Capon Beamformer Research Articles

Generalized least squares beamforming of infrasound data

Generalized least squares (GLS) beamforming is a method for determining the direction of arrival and trace velocity of transient infrasound signals that may be otherwise obscured by persistent, correlated background noise, such as microbaroms. This method complements the adaptive F-detector by using an estimate of the noise background to form a generalized power ratio, which is used to estimate plane wave parameters (trace velocity and back-azimuth). Using a suite of fully synthetic signals, we first investigate the resolving power of the GLS estimator as a function of signal to noise ratio compared with a conventional, non-adaptive estimator. Fstatistic and plane wave parameter estimates will then be compared between GLS beamforming, conventional Bartlett beamforming, Capon beamforming, and the MUSIC algorithm. Recorded infrasonic signals from the Forensics Surface Experiment, where a persistent signal was observed from the south, will then be used to evaluate the GLS method. Initial analyses suggest that GLS beamforming results in a lower F-statistic during noise regions and a higher F-statistic value for transient signals compared to the Bartlett beam. Algorithmically determining an optimal window to characterize the background noise presents a significant challenge and different approaches will be discussed.

3-D Passive Cavitation Imaging Using Adaptive Beamforming and Matrix Array Transducer With Random Apodization.

With the development of promising cavitation-based treatments, the interest in cavitation monitoring with passive acoustic mapping (PAM) is significantly increasing. While most of studies regarding PAM are performed in 2-D, 3-D imaging modalities are getting more attention relying on either custom-made or commercial matrix probes. Unless specific phased-arrays are used for a specific application, limitations due to probe apertures often results in poor performances of the 3-D mapping, due to the use of a delay-and-sum (DAS) classic beamformer, which results in strong artifacts and large main lobe sizes. In this article, 3D-PAM is achieved by performing adaptive beamforming in the frequency domain (FD) in 3-D, and using a random sparse apodization of a commercial matrix array driving only 256 elements among the 1024 available. It reduces the computation time and makes use of only one 256-channel research platform. Three beamformers have been implemented in 3-D and in the FD: the DAS beamformer, which corresponds to the beamformer used in previous 3D-PAM studies, the robust capon beamformer (RCB), an adaptive algorithm widely used in 2D-PAM for its high performances, and the MidWay (MW) beamformer, an adaptive algorithm with a computation complexity equivalent to the one of DAS. These algorithms are evaluated both in simulations and experiments with a harmonic source at different positions, and are also applied to real cavitation signals. The results show that, in the case of matrix arrays of small aperture such as generic commercial matrix probes, the DAS beamformer leads to large main lobe sizes, while adaptive beamformers largely improve the performances of the mapping. The low computation time and its parameter-free character make MW beamformer a good compromise for 3D-PAM applications. It thus appears that a random sparse apodization combined with adaptive beamforming is a good solution to achieve high-performance 3D-PAM with manageable devices.

On the 2D Beampattern Optimization of Sparse Group-Constrained Robust Capon Beamforming with Conformal Arrays

To overcome the problems of the high sidelobe levels and low computational efficiency of traditional Capon-based beamformers in optimizing the two-dimensional (elevation–azimuth) beampatterns of conformal arrays, in this paper, we propose a robust Capon beamforming method with sparse group constraints that is solved using the alternating-direction method of multipliers (ADMM). A robustness constraint based on worst-case performance optimization (WCPO) is imposed on the standard Capon beamformer (SCB) and then the sparse group constraints are applied to reduce the sidelobe level. The constraints are two sparsity constraints: the group one and the individual one. The former was developed to exploit the sparsity between groups based on the fact that the sidelobe can be divided into several different groups according to spatial regions in two-dimensional beampatterns, rather than different individual points in one-dimensional (azimuth-only) beampatterns. The latter is considered to emphasize the sparsity within groups. To solve the optimization problem, we introduce the ADMM to obtain the closed-form solution iteratively, which requires less computational complexity than the existing methods, such as second-order cone programming (SOCP). Numerical examples show that the proposed method can achieve flexible sidelobe-level control, and it is still effective in the case of steering vector mismatch.

Low-Complexity DOA Estimation Method Based on Joined Coprime Array

In this article, the elimination of ambiguity of a joined coprime array has been examined, with a focus on such of its properties as large aperture size and complete degree of freedom (DOF). The existing methods suffer from a high degree of computation complexity due to the loss constant characteristic and high peak searching. Therefore, in this paper, a DOA estimation method for a jointed coprime array, characterized by a low degree of computational complexity, is proposed. The variance of the diagonal eigenvalues of the estimated covariance matrix is designed to enhance the accuracy of the covariance matrix of the joined coprime array. Then, the Capon beamforming methods is employed for peak searching. The simulation shows that the proposed method accomplishes accurate estimation with shorter computation times and fewer operations compared to other DOA estimation methods.

High-Resolution Stacking of Seismic Data With Fast Capon Beamforming

High-Resolution Stacking of Seismic Data With Fast Capon Beamforming

Doppler Ambiguity Suppression for Multichannel RoSAR Imaging With Doubly Constrained Robust Capon Beamformer

Doppler Ambiguity Suppression for Multichannel RoSAR Imaging With Doubly Constrained Robust Capon Beamformer

An Inverse Method Using Cross-Spectral Matrix Fitting for Passive Cavitation Imaging.

High-intensity focused ultrasound (HIFU) can produce cavitation, which requires monitoring for specific applications such as sonoporation, targeted drug delivery, or histotripsy. Passive acoustic mapping has been proposed in the literature as a method for monitoring cavitation, but it lacks spatial resolution, primarily in the axial direction, due to the absence of a time reference. This is a common issue with passive imaging compared to standard pulse-echo ultrasound. In order to improve the axial resolution, we propose an adaptation of the cross spectral matrix fitting (CMF) method for passive cavitation imaging, which is based on the resolution of an inverse problem with different regularizations that promote sparsity in the reconstructed cavitation maps: Elastic Net (CMF-ElNet) and sparse Total Variation (CMF-spTV). The results from both simulated and experimental data are presented and compared to state-of-the-art approaches, such as the frequential delay-and-sum (DAS) and the frequential robust capon beamformer (RCB). We show the interest of the method for improving the axial resolution, with an axial full width half maximum (FWHM) divided by 3 and 5 compared to RCB and DAS, respectively. Moreover, CMF-based methods improve contrast-to-noise ratio (CNR) by more than 15 dB in experimental conditions compared to RCB. We also show the advantage of the sparse Total Variation (spTV) prior over Elastic Net (ElNet) when dealing with cloud-shaped cavitation sources, that can be assumed as sparse grouped sources.

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.

Real-Time Passive Acoustic Mapping With Enhanced Spatial Resolution in Neuronavigation-Guided Focused Ultrasound for Blood-Brain Barrier Opening.

Passive acoustic mapping (PAM) provides the spatial information of acoustic energy emitted from microbubbles during focused ultrasound (FUS), which can be used for safety and efficacy monitoring of blood-brain barrier (BBB) opening. In our previous work with a neuronavigation-guided FUS system, only part of the cavitation signal could be monitored in real time due to the computational burden although full-burst analysis is required to detect transient and stochastic cavitation activity. In addition, the spatial resolution of PAM can be limited for a small-aperture receiving array transducer. For full-burst real-time PAM with enhanced resolution, we developed a parallel processing scheme for coherence-factor-based PAM (CF-PAM) and implemented it onto the neuronavigation-guided FUS system using a co-axial phased-array imaging transducer. Simulation and in-vitro human skull studies were conducted for the performance evaluation of the proposed method in terms of spatial resolution and processing speed. We also carried out real-time cavitation mapping during BBB opening in non-human primates (NHPs). CF-PAM with the proposed processing scheme provided better resolution than that of traditional time-exposure-acoustics PAM with a higher processing speed than that of eigenspace-based robust Capon beamformer, which facilitated the full-burst PAM with the integration time of 10 ms at a rate of 2 Hz. In vivo feasibility of PAM with the co-axial imaging transducer was also demonstrated in two NHPs, showing the advantages of using real-time B-mode and full-burst PAM for accurate targeting and safe treatment monitoring. This full-burst PAM with enhanced resolution will facilitate the clinical translation of online cavitation monitoring for safe and efficient BBB opening.

A novel adaptive beamforming scheme for array signal data processing

When the desired signal data exists in the array received data or the steering vector has a mismatch problem, the current traditional adaptive beamformers will suffer from the effect of the desired signal cancelation phenomenon, resulting in a sharp decline in performance. To address the occurrence of desired signal cancelation, an improved matrix projection-based efficient beamforming method is proposed. Firstly, based on spatial partitioning (SP) technology, a significant projection matrix for interference-plus-noise space (INS) is constructed. Secondly, using the constructed key projection matrix, the sample data covariance matrix is projected into the INS to achieve the goal of suppressing the desired signal data information. Finally, the weight data vector is calculated by Capon beamformer. The proposed algorithm does not require an iterative search for the optimal solution, which has the advantage of a small amount of calculation. Simulation experiments have verified that the proposed method has significant advantages in suppressing the desired data signals. Especially when the desired data signal has large power, the signal-to-interference-plus-noise ratio (SINR) of the proposed algorithm is better than that of the compared algorithms under the conditions of random directionality errors or local scattering errors between the desired signal and interference.

Fast Adaptive Beamforming for Weather Observations with Convolutional Neural Networks

Polarimetric phased array radar (PAR) can achieve high temporal resolutions for improved meteorological observations with digital beamforming (DBF). The Fourier method performs DBF deterministically, and produces antenna radiation patterns with fixed sidelobe levels and angular resolution by pre-computing the beamforming weights based on the geometry of receivers. In contrast, the Capon method performs DBF adaptively in response to the changing environment by computing the beamforming weights from the received signals at multiple channels. However, it becomes computationally expensive as the number of receivers grows. This paper presents computationally efficient adaptive beamforming with an application of convolutional neural networks, named ABCNN. ABCNN is trained with the phase and amplitude of complex-valued time-series IQ signals and the Capon beamforming weights as input and output. ABCNN is tested and evaluated using simulated time-series data from both point targets and weather scatterers for a planar of fully digital PAR architecture. The preliminary results show that ABCNN lowers computation time by a factor of three, compared to the Capon method, for a phased array antenna with 1024 elements, while mitigating the contamination from sidelobes by placing nulls at the location of the clutter. Furthermore, ABCNN produces antenna patterns similar to those from the Capon method, which shows that it has successfully learned the data.

Passive Cavitation Imaging Artifact Reduction Using Data-Adaptive Spatial Filtering.

Passive cavitation imaging (PCI) with a clinical diagnostic array results in poor axial localization of bubble activity due to the size of the point spread function (PSF). The objective of this study was to determine if data-adaptive spatial filtering improved PCI beamforming performance relative to standard frequency-domain delay, sum, and integrate (DSI) or robust Capon beamforming (RCB). The overall goal was to improve source localization and image quality without sacrificing computation time. Spatial filtering was achieved by applying a pixel-based mask to DSI- or RCB-beamformed images. The masks were derived from DSI, RCB, or phase or amplitude coherence factors (ACFs) using both receiver operating characteristic (ROC) and precision-recall (PR) curve analyses. Spatially filtered passive cavitation images were formed from cavitation emissions based on two simulated sources densities and four source distribution patterns mimicking cavitation emissions induced by an EkoSonic catheter. Beamforming performance was assessed via binary classifier metrics. The difference in sensitivity, specificity, and area under the ROC curve (AUROC) differed by no more than 11% across all algorithms for both source densities and all source patterns. The computational time required for each of the three spatially filtered DSIs was two orders of magnitude less than that required for time-domain RCB and thus this data-adaptive spatial filtering strategy for PCI beamforming is preferable given the similar binary classification performance.

Convolutional neural network for fast adaptive beamforming of phased array weather radar

PurposeThe purpose of this paper is to present a deep-learning-based beamforming method for phased array weather radars, especially whose antenna arrays are equipped with large number of elements, for fast and accurate detection of weather observations.Design/methodology/approachThe beamforming weights are computed by a convolutional neural network (CNN), which is trained with input–output pairs obtained from the Wiener solution.FindingsTo validate the robustness of the CNN-based beamformer, it is compared with the traditional beamforming methods, namely, Fourier (FR) beamforming and Capon beamforming. Moreover, the CNN is compared with a radial basis function neural network (RBFNN) which is a shallow type of neural network. It is shown that the CNN method has an excellent performance in radar signal simulations compared to the other methods. In addition to simulations, the robustness of the CNN beamformer is further validated by using real weather data collected by the phased array radar at Osaka University (PAR@OU) and compared to, besides the FR and RBFNN methods, the minimum mean square error beamforming method. It is shown that the CNN has the ability to rapidly and accurately detect the reflectivity of the PAR@OU with even less clutter level in comparison to the other methods.Originality/valueMotivated by the inherit advantages of the CNN, this paper proposes the development of a CNN-based approach to the beamforming of PAR using both simulated and real data. In this paper, the CNN is trained on the optimum weights of Wiener solution. In simulations, it is applied on a large 32 × 32 planar phased array antenna. Moreover, it is operated on real data collected by the PAR@OU.

PAM, not spam: Towards quantitative, reproducible, and energy-preserving cavitation imaging

Since the development of the original passive acoustic mapping (PAM) algorithm for cavitation imaging in 2008, which employed a conventional beamformer adapted from seismology (time exposure acoustics), sequential algorithmic improvements have sought to enhance spatial resolution, reduce computation time and enable increasingly setup-independent reporting of cavitation activity. These enhancements have included the use of frequency-domain rather than time-domain implementations to improve computational efficiency, the introduction of the Robust Capon Beamformer to reduce artefacts, sub-aperture processing to further increase frame rate and the implementation of corrections for frequency-dependent attenuation and for array sensitivity and diffraction to account for probe- and depth-related variability. Once these corrections are taken into account, current PAM algorithms produce accurate estimates of cavitation source strength at a single location, but not in the surrounding region, leading to inaccurate estimates of the total cavitation energy over the treatment volume. We present an energy-preserving and computationally efficient PAM algorithm based on Lucy-Richardson deconvolution, that enables the calculation of a set-up independent Cavitational Radiated Energy Density (CRED) that ensures cavitation images accurately reflect the total energy of radiated acoustic emissions within the imaging domain.

A comparison of robust capon beamformers using a large-scale microphone array for speech extraction

The Capon beamformer has been widely studied in narrowband applications and has already been extended to wideband signals, such as speech. For beamforming-based speech extraction applications, it is still a hot topic in improving the robustness and reducing the computational load, especially when the number of microphones is relatively large. This is because the Capon beamformer with more microphones becomes more sensitive to signal model errors and its computational complexity also increases dramatically. To improve the robustness, a variety of robust Capon beamformers have already been proposed for narrowband signals in recent years, while it lacks a comprehensive evaluation of these beamformers with a large-scale microphone array in noisy and reverberant environments for speech extraction. This paper focuses on evaluating some representative Capon beamformers by simulations and practical experiments. Besides, a low computational complexity robust Capon beamformer is proposed by integrating one-bit quantization and the Kronecker product into a complex generalized Gaussian distribution based maximum likelihood distortionless response beamformer. Simulation and experimental results show that robust Capon beamformers frequently outperform the standard Capon beamformer and traditional fixed beamformers in terms of both objective and subjective measures. It is also demonstrated that the newly proposed beamformer is more computationally efficient and outperforms other existing robust Capon beamformers.

A dual beam adaptive beamforming algorithm with sidelobe suppression

A new adaptive beamforming algorithm is developed not only to provide distortionless responses towards the two desired signals in the presence of interferences and noise but also to control the sidelobe level (SLL). The conventional standard Capon beamformer (SCB) deals with only one desired signal at a time and also offers much high SLL which can enhance unanticipated interferences. So, the conventional SCB is modified for incorporating two signals of interest (SOI) and a limited number of constraints are introduced for suppressing the SLL. Unity gain is maintained towards the second desired signal by employing an additional constraint in the conventional SCB. To control the SLL, a limited number of angles are sampled in the sidelobe region and the powers that correspond to these sampled angles are constrained to a specified level. The sampled angles are chosen from the particular sidelobe regions around the main beams and an empirical formula is given for determining the number of constraints. The resulting optimization problem is convex and solved by the CVX solver of Matlab to obtain the optimum weight vector. Finally, simulations are performed for various scenarios to evaluate the performance of the proposed algorithm. Simulation results illustrate that the proposed algorithm can receive two desired signals simultaneously and also becomes less vulnerable to unpredicted interferences in the vicinity of main beams as the SLL is minimized. The proposed algorithm achieves the maximum improvements of 20 dB and 16 dB in the SLL for two different scenarios as compared to the conventional algorithm. Moreover, the proposed algorithm preserves the SINR as that of SCB dual beam algorithm. In addition, the proposed algorithm can be used in medical imaging to resolve dual targets using two beams.

Adaptive Capon beamforming for lensless electron cyclotron emission imaging with high spatial resolution

Electron cyclotron emission (ECE) imaging diagnostics incorporating a lensless approach have been developed for measurements involving active spatial selectivity and direction-of-arrival estimation. The Capon method for adaptive-array analysis was proposed to improve the spatial resolution of the two-dimensional ECE imaging technique. Broadband noise source emissions were used to simulate the ECE to verify the practical effectiveness of the Capon method in the ECE imaging. Multiple noise source emission positions were properly estimated with a high spatial resolution using the Capon method.

Robust Adaptive Transmit Beamforming under the Constraint of Low Peak-to-Average Ratio.

In radar detection, in order to make the beam have variable directivity, a Capon beamformer is usually used. Although this traditional beamformer enjoys both high resolution and good interference suppression, it usually leads to high sidelobe and is sensitive to array steering vector (ASV) mismatch. To overcome such problems, this study devises a novel, robust adaptive beamformer that is robust to ASV mismatch under the constraint where the sidelobe is oriented to the ground. Moreover, to make full use of the transmit power, the constraint of a low peak-to-average power ratio (PAPR) is also taken into consideration. Accordingly, this robust adaptive beamformer is developed by optimizing a transmitting beamformer constrained by ASV mismatch and low PAPR. This optimization problem is transformed into a second-order cone programming (SOCP) problem which can be efficiently and exactly solved. The proposed transmit beamformer possesses not only adaptive interference rejection ability and robustness against ASV mismatch, but also direct sidelobe control and a low PAPR. Simulation results are presented to demonstrate the superiority of the proposed approach. The proposed method can make the peak sidelobe level (PSL) level on the ground side below −30 dB.

Simultaneous Monitoring of Multiple People’s Vital Sign Leveraging a Single Phased-MIMO Radar

Vital sign monitoring plays a critical role in tracking the physiological state of people and enabling various health-related applications (e.g., recommending a change of lifestyle, examining the risk of diseases). Traditional approaches rely on hospitalization or body-attached instruments, which are costly and intrusive. However, in recent years there is an emergence of contact-less vital sign monitoring techniques that rely on radio frequency signals. Early studies with continuous wave radars/WiFi devices have shown good success in detecting the vital signs of a single individual, while simultaneous monitoring of the vital signs of multiple, closely spaced subjects remains a challenge. In this paper, using an off-the-shelf Texas Instrument automotive FMCW radar, we design and implement a time-division multiplexing (TDM) phased-MIMO radar sensing system that allows high-precision vital sign monitoring of multiple subjects. The proposed sensing system can steer the beam towards the desired directions with a micro-second delay. The steerable beam enables capturing the vital signs of multiple individuals at the same radial distance to the radar. The proposed system enables the formation of a virtual array with aperture longer than that of the physical array. A Capon beamformer is used at the receiver side to combine the data collected from different transmit and receive antenna pairs corresponding to the virtual array. As all those pairs provide independent information about the targets, their combination significantly boosts the receiver signal-to-noise ratio. Based on the designed TDM phased-MIMO radar, we develop a system to automatically localize multiple human subjects and estimate their vital signs. Extensive evaluations show that under two-subject scenarios, our system can achieve more than 98.06% accuracy for breathing rate (BR) and more than 82.89% accuracy for heartbeat rate (HR) estimation, at a subject-to-radar distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1.6}\;m$</tex-math></inline-formula> when the targets are facing the radar. The minimal subject-to-subject angle separation is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$30^\circ $</tex-math></inline-formula> at a subject-to-radar distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1.6}\;m$</tex-math></inline-formula> , corresponding to a close distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{0.3}\;m$</tex-math></inline-formula> between two subjects, which outperforms the state-of-the-art.

A Robust Lamb Wave Imaging Approach to Plate-Like Structural Health Monitoring of Materials With Transducer Array Position Errors

The Lamb-wave-based damage imaging via beamforming techniques, which can visualize the location of damage in the structure intuitively, is one of the most promising methods in the field of structural health monitoring (SHM). However, transducer array position errors are inevitable in practical application, which may lead to serious degradation in imaging performance. In this study, it is shown that the uncertainty of the steering vectors led by the imprecise position of transducers in an array can be suppressed by the doubly constrained robust Capon beamformer (DCRCB). After the unwanted side lobes are restrained by the DCRCB-based coherence factor (CF) weighting, an effective adaptive beamforming damage imaging method robust to transducer position errors is proposed. The numerical simulation and imaging experiment of damage on an aluminum plate are carried out to verify the effectiveness of the proposed algorithm. The results show that the proposed Lamb wave damage imaging method performs better than the reported beamforming ones in literature in terms of resolution, contrast, and robustness to transducer position errors.