests a controlled frequency response to target signal. In this paper, we propose a new adaptive microphone array implemented in frequency domain with controlled mainlobe and frequency response. A compact ASV uncertainty set explicitly modelling steering direction error and the other arbitrary ASV errors is exploited to derive beamformer with robust constraints on array magnitude response. Numerical results show that the proposed microphone array not only produces large controlled robust response region and robust frequency response, but also achieves high performance in SINR enhancement.

Performance Evaluation of Hexagonal Array Adaptive Beamforming Algorithm Based on Inverse QR-RLS for Active Sonar Application

In shallow water areas, to enhance underwater targets detection performance improve computation efficiency of active sonar, a computationally efficient adaptive beamformer (spatial filter) based on inverse QR (IQR) and recursive least-squares (RLS) is developed under fast Fourier transform framework, for standard hexagonal receiving array implementation. The IQR-RLS algorithm has good numerical stability and can be mapped onto coordinate rotation digital computer processor-based systolic arrays, which is suitable for real time applications. Using the proposed scheme to construct beamformer, which reduces computational complexity significantly and offers better converge rate than conventional adaptive beamformer. The simulation and lake test results demonstrates the algorithm improves interference (reverberation) suppression ability. It improves SNR about 2dB of still bottom target detection in reverberation limited area.

Robust beamforming methods for multipath signal reception

Novel robust beamforming algorithms are proposed to avoid signal cancellation in a multipath environment. The robustness is achieved by forcing the array responses to the signal of interest and its multipath signals in the pre-estimated clusters to be no less than unity while minimising the output power. Since the array responses to all the multipath signals are constrained, they will not cancel the signal of interest completely as in the conventional adaptive beamforming methods. The effectiveness of the proposed algorithms is verified by computer simulations.