Linearly Constrained Minimum Variance Beamformer Research Articles

Optimal distributed minimum-variance beamforming approaches for speech enhancement in wireless acoustic sensor networks

In multiple speaker scenarios, the linearly constrained minimum variance (LCMV) beamformer is a popular microphone array-based speech enhancement technique, as it allows minimizing the noise power while maintaining a set of desired responses towards different speakers. Here, we address the algorithmic challenges arising when applying the LCMV beamformer in wireless acoustic sensor networks (WASNs), which are a next-generation technology for audio acquisition and processing. We review three optimal distributed LCMV-based algorithms, which compute a network-wide LCMV beamformer output at each node without centralizing the microphone signals. Optimality here refers to equivalence to a centralized realization where a single processor has access to all signals. We derive and motivate the algorithms in an accessible top-down framework that reveals their underlying relations. We explain how their differences result from their different design criterion (node-specific versus common constraints sets), and their different priorities for communication bandwidth, computational power, and adaptivity. Furthermore, although originally proposed for a fully connected WASN, we also explain how to extend the reviewed algorithms to the case of a partially connected WASN, which is assumed to be pruned to a tree topology. Finally, we discuss the advantages and disadvantages of the various algorithms

Non-Gaussian probabilistic MEG source localisation based on kernel density estimation

There is strong evidence to suggest that data recorded from magnetoencephalography (MEG) follows a non-Gaussian distribution. However, existing standard methods for source localisation model the data using only second order statistics, and therefore use the inherent assumption of a Gaussian distribution. In this paper, we present a new general method for non-Gaussian source estimation of stationary signals for localising brain activity from MEG data. By providing a Bayesian formulation for MEG source localisation, we show that the source probability density function (pdf), which is not necessarily Gaussian, can be estimated using multivariate kernel density estimators. In the case of Gaussian data, the solution of the method is equivalent to that of widely used linearly constrained minimum variance (LCMV) beamformer. The method is also extended to handle data with highly correlated sources using the marginal distribution of the estimated joint distribution, which, in the case of Gaussian measurements, corresponds to the null-beamformer. The proposed non-Gaussian source localisation approach is shown to give better spatial estimates than the LCMV beamformer, both in simulations incorporating non-Gaussian signals, and in real MEG measurements of auditory and visual evoked responses, where the highly correlated sources are known to be difficult to estimate.

Distributed LCMV Beamforming in a Wireless Sensor Network With Single-Channel Per-Node Signal Transmission

Linearly constrained minimum variance (LCMV) beamforming is a popular spatial filtering technique for signal estimation or signal enhancement in many different fields. We consider distributed LCMV (D-LCMV) beamforming in wireless sensor networks (WSNs) with either a fully connected or a tree topology. In the D-LCMV beamformer algorithm, each node fuses its multiple sensor signals into a single-channel signal of which observations are then transmitted to other nodes. We envisage an adaptive/time-recursive implementation where each node adapts its local LCMV beamformer coefficients to changes in the local sensor signal statistics, as well as to changes in the statistics of the wirelessly received signals. Although the per-node signal transmission and computational power is greatly reduced compared to a centralized realization, we show that it is possible for each node to generate the centralized LCMV beamformer output as if it had access to all sensor signals in the entire network, without an explicit computation of the network-wide sensor signal covariance matrix. We provide sufficient conditions for convergence and optimality of the D-LCMV beamformer. The theoretical results are validated by means of Monte Carlo simulations, which demonstrate the performance of the D-LCMV beamformer.

Localization of coherent sources by simultaneous MEG and EEG beamformer

Simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) analysis is known generally to yield better localization performance than a single modality only. For simultaneous analysis, MEG and EEG data should be combined to maximize synergistic effects. Recently, beamformer for simultaneous MEG/EEG analysis was proposed to localize both radial and tangential components well, while single modality analyses could not detect them, or had relatively higher location bias. In practice, most interesting brain sources are likely to be activated coherently; however, conventional beamformer may not work properly for such coherent sources. To overcome this difficulty, a linearly constrained minimum variance (LCMV) beamformer may be used with a source suppression strategy. In this work, simultaneous MEG/EEG LCMV beamformer using source suppression was formulated firstly to investigate its capability over various suppression strategies. The localization performance of our proposed approach was examined mainly for coherent sources and compared thoroughly with the conventional simultaneous and single modality approaches, over various suppression strategies. For this purpose, we used numerous simulated data, as well as empirical auditory stimulation data. In addition, some strategic issues of simultaneous MEG/EEG analysis were discussed. Overall, we found that our simultaneous MEG/EEG LCMV beamformer using a source suppression strategy is greatly beneficial in localizing coherent sources.

EEG Source Reconstruction Reveals Frontal-Parietal Dynamics of Spatial Conflict Processing

Cognitive control requires the suppression of distracting information in order to focus on task-relevant information. We applied EEG source reconstruction via time-frequency linear constrained minimum variance beamforming to help elucidate the neural mechanisms involved in spatial conflict processing. Human subjects performed a Simon task, in which conflict was induced by incongruence between spatial location and response hand. We found an early (∼200 ms post-stimulus) conflict modulation in stimulus-contralateral parietal gamma (30–50 Hz), followed by a later alpha-band (8–12 Hz) conflict modulation, suggesting an early detection of spatial conflict and inhibition of spatial location processing. Inter-regional connectivity analyses assessed via cross-frequency coupling of theta (4–8 Hz), alpha, and gamma power revealed conflict-induced shifts in cortical network interactions: Congruent trials (relative to incongruent trials) had stronger coupling between frontal theta and stimulus-contrahemifield parietal alpha/gamma power, whereas incongruent trials had increased theta coupling between medial frontal and lateral frontal regions. These findings shed new light into the large-scale network dynamics of spatial conflict processing, and how those networks are shaped by oscillatory interactions.

빔포밍 및 DOA 기반의 마스킹을 이용한 2채널 잡음제거

본 논문에서는 빔포밍과 입사각분석 기반 마스킹을 이용한 다채널 음성개선 알고리즘이 제안된다. 제안된 알고리즘에서는 LCMV 빔포밍을 수행한 후에 입사각 분석을 이용한 멜-주파수 위너필터가 적용되어 잔존하는 잡음을 제거한다. 성능 향상을 위해서 빔포밍의 적응 필터 학습률과 목표 음성 스펙트럼 검출을 위한 입사각 임계치가 최적화된다. 성능 지수로서 PESQ와 출력 SNR이 측정되었으며 실험 결과 제안한 알고리즘이 종전의 최소분산 빔포밍 기법보다 PESQ 관점에서 0.09, 출력 SNR 관점에서 5.75 dB의 성능 향상시킴을 알 수 있었다. In this paper, we propose a multi-channel speech enhancement algorithm using beamforming and direction-of-arrival (DOA)-based masking. The proposed algorithm enhances noisy speech basically by the linearly constrained minimum variance (LCMV) algorithm and then a mel-scale Wiener filter designed using DOA-based masking is applied to remove still remaining noises. To improve the performance, we optimize the learning rate of the adaptive filters in LCMV and the DOA threshold to detect target speech spectrum. As performance indices, the perceptual evaluation of speech quality (PESQ) score and output SNRs are measured. Experimantal results show that the proposed algorithm outperforms the conventional LCMV beamformer by 0.09 in PESQ score and 5.75 dB in output SNR, respectively.

Low-Complexity Addition or Removal of Sensors/Constraints in LCMV Beamformers

We address the application of the linearly constrained minimum variance (LCMV) beamformer in sensor networks. In signal processing applications, it is common to have a redundancy in the number of nodes, fully covering the area of interest. Here we consider suboptimal LCMV beamformers utilizing only a subset of the available sensors for signal enhancement applications. Multiple desired and interfering sources scenarios in multipath environments are considered. We assume that an oracle entity determines the group of sensors participating in the spatial filtering, denoted as the active sensors. The oracle is also responsible for updating the constraints set according to either sensors or sources activity or dynamics. Any update of the active sensors or of the constraints set necessitates recalculation of the beamformer and increases the power consumption. As power consumption is a most valuable resource in sensor networks, it is important to derive efficient update schemes. In this paper, we derive procedures for adding or removing either an active sensor or a constraint from an existing LCMV beamformer. Closed-form, as well as generalized sidelobe canceller (GSC)-form implementations, are derived. These procedures use the previous beamformer to save calculations in the updating process. We analyze the computational burden of the proposed procedures and show that it is much lower than the computational burden of the straightforward calculation of their corresponding beamformers.

Distributed Node-Specific LCMV Beamforming in Wireless Sensor Networks

In this paper, we consider the linearly constrained distributed adaptive node-specific signal estimation (LC-DANSE) algorithm, which generates a node-specific linearly constrained minimum variance (LCMV) beamformer, i.e., with node-specific linear constraints, at each node of a wireless sensor network. The algorithm significantly reduces the number of signals that are exchanged between nodes, and yet obtains the optimal LCMV beamformers as if each node has access to all the signals in the network. We consider the case where all the steering vectors are known, as well as the blind beamforming case where the steering vectors are not known. We formally prove convergence and optimality for both versions of the LC-DANSE algorithm. We also consider the case where nodes update their local beamformers simultaneously instead of sequentially, and we demonstrate by means of simulations that applying a relaxation is often required to obtain a converging algorithm in this case. We also provide simulation results that demonstrate the effectiveness of the algorithm in a realistic speech enhancement scenario.

FINITE DATA PERFORMANCE ANALYSIS OF LCMV ANTENNA ARRAY BEAMFORMERS WITH AND WITHOUT SIGNAL BLOCKING

A linearly constrained minimum variance (LCMV) antenna array beamformer using flnite data samples sufiers from slow convergence when the received array data contain the desired signal. It has been reported that signal blocking techniques speed up the convergence rate and increase the robustness of LCMV antenna array beamformers. However, the reason of this improvement has not been explored in the literature. Moreover, the existing formulas for the output signal-to-interference-plus-noise ratio (SINR) are too rough to realize the in∞uence of signal blocking techniques on the performance. In this paper, we show that the correlation due to flnite samples causes the redundant component (termed as the cross weight) embedded in the weight vector of a LCMV beamformer even if the signal sources and noise are independent. The cross power results from the cross weight degrades the performance when the sample size is small. In contrast, the cross weight and cross power can be fully eliminated when a signal blocking technique is used. The theoretical results presented in this paper provide a comprehensive description on the efiectiveness and the price of using signal blocking for antenna array beamforming. Simulation results are also given for conflrming the validity of the theoretical results.

PERFORMANCE ANALYSIS OF ANTENNA ARRAY BEAMFORMERS WITH MUTUAL COUPLING EFFECTS

Antenna array beamformers sufier from performance deterioration in the presence of mutual coupling (MC) between array sensors. In this paper, we present a theoretical analysis in terms of the output signal-to-interference-plus-noise ratio (SINR) for the performance of antenna array beamformers under MC efiects. Based on the model of a distortion matrix to encapsulate the MC efiects, 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 distortion matrix estimated from collected measurement data. The SINR formulas provide insights into the in∞uence of the MC efiects on the performances of the linearly constrained minimum variance (LCMV) beamformer and the eigenspace-based (ESB) beamformer. It is shown that the ESB beamformer outperforms the LCMV beamformer under MC efiects. Moreover, we derive the formulas for computing the eigenvalues of signal correlation matrix under MC efiects. Simulation results are presented for conflrming the validity of the theoretical results.

A method for MEG data that obtains linearly-constrained minimum-variance beamformer solution by minimum-norm least-squares method

Event Abstract Back to Event A method for MEG data that obtains linearly-constrained minimum-variance beamformer solution by minimum-norm least-squares method Toshiaki Imada1* 1 University of Washington, Athena project team, United States A method to obtain the linearly-constrained minimum-variance (LCMV) beamformer solution simply by applying the minimum-norm least-squares (MNLS) method to the recorded brain magnetic fields is theoretically shown. First, apply the prewhitening process to the recorded data using the data vari-ance-covariance matrix. Then, apply the MNLS method to its outcome. The obtained solution is mathematically proved to be equivalent to the one obtained by the original LCMV beamformer. This method works only when the number of independent neural currents (equivalent to double of the num-ber of specified neural current locations if a spherical head model is used) in the brain to be calculated is not more than the number of magnetic sensors. This is because linear independence of the neural currents is one of prerequisites for obtaining the LCMV beamformer weight matrices. When it is more, the solution currents at different locations are not line-arly independent, meaning that the obtained neural currents are mathematically, rather than physiologically, determined by the beamformer weight matrices or the MNLS pseudoin-verse matrix, which should be avoided for further analyses on the obtained neural currents. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: MEG Modeling Citation: Imada T (2010). A method for MEG data that obtains linearly-constrained minimum-variance beamformer solution by minimum-norm least-squares method. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00056 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 21 Mar 2010; Published Online: 21 Mar 2010. * Correspondence: Toshiaki Imada, University of Washington, Athena project team, Seattle, United States, imada@u.washington.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Toshiaki Imada Google Toshiaki Imada Google Scholar Toshiaki Imada PubMed Toshiaki Imada Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Beamformer Suppression of Cochlear Implant Artifacts in an Electroencephalography Dataset

Localization of cortical auditory evoked potentials in cochlear implant (CI) users is confounded by the presence of a stimulus artifact produced by the implant. Linearly constrained minimum variance (LCMV) beamformers are a class of adaptive spatial filters that localize sources of interest by minimizing the contributions of other uncorrelated sources. We have developed an artifact suppression method that enables an LCMV beamformer to reconstruct cortical activity with minimal artifact interference. This is accomplished by formulating the beamformer to enforce zero-gain on sources that generate the artifact lead potential. The artifact suppression method is first applied to normal hearing subject data to verify that it does not significantly distort the measured cortical responses. The effectiveness of the method is then demonstrated using simulated data and electroencephalography data from a CI user.

Adaptive reduced-rank LCMV beamforming algorithms based on joint iterative optimization of filters: Design and analysis

This paper presents reduced-rank linearly constrained minimum variance (LCMV) beamforming algorithms based on joint iterative optimization of filters. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of filters according to the minimum variance criterion. The proposed optimization procedure adjusts the parameters of a projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe LCMV expressions for the design of the projection matrix and the reduced-rank filter. We then describe stochastic gradient and develop recursive least-squares adaptive algorithms for their efficient implementation along with automatic rank selection techniques. An analysis of the stability and the convergence properties of the proposed algorithms is presented and semi-analytical expressions are derived for predicting their mean squared error (MSE) performance. Simulations for a beamforming application show that the proposed scheme and algorithms outperform in convergence and tracking the existing full-rank and reduced-rank algorithms while requiring comparable complexity.

Multichannel Eigenspace Beamforming in a Reverberant Noisy Environment With Multiple Interfering Speech Signals

In many practical environments we wish to extract several desired speech signals, which are contaminated by nonstationary and stationary interfering signals. The desired signals may also be subject to distortion imposed by the acoustic room impulse responses (RIRs). In this paper, a linearly constrained minimum variance (LCMV) beamformer is designed for extracting the desired signals from multimicrophone measurements. The beamformer satisfies two sets of linear constraints. One set is dedicated to maintaining the desired signals, while the other set is chosen to mitigate both the stationary and nonstationary interferences. Unlike classical beamformers, which approximate the RIRs as delay-only filters, we take into account the entire RIR [or its respective acoustic transfer function (ATF)]. The LCMV beamformer is then reformulated in a generalized sidelobe canceler (GSC) structure, consisting of a fixed beamformer (FBF), blocking matrix (BM), and adaptive noise canceler (ANC). It is shown that for spatially white noise field, the beamformer reduces to a FBF, satisfying the constraint sets, without power minimization. It is shown that the application of the adaptive ANC contributes to interference reduction, but only when the constraint sets are not completely satisfied. We show that relative transfer functions (RTFs), which relate the desired speech sources and the microphones, and a basis for the interference subspace suffice for constructing the beamformer. The RTFs are estimated by applying the generalized eigenvalue decomposition (GEVD) procedure to the power spectral density (PSD) matrices of the received signals and the stationary noise. A basis for the interference subspace is estimated by collecting eigenvectors, calculated in segments where nonstationary interfering sources are active and the desired sources are inactive. The rank of the basis is then reduced by the application of the orthogonal triangular decomposition (QRD). This procedure relaxes the common requirement for nonoverlapping activity periods of the interference sources. A comprehensive experimental study in both simulated and real environments demonstrates the performance of the proposed beamformer.

Efficient implementation of robust adaptive beamforming based on worst-case performance optimisation

Traditional adaptive beamforming methods undergo serious performance degradation when a mismatch between the presumed and the actual array responses to the desired source occurs. Such a mismatch can be caused by desired look direction errors, distortion of antenna shape, scattering due to multipath, signal fading as well as other errors. This mismatch entails robust design of the adaptive beamforming methods. Here, the robust minimum variance distortionless response (MVDR) beamforming based on worst-case (WC) performance optimisation is efficiently implemented using a novel ad hoc adaptive technique. A new efficient implementation of the robust MVDR beamformer with a single WC constraint is developed. Additionally, the WC optimisation formulation is generalised to include multiple WC constraints which engender a robust linearly constrained minimum variance (LCMV) beamformer with multiple-beam WC (MBWC) constraints. Moreover, the developed LCMV beamformer with MBWC constraints is converted to a system of nonlinear equations and is efficiently solved using a Newton-like method. The first proposed implementation requires low computational complexity compared with the existing techniques. Furthermore, the weight vectors of the two developed adaptive beamformers are iteratively updated using iterative gradient minimisation algorithms which eliminate the estimation of the sample matrix inversion. Several scenarios including angle-of-incidence mismatch and multipath scattering with small and large angular spreads are simulated to study the robustness of the developed algorithms.

Adaptive reduced-rank LCMV beamforming algorithms based on joint iterative optimisation of filters

A novel approach to linearly constrained minimum variance (LCMV) beamforming based on reduced-rank processing is proposed. The method is based on a constrained joint iterative optimisation of an adaptive projection matrix and a reduced-rank filter according to the minimum variance criterion. We derive LCMV expressions for the design of the projection matrix and the reduced-rank filter and present low-complexity adaptive algorithms for their efficient implementation. Simulations show that the proposed scheme outperforms the full-rank and existing reduced-rank methods with low complexity.

Outage Probabilities of Wireless Systems with LCMV Beamforming

This paper investigates the outage probability of a wireless system with linear constrained minimum variance (LCMV) beamforming using a uniform linear array beamformer. LCMV beamforming is able to perfectly cancel a number of dominant interferers while other interferers remain. A simplified beamforming model is used to derive closed-form outage probability expressions considering the impact of LCMV beam patterns on various interferers. Fading statistics of Rayleigh, Rician, and Nakagami are used to characterize the desired signal, whereas interferers are assumed to be subject to Rayleigh fading. One important aspect of this paper is the consideration of the directions of arrivals (DOA) of the dominant interferers and the exact beam patterns in the outage performance evaluations of LCMV beamforming systems. Numerical results of the outage probability are presented to illustrate the impact of DOA's of the dominant interferers and the impact of different fading scenarios. The paper also presents performance comparison between LCMV beamforming and conventional beamforming considering different interference scenarios (DOA's of dominant interferers).

LCMV Beamforming for a Novel Wireless Local Positioning System: Nonstationarity and Cyclostationarity Analysis

This paper investigates the implementation of a novel wireless local positioning system (WLPS). WLPS main components are: (a) a dynamic base station (DBS) and (b) a transponder, both mounted on mobiles. The DBS periodically transmits ID request signals. As soon as the transponder detects the ID request signal, it sends its ID (a signal with a limited duration) back to the DBS. Hence, the DBS receives noncontinuous signals periodically transmitted by the transponder. The noncontinuous nature of the WLPS leads to nonstationary received signals at the DBS receiver, while the periodic signal structure leads to the fact that the DBS received signal is also cyclostationary. This work discusses the implementation of linear constrained minimum variance (LCMV) beamforming at the DBS receiver. We demonstrate that the nonstationarity of the received signal causes the sample covariance to be an inaccurate estimate of the true signal covariance. The errors in this covariance estimate limit the applicability of LCMV beamforming. A modified covariance matrix estimator, which exploits the cyclostationarity property of WLPS system is introduced to solve the nonstationarity problem. The cyclostationarity property is discussed in detail theoretically and via simulations. It is shown that the modified covariance matrix estimator significantly improves the DBS performance. The proposed technique can be applied to periodic-sense signaling structures such as the WLPS, RFID, and reactive sensor networks.

Tumor localization using diffuse optical tomography and linearly constrained minimum variance beamforming

We present a tumor localization method for diffuse optical tomography using linearly constrained minimum variance (LCMV) beamforming. Beamforming is a spatial filtering technique where signals from certain directions can be enhanced while noise and interference from other directions are suppressed. In our method, we tessellate the domain into small voxels and regard each voxel as a possible position of abnormality (e.g., tumor).We then design a spatial filter based on the linearly constrained minimum variance criterion and apply it to each voxel in the domain. The abnormality is localized by observing the peak in the filter output signals. We test our method using simulated 3D examples. We assume a cubic transmission geometry and consider different cases where the abnormality is an absorber, a scatterer, and both. We also give examples showing the resolution of our method and its performance under different perturbation levels and noise levels. Simulation results show that LCMV beamforming can localize the abnormality well with good computational efficiency. It can be used alone for tumor localization and also as an effective preprocessing tool for improving the image reconstruction performances of other inverse methods.

On the Implementation of the Linearly Constrained Minimum Variance Beamformer

The linearly constrained minimum variance (LCMV) method, which allows multiple linear constraints, is an extension of the classical minimum variance distortionless response filter. Depending on the spatial filter length and the desired frequency grid, a direct computation of the resulting spatial beam pattern may be prohibitive. This brief exploits the rich structure of the LCMV expression to find a nonrecursive computationally efficient implementation of the LCMV beamformer with fixed constraints. The implementation is formed via the use of the matrix inversion lemma and the fast Fourier transform. Numerical simulations indicate a dramatic computational gain, especially for fine frequency grids and multiple constraints