Standard Capon Beamformer Research Articles

Review of user parameter-free robust adaptive beamforming algorithms

This paper provides a comprehensive review of user parameter-free robust adaptive beamforming algorithms. We present the ridge regression Capon beamformers (RRCBs), the mid-way (MW) algorithm, and the convex combination (CC) as well as the general linear combination (GLC) approaches. The purpose of these methods is to mitigate the effect of small sample size and steering vector errors on the standard Capon beamformer (SCB). We also present sparsity based iterative beamforming algorithms, namely the iterative adaptive approach (IAA), maximum likelihood based IAA (referred to as IAA-ML) and M-SBL (multi-snapshot sparse Bayesian learning), which exploit sparsity to estimate the signal parameters. We provide a thorough evaluation of these beamforming methods in terms of power and spatial spectrum estimation accuracies, output signal-to-interference-plus-noise ratio (SINR) and resolution under various scenarios including coherent, non-coherent and distributed sources, steering vector mismatches, snapshot limitations and low signal-to-noise ratio (SNR) levels. Furthermore, we discuss the computational complexities of the algorithms and provide insights into which algorithm is the best choice under which circumstances.

Non-sensitive adaptive beamforming against mutual coupling

The standard Capon beamformer (SCB) is known to suffer from severe performance degradation when there is a mismatch between the presumed signal steering vector and the actual one. There may be several reasons leading to this result such as mutual coupling between array elements. The problem of adaptive beamforming in the presence of mutual coupling is studied based on a uniform linear array (ULA). By setting a group of auxiliary elements on each side of the ULA, the authors prove that the proposed method can inherently compensate the effect caused by the mutual coupling and greatly decrease the sensitivity of the SCB against mutual coupling. This technique can also be applied to most of the existing robust beamforming methods to further improve their performances. Theoretical analysis and simulation results demonstrate the robustness and effectiveness of this technique.

Knowledge-aided adaptive beamforming

In array processing, when the available snapshot number is comparable with or even smaller than the sensor number, the sample covariance matrix R̂ is a poor estimate of the true covariance matrix R. To estimate R more accurately, prior environmental knowledge can be used, which is manifested as knowing an a priori covariance matrix R0. In practice, R0 usually represents prior knowledge on dominant sources or interferences. Since the noise power level is unknown, and thus cannot be included into the a priori covariance matrix, R0 is often rank deficient. Both modified general linear combinations (MGLC) and modified convex combinations (MCC) of the a priori covariance matrix R0, the sample covariance matrix R̂ and an identity matrix I to obtain an enhanced estimate of R, denoted as R̃ are considered. Both MGLC and MCC can choose the combination weights fully automatically. Moreover, both the MGLC and MCC methods can be extended to deal with linear combinations of an arbitrary number of positive semi-definite matrices. Both approaches can be formulated as convex optimisation problems that can be solved efficiently to obtain globally optimal solutions. Numerical examples are provided to demonstrate the type of achievable performance by using R̃ instead of R̂ in the standard Capon beamformer.

A Robust Capon Beamformer against Uncertainty of Nominal Steering Vector

A robust Capon beamformer (RCB) against the uncertainty of nominal array steering vector (ASV) is formulated in this paper. The RCB, which can be categorized as diagonal loading approach, is obtained by maximizing the output power of the standard Capon beamformer (SCB) subject to an uncertainty constraint on the nominal ASV. The bound of its output signal-to-interference-plus-noise ratio (SINR) is also derived. Simulation results show that the proposed RCB is robust to arbitrary ASV error within the uncertainty set.

Autocalibration Algorithm for Robust Capon Beamforming

The robust Capon beamformer (RCB) is more robust than the standard Capon beamformer when there is uncertainty, as in the case of a sensor location error or an array model mismatch. However, the RCB suffers from mutual coupling between the array sensors, which is difficult to neglect in practice. In this work, an autocalibration algorithm is described that improves the RCB by recursively calibrating the uncertainty due to mutual coupling. The proposed method is better able to estimate the angle-of-arrival and power of the signal of interest than the RCB, as shown by numerical simulation and practical analysis of experimental data obtained in an anechoic chamber

Adaptive beamforming for quadrupole resonance

We present several adaptive beamforming approaches to improve the quadrupole resonance (QR) signal detection performance via exploiting both the spatial and temporal correlation of radio frequency interferences (RFIs). We operate in the framework of signal amplitude estimation with known signal waveform and make use of three adaptive beamforming approaches, viz., the standard Capon beamformer (SCB), the robust Capon beamformer (RCB), and the amplitude and phase estimation (APES) algorithm, to develop several new approaches for mitigating the spatially and temporally correlated RFIs. Simulated and experimental results are provided to demonstrate the effectiveness of the proposed approaches.

Time-delay- and time-reversal-based robust capon beamformers for ultrasound imaging

Currently, the nonadaptive delay-and-sum (DAS) beamformer is extensively used for ultrasound imaging, despite the fact that it has lower resolution and worse interference suppression capability than the adaptive standard Capon beamformer (SCB) if the steering vector corresponding to the signal of interest (SOI) is accurately known. The main problem which restricts the use of SCB, however, is that SCB lacks robustness against steering vector errors that are inevitable in practice. Whenever this happens, the performance of SCB may hecome worse than that of DAS. Therefore, a robust adaptive beamformer is desirable to maintain the robustness of DAS and adaptivity of SCB. In this paper we consider a recent promising robust Capon beamformer (RCB) for ultrasound imaging. We propose two ways of implementing RCB, one based on time delay and the other based on time reversal. RCB extends SCB by allowing the array steering vector to be within an uncertainty set. Hence, it restores the appeal of SCB including its high resolution and superb interference suppression capabilities, and also retains the attractiveness of DAS including its robustness against steering vector errors. The time-delay-based RCB can tolerate the misalignment of data samples and the time-reversal-based RCB can withstand the uncertainty of the Green's function. Both time-delay-based RCB and time-reversal-based RCB can be efficiently computed at a comparable cost to SCB. The excellent performances of the proposed robust adaptive beamforming approaches are demonstrated via a number of simulated and experimental examples.

Constant-beamwidth and constant-powerwidth wideband robust Capon beamformers for acoustic imaging

The standard Capon beamformer (SCB) is sensitive to the mismatch between the assumed and actual array steering vector, which occurs often in practice. Recently a robust Capon beamformer (RCB) was proposed by extending the SCB to the case of uncertain array steering vectors. In certain applications such as acoustic imaging, it is desirable that the beamwidth is constant across the frequency bins. This prevents future corrections for different frequencies and contributes to consistent sound pressure level (SPL) estimation, which means that for an acoustic wideband monopole source with a flat spectrum the acoustic image for each frequency bin stays the same. However, the beamwidth of RCB decreases with frequency, which can lead to inconsistent imaging results across the frequencies. In this paper two beamformers are proposed, namely a constant-beamwidth robust Capon beamformer (CBRCB) and a constant-powerwidth robust Capon beamformer (CPRCB), as extensions of RCB for consistent wideband acoustic imaging. Both CBRCB and CPRCB are more robust against array steering vector errors and finite sample size problems than SCB and have better resolution and interference suppression capability than data-independent beamformers. Moreover, they both can be efficiently implemented. The effectiveness of CBRCB and CPRCB is demonstrated via a number of simulated and experimental examples.

Doubly constrained robust Capon beamformer

The standard Capon beamformer (SCB) is known to have better resolution and much better interference rejection capability than the standard data-independent beamformer when the array steering vector is accurately known. However, the major problem of the SCB is that it lacks robustness in the presence of array steering vector errors. In this paper, we will first provide a complete analysis of a norm constrained Capon beamforming (NCCB) approach, which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise. Our analysis of NCCB is thorough and sheds more light on the choice of the norm constraint than what was commonly known. We also provide a natural extension of the SCB, which has been obtained via covariance matrix fitting, to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector, viz. a constant norm constraint and a spherical uncertainty set constraint, which we refer to as the doubly constrained robust Capon beamformer (DCRCB). NCCB and DCRCB can both be efficiently computed at a comparable cost with that of the SCB. Performance comparisons of NCCB, DCRCB, and several other adaptive beamformers via a number of numerical examples are also presented.

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.