A geometrical approach to robust minimum variance beamforming

This paper presents a highly efficient geometrical approach for designing robust minimum variance (RMV) beamformers against uncertainties in the array steering vector. Instead of the conventional approach of modeling the uncertainty region by a convex closed space, the proposed algorithm exploits the optimization constraint and shows that optimization only needs to be done on the intersection of a hyperplane and a second-order cone (SOC). The problem can then be cast as a second-order cone programming (SOCP) problem so as to enjoy the high efficiency of a class of interior point algorithms. A general case of modeling the uncertainties of an array using complex-plane trapezoids is investigated. The efficiency and tightness of the proposed method over other schemes are demonstrated with numerical examples.published_or_final_versio

A second-order cone bounding algorithm for robust minimum variance beamforming

We present a geometrical approach for designing robust minimum variance (RMV) beamformers against steering vector uncertainties. Conventional techniques enclose the uncertainties with a convex set; the antenna weights are then designed to minimize the maximum array output variance over this set. In contrast, we propose to cover the uncertainty by a second-order cone (SOC). The optimization problem, with optional robust interference rejection constraints, then reduces to the minimization of the array output variance over the intersection of the SOC and a hyperplane. This is cast into a standard second-order cone programming (SOCP) problem and solved efficiently. We study the computationally efficient case wherein the uncertainties are embedded in complex-plane trapezoids. The idea is then extended to arbitrary uncertainty geometries. Effectiveness of the proposed approach over other schemes and its fast convergence in signal power estimation are demonstrated with numerical examples. © Springer-Verlag Berlin Heidelberg 2005.postprin

A robust minimum variance beamforming approach for the removal of the eye-blink artifacts from EEGs

In this paper a novel scheme for the removal of eye-blink (EB) artifacts from electroencephalogram (EEG) signals based on the robust minimum variance beamformer (RMVB) is proposed. In this method, in order to remove the artifact, the RMVB is provided with a priori information, i.e., an estimation of the steering vector corresponding to the point source EB artifact. The artifact-removed EEGs are subsequently reconstructed by deflation. The a priori knowledge, namely the vector corresponding to the spatial distribution of the EB factor, is identified using a novel space-time-frequency-time/segment (STF-TS) model of EEGs, provided by a four-way parallel factor analysis (PARAFAC) approach. The results demonstrate that the proposed algorithm effectively identifies and removes the EB artifact from raw EEG measurements

A Robust Beamformer Based on Weighted Sparse Constraint

Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe level of a minimum variance distortionless response (MVDR) beamformer. In this letter, we introduce a weighted sparse constraint in the beamformer design to provide a lower sidelobe level and deeper nulls for interference avoidance, as compared with a conventional MVDR beamformer. The proposed beamformer also shows improved robustness against the mismatch between the steering angle and the direction of arrival (DOA) of the desired signal, caused by imperfect estimation of DOA.Comment: 4 pages, 2 figure

Modified null broadening adaptive beamforming: constrained optimisation approach

A constrained optimisation approach for null broadening adaptive beamforming is proposed. This approach improves the robustness of the traditional MVDR beamformer by broadening nulls for interference direction and the mainlobe for the desired direction. This optimisation is efficiently solved by semidefinite programming. The proposed approach, when applied to high altitude platform communications using a vertical linear antenna array, provides significantly better coverage performance than a previously reported null broadening technique

Performance analysis for a class of robust adaptive beamformers

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. Recently, worst-case approaches which consist of protecting the array's response in an ellipsoid centered around the nominal steering vector have been proposed. They amount to generalized (i.e. non necessarily diagonal) loading of the covariance matrix. In this paper, we present a theoretical analysis of the signal to interference plus noise ratio (SINR) for this class of robust beamformers, in the presence of random steering vector errors. A closed-form expression for the SINR is derived which is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Steering vector errors and diagonal loading

Diagonal loading is one of the most widely used and effective methods to improve robustness of adaptive beamformers. In this paper, we consider its application to the case of steering vector errors, i.e. when there exists a mismatch between the actual steering vector of interest and the presumed one. More precisely, we address the problem of optimally selecting the loading level with a view to maximise the signal to interference plus noise ratio in the presence of random steering vector errors. First, we derive an expression for the optimal loading for a given steering vector error and we show that this loading is negative. Next, this optimal loading is averaged with respect to the probability density function of the steering vector errors, yielding a very simple expression for the average optimal loading. Numerical simulations attest to the validity of the analysis and show that diagonal loading with the optimal loading factor derived herein provides a performance close to optimum

Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random steering vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR