Robust Capon Beamformer Research Articles

Reduced-dimension robust capon beamforming using Krylov-subspace techniques

We present low-complexity, quickly converging robust adaptive beamformers, for beamforming large arrays in snapshot deficient scenarios. The proposed algorithms are derived by combining data-dependent Krylov-subspace-based dimensionality reduction, using the Powers-of-R or conjugate gradient (CG) techniques, with ellipsoidal uncertainty set based robust Capon beamformer methods. Further, we provide a detailed computational complexity analysis and consider the efficient implementation of automatic, online dimension-selection rules. We illustrate the benefits of the proposed approaches using simulated data.

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.

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.

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.

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.

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.

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.

Wideband Robust Capon Beamforming for Passive Sonar

In passive sonar, narrowband adaptive beamforming techniques can be exploited to increase the signal-to-interference-plus-noise ratio (SINR), providing that array steering vector (ASV) errors and cross-spectral density matrix (CSDM) estimation errors can be controlled. When beamforming large aperture, many-element arrays in dynamic scenarios, the number of stationary snapshots available for CSDM estimation can be small compared to the number of array elements, leading to the problem of snapshot deficiency. Furthermore, common narrowband approaches become computationally prohibitive for large bandwidths. Here, we exploit the wideband nature of passive sonar signals to alleviate snapshot deficiency and reduce computational complexity. Narrowband robust Capon beamformers (RCBs), which exploit ellipsoidal ASV uncertainty sets to maintain high SINR, are extended to the wideband problem via the steered covariance matrix (STCM) method, yielding wideband RCBs (WBRCBs). To further reduce computational complexity and speed up algorithm convergence, subarray techniques are also incorporated, yielding wideband subarray RCBs (WBSARCBs). These algorithms, which are applicable to arbitrary array geometries, are evaluated using simulated and experimental passive sonar data.

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.

Robust Capon-based direction-of-arrival estimators in partly calibrated sensor array

In this paper a problem of direction-of-arrival (DOA) estimation in partly calibrated sensor arrays is considered. It is assumed that a sensor array consists of subarrays with full inner calibration and unknown intersubarray distortions. Capon-based methods are proposed for DOA estimation as suitable techniques have robustness to intersubarray distortions. These methods are an extension of robust Capon beamformer developed for partly calibrated array to the DOA estimation. The simulations validate efficiency of the proposed algorithms.

Automatic computation of diagonal loading factor for robust adaptive beamforming based on Gaussian distribution

One of the most well-known robust adaptive beamforming techniques is diagonal loading (DL). The main drawback of this approach is that the loading factor is hard to be reliably determined. Recently, the general linear combination (GLC)-based robust Capon beamformer is presented to fully automatically determine the loading factor only from the given data. In this paper, we propose an enhanced GLC-based beamforming technique based on the Gaussian assumption. It provides an analytic solution of the loading factor, which can be calculated more efficiently. The simulations show that it decreases the computational load without the degradation of performance.

Robust Capon beamforming in presence of large DOA mismatch

In the presence of significant direction-of-arrival (DOA) mismatch, a robust Capon beamforming approach is proposed. The basic idea of the proposed method is first to estimate a set of the desired steering vectors corresponding to DOAs coming from a DOA uncertainty region by using the uncertainty set based approach, then a Bayesian approach is employed to obtain the weight vector.

Beam Width Performance of the Adaptive Beam Former Based on Pseudo-Interference Technique

In this paper, we examine the beam width performance of the recently addressed robust Capon beam formers. This adaptive array employs the estimated steering vector, injected noise, and pseudo-interference to provide robustness against direction mismatch. With the generalized side lobe canceller (GSC) as the underlying structure, we first derive the effect of angular mismatch on the estimated interference correlation matrix. Then, a simple approximate expression is presented for output signal-to-interference-plus-noise-ratio (SINR) of this new beam former. Based on this expression, the angular beam width of this robust beam former is investigated. Simulation results verify the analytically predicted performance.

Robust Capon beamformer based on direction search

In the presence of pointing errors, a direction search based robust Capon beamformer is proposed. The direction of the desired signal is first estimated by searching for the local maximum of the array output power using the first-order Taylor series expansion of the array steering vector, and then the robust Capon beamformer is developed with the estimated direction as the presumed one.

Linearly Constrained Robust Capon Beamforming

In this paper, a novel linearly constrained robust Capon beamformer (LCRCB) framework is proposed. In the LCRCB, linear constraints can be used, e.g., for beampattern control and ellipsoidal array steering vector sets can be exploited, using robust Capon beamforming techniques, e.g., to allow for arbitrary array steering vector errors, such as those arising from calibration errors. The LCRCB is applicable to arbitrary array geometries and can be computed efficiently. For the limiting case that the ellipsoid is a point, we show that the LCRCB coincides with a linearly constrained minimum variance beamformer. To show the utility of the LCRCB, mainbeam and null-pattern control examples are included.

Robust and Automatic Data-Adaptive Beamforming for Multidimensional Arrays

The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, for example, by calibration and/or angle-of-arrival (AOA) errors, which would, otherwise, seriously degrade the performance of an adaptive beamformer. Here, we examine robust Capon beamforming of multidimensional arrays, where robustness to AOA errors is needed in both azimuth and elevation. It is shown that the commonly used spherical uncertainty sets are unable to control robustness in each of these directions independently. Here, we instead propose the use of flat ellipsoidal sets to control the AOA uncertainty. To also allow for other errors, such as calibration errors, we combine these flat ellipsoids with a higher dimension error ellipsoid. Computationally efficient automatic techniques for estimating the necessary uncertainty sets are derived, and the proposed methods are evaluated using both simulated data and experimental underwater acoustic measurements, clearly showing the benefits of the technique.