Capon Beamformer Research Articles

Fully automatic robust adaptive beamforming using the constant modulus feature

The diagonal loading (DL) technique is the most widely used method to improve the robustness of the Capon beamformer in the presence of imprecise knowledge of the covariance matrix and the desired signal's steering vector. The selection of the DL level is challenging in practice and might depend on some user-defined parameters which are possibly hard to be determined. A fully automatic and training-free method for the DL level selection is herein presented to extract the desired signal with constant modulus, which is a common feature for communication signals. Simulated results of the beamforming performance have demonstrated the efficacy of the proposed method.

Passive acoustic mapping of stable and inertial cavitation during ultrasound therapy

Accurate spatio-temporal characterization, quantification, and control of the type and extent of cavitation activity is crucial for a wide range of therapeutic ultrasound applications, ranging from ablation to sonothrombolysis, opening of the blood-brain barrier and drug delivery for cancer. Passive Acoustic Mapping (PAM) is a technique that utilizes arrays of acoustic detectors, typically coaxially aligned or coincident with the therapeutic elements, to receive acoustic emissions outside the main frequency band of the therapy pulse. The signals received by each detector are then filtered in the frequency domain into harmonics and ultra/subharmonics of the fundamental therapeutic frequency and other broadband components, and subsequently beamformed using a multi-correlation algorithm, which uses measures of similarity between the signals rather than time-of-flight information in order to map sources of non-linear emissions in real time. 2D and 3D cavitation maps obtained using time exposure acoustics beamforming will be presented, and juxtaposed to the greater spatial resolution but increased computational complexity afforded by more advanced algorithms such as the Robust Capon Beamformer (RCB). The spatial correlation between cavitation maps produced using PAM and the associated therapeutic effect will also be discussed in the context of cavitaion-enhanced ablation and drug delivery.

Improved performance over time of integration in momentum flux estimation using Postset Beam Steering technique

Using time series of vertical data collected from middle and upper atmospheric (MU) radar, the adaptive Capon beamforming technique is used to synthesize beams in the desired pointing directions within the radar beamwidth. Beam synthesis has been performed at the tilt angle of 1.5° with different beam configurations (4 beams, 8 beams, 16 beams, 32 beams, 48 beams and 64 beams), which are equally separated azimuth plane. The Power Spectral Density (PSD) is obtained from the synthesized beam using the eigenvector (EV) sub-space based spectral estimation method. The first moment is derived from the EV produced spectrum using the adaptive moment estimation method. From the first order moments derived along equally spaced pointing directions, radial wind velocities are readily obtained in the corresponding directions. From radial velocity obtained in various pointing directions, momentum flux of short duration (<2h) is estimated using the symmetric beam method (SBM) which requires 4 symmetric beams separated by 90° in the azimuth plane. A comparative study has been performed to study the optimum beam configuration, required for the flux estimation, which shows that 32 beam configuration is sufficient to estimate the flux with least error. Study with 32 beam configuration, gives 8 sets of symmetric beams (8×4). Using 8 set of beams, the flux is estimated for each set of beams and averaged. The averaged flux is further integrated over different lengths of time up to 14h. This systematic method for the estimation of momentum flux reveals that spatial averaging of beams in azimuth and integration over different lengths of time have reduced the time of integration from 15 to 16h for the conventional approach to 8–9h for the new approach using Postset Beam Steering (PBS) technique. The flux estimated with spatial-averaging of beam using PBS technique has been compared with other standard methods.

Norm-Constrained Capon Beamforming Using Multirank Signal Models With Kalman Filter Implementation

The performance of the Capon beamforming is known to degrade dramatically in the presence of model mismatches, especially when the desired signal is present in the training data. To improve the robustness, the diagonal loading technique was introduced. However, the major drawback is the selection of the diagonal loading level, which is related to the unknown signal powers. Another way to alleviate performance degradation is to use a more accurate signal model of the array response. In this paper, a norm-constrained Capon beamforming using multirank signal models is proposed. Based on the pseudo-observation method, the quadratic constraints can be easily constructed. The problem is solved by a nonlinear Kalman filter which can be implemented on-line. The simulation results show that the design of the norm-constraint value is less sensitive to the signal powers, small angle mismatches, and number of sensors with a standard linear array. Further, it is shown that the use of a multirank signal model and Kalman filter technique result in less self-cancellation and performance degradation than that of the rank-1 signal model and the estimation of sample matrix.

Capon beamforming and moving objects--an analysis of lateral shift-invariance.

If an ultrasound imaging system provides a presentation of a moving object which is sensitive to small spatial shifts, the system is said to be locally spatially shift-variant. This can happen, for instance, if the axial or lateral sampling is insufficient. The Capon beamformer has been shown to provide increased lateral resolution in ultrasound images. Increased lateral resolution should demand denser lateral sampling. However, in previous literature on Capon beamforming for medical ultrasound imaging, only single-frame scenarios have been simulated. Temporal behavior and effects caused by the increased resolution and lack of oversampling have therefore been neglected. In this paper, we analyze the local lateral shift-invariance of the Capon beamformer when imaging moving objects. We show that insufficient lateral sampling makes an imaging system based on the Capon beamformer laterally shift-variant. Different methods for oversampling on transmit and receive are then discussed and investigated to improve on the Capon beamformer. It is shown that lateral shift-invariance can be improved by oversampling based on phase rotation on receive without affecting the acquisition frame rate and with a minor change in processing complexity.

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal׳s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs.

Robust Capon beamforming exploiting the second-order noncircularity of signals

This paper extends the worst-case performance optimization based robust Capon beamformer (RCB) to the generalized case with possible noncircular signal-of-interest (SOI) and/or noncircular interferences. The proposed widely linear (WL) beamformer exploits the second-order noncircularity of the SOI and interferences simultaneously, and it is robust against the errors in the steering vector, sample covariance matrix and estimated noncircularity coefficient of the SOI. Further, a theoretical performance analysis for the class of WL beamformers using generalized loading in the presence of steering vector errors is presented. The superior performance of the proposed beamformer over the RCB is demonstrated by the theoretical results and various numerical experiments.

Estimation and Comparison of Horizontal Winds Using Various Spectral Estimation Methods on Profiler Radars

Abstract The lower atmospheric wind profiles are obtained by the postset beam steering (PBS) technique on middle and upper (MU) atmosphere radar data. The Capon beamformer is used to improve the beam synthesizing in the desired directions within the radar transmit beamwidth. From a synthesized beam, the power spectrum is obtained by various spectral estimators, such as Fourier, multiple signal classification (MUSIC), and eigenvector (EV). The wind vector components are derived from radial velocities estimated from the power spectra of synthesized beams. As the reliability of the PBS wind estimate depends on the choice of spectral estimators, a detailed analysis is carried out to compare the performance of estimators in deriving wind profiles on the radar data. The results suggest that EV shows a better performance in deriving possible spectrum parameters and is useful for reliable wind profiling up to the lower stratosphere. The wind profiles derived by PBS with EV are more consistent with near-time observations using GPS sonde and Doppler beam swinging (DBS) methods. The study also suggests that MUSIC cannot be used to reliably estimate atmospheric spectrum parameters.

Application of Manifold Separation to Polarimetric Capon Beamformer and Source Tracking

Two adaptive Capon methods that jointly estimate the azimuth-angle and polarization of the sources in a closed-form are proposed. It is shown that the azimuth-angles of the sources may be estimated from the roots of a complex-valued polynomial or by rooting a real-valued polynomial, instead. The latter method is particularly useful in tracking arbitrarily polarized sources in a sequential snapshot-by-snapshot manner using root-tracking techniques. The proposed polynomial rooting based methods are applicable to polarization sensitive arrays regardless of the array geometry including conformal arrays, and take into account array nonidealities. A large-sample analysis of the polarimetric Capon method is also provided showing that it converges, up to a multiplicative factor that depends on the interference-plus-noise power, to the polarimetric MUSIC method in the high SINR regime. Such a result gives a new insight into the well-known Capon and MUSIC methods. This paper also shows that employing manifold separation in robust Capon beamforming as well as in transmit beamforming schemes leads to improved performance in terms of received SINR when array calibration measurements are used. Extensive numerical results employing real-world polarimetric arrays are given. Results show that employing manifold separation leads to improved performance in many array processing tasks.

Implementing capon beamforming on a GPU for real-time cardiac ultrasound imaging

Capon beamforming is associated with a high computational complexity, which limits its use as a real-time method in many applications. In this paper, we present an implementation of the Capon beamformer that exhibits realtime performance when applied in a typical cardiac ultrasound imaging setting. To achieve this performance, we make use of the parallel processing power found in modern graphics processing units (GPUs), combined with beamspace processing to reduce the computational complexity as the number of array elements increases. For a three-dimensional beamspace, we show that processing rates supporting real-time cardiac ultrasound imaging are possible, meaning that images can be processed faster than the image acquisition rate for a wide range of parameters. Image quality is investigated in an in vivo cardiac data set. These results show that Capon beamforming is feasible for cardiac ultrasound imaging, providing images with improved lateral resolution both in element-space and beamspace.

A new robust adaptive beamforming and the one-dimensional search strategy

Adaptive beamforming methods will be degraded sharply in the presence of steering vector errors. The design methods of robust adaptive beamforming become more flexible when the convex optimization technique is used. However, this leads to high computational-complexity and more difficulties for engineering applications. To solve these problems, a robust adaptive beamforming based on the least square estimation is proposed, and a laconic solution method using one-dimensional search is derived. The standard Capon beamformer (SCB) is converted to a robust least-square problem based on the principle of generalized sidelobe canceller, and is then changed into a problem of second-order program. In order to reduce the amount of computation, a one-dimensional search method is deduced using the relationship between the primal and dual problems of second-order program, and Newton iteration method is adopted to obtain the optimal solution. The computational complexity of the proposed algorithm is in the same order of magnitude as that of the SCB. Simulation results demonstrate the robustness of the proposed algorithm in the case of steering vector mismatch and snapshot deficiency.

Ultra-wideband microwave robust Capon beamforming imaging system for early breast cancer detection

An ultra-wideband (UWB) microwave robust Capon beamforming imaging system is presented based on a self-designed compact UWB antenna for early breast cancer detection. Simulation results show that the proposed detection system is sensitive to tumor response. Simulated tumor detection experiments are carried out in both simple planar breast model and magnetic resonance imagining (MRI)-derived model using the antenna array. Robust Capon beamforming algorithm is employed to reconstruct the breast image. Successful detection of 3-mm-diameter tumor is achieved in the planar model and the same detection result of 4-mm-diameter tumor is achieved in the MRI-derived model. The right information of the tumor can be obtained from the imaging results, which demonstrates the feasibility of the proposed system in early breast cancer detection.

IMPROVED BEAMFORMING ALGORITHM FOR IMAGING RECONSTRUCTION FOR EARLY BREAST CANCER DETECTION BY UWB

Ultra-wide band (UWB) microwave imaging is a promising method for the breast cancer detection based on the large contrast of electric parameters between the malignant tumor and its surrounded normal organisms. In this paper, a two-dimensional model of the breast organisms is numerically carried by the finite difference time domain (FDTD) method. The dispersion characteristics of the breast media are taken into account by single pole Debye model to approach the actual properties of the breast organism. In this method, a tumor is assumed in the model with two cases. The standard Capon beamforming (SCB) and doubly constrained robust Capon beamforming (DCRCB) algorithm performed to reconstruct the image is described in detail. The tumor can be detected and localized using the proposed algorithm and the result demonstrates a good stability of DCRCB algorithm.

Interference covariance matrix reconstruction via steering vectors estimation for robust adaptive beamforming

In the presence of steering vector model mismatches, a novel robust adaptive beamformer is proposed based on interference-plus-noise covariance matrix reconstruction. An interference region is first selected according to the coarsely estimated desired signal direction, and then the interference steering vectors are estimated with the robust Capon beamformer. Finally, the interference-plus-noise covariance matrix is reconstructed by integrating the Capon spatial spectrum over the interference region by using the estimated steering vectors.

Pseudo-Interference Technique for Reducing the Mutual Coupling Effects in Adaptive Beamformers

A robust beamformer with pseudo-interference approach for reducing the effect of mutual coupling is present in this paper. This technique uses injected interference to improve the equivalent interference-to-noise ratio in the diagonally loaded Capon beamformer. The mutual coupling coefficients are estimated for interference correlation matrix reconstruction. The resulted beamformer is insensitive to the mutual coupling effects and angular mismatch.

A double constrained robust capon beamforming based imaging method for early breast cancer detection

Ultra-wideband (UWB) microwave images are proposed for detecting small malignant breast tumors based on the large contrast of electric parameters between a malignant tumor and normal breast tissue. In this study, an antenna array composed of 9 antennas is applied to the detection. The double constrained robust capon beamforming (DCRCB) algorithm is used for reconstructing the breast image due to its better stability and high signal-to-interference-plus-noise ratio (SINR). The successful detection of a tumor of 2 mm in diameter shown in the reconstruction demonstrates the robustness of the DCRCB beamforming algorithm. This study verifies the feasibility of detecting small breast tumors by using the DCRCB imaging algorithm.

Robust Adaptive Beamforming Applied to Planar Array

Capon beamforming has better resolution and interference rejection capability. However, its performance will seriously degrade due to noise, array steering vector error, and other factors. In this paper, a robust Capon beamforming applied to a planar array is described. It is shown that the proposed method is the natural extension of the original Vector Optimization Robust Beamforming algorithm to the case of a planar array, and can be reformulated as a convex second-order cone program and solved by SEDUMI. Computer simulation has shown that the proposed method has better performance than other conventional methods, such as narrower main lobe and lower side lobe.

A class of diagonally loaded robust Capon beamformers for noncircular signals of interest

Diagonal loading is a simple and effective method for robustness enhancement of the Capon beamformer against perturbation in the presumed steering vector of the signal-of-interest (SOI). However, the determination of an appropriate diagonal loading level is not a trivial task. Three noncircularity restoral based methods are herein proposed for selecting the diagonal loading level to recover a noncircular SOI buried in circular and/or noncircular interferences plus circular background noise. Monte Carlo simulations are performed to verify the efficacy of the proposed methods.

Application of the alternating projection strategy to the Capon beamforming and the MUSIC algorithm for azimuth/elevation AOA estimation

In this paper, the alternating projection (AP) scheme is applied to get the initial and the final estimates of the Capon beamforming algorithm and the MUSIC algorithm. In a previous paper, the AP scheme has been proposed as a computationally efficient method for the initialization and optimization of the cost function for the ML-based angle of arrival (AOA) estimation problem. We call the AP scheme in the previous paper the brute-force AP strategy. To improve the brute-force AP, we suggest the Newton AP which consists of the successive one-dimensional Newton search. The brute-force AP can be used for the initialization and the optimization of the cost function of AOA estimation, and the Newton AP can be used for the optimization of the cost function for the AOA problem. We compare the performance of the AP-based approach with the conventional implementation of the AOA estimation algorithm using two-dimensional brute-force search.

Maximally Robust Capon Beamformer

The standard Capon beamformer (SCB) achieves the maximum output signal-to-interference-plus-noise ratio in the error-free case. However, estimation errors of the signal steering vector and the array covariance matrix can result in severe performance deteriorations of the SCB, especially if the training data contains the desired signal component. A popular technique to improve the robustness against model errors is to compute the Capon beamformer with the maximum output power, considering an uncertainty set for the signal steering vector. However, maximizing the total beamformer output power may result in an insufficient suppression of interferers and noise. As an alternative approach to mitigate the detrimental effect of model errors, we propose to compute the Capon beamformer with the minimum sensitivity, considering the uncertainty set for the signal steering vector. The proposed maximally robust Capon beamformer (MRCB) is at least as robust as the maximum output power Capon beamformer with the same uncertainty set for the signal steering vector. We show that the MRCB can be implemented efficiently using Lagrange duality. Simulation results demonstrate that the MRCB outperforms state-of-the-art robust adaptive beamformers in many scenarios.