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Blind Beamforming for Non Gaussian Signals
 IEE ProceedingsF
, 1993
"... This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray mani ..."
Abstract

Cited by 494 (31 self)
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This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors, etc ... so that neither array calibration nor physical modeling are necessary. Rather surprisingly, `blind beamformers' may outperform `informed beamformers' in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption blind identification relies on is the statistical independence of the sources, which we exploit using fourthorder cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4thorder cumulant matrices
Equivariant Adaptive Source Separation
 IEEE Trans. on Signal Processing
, 1996
"... Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Eq ..."
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Cited by 381 (10 self)
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Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Equivariant Adaptive Separation via Independence) . The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions and interference rejection levels depend only on the (normalized) distributions of the source signals. Close form expressions of these quantities are given via an asymptotic performance analysis. This is completed by some numerical experiments illustrating the effectiveness of the proposed ap...
A Blind Source Separation Technique Using Second Order Statistics
, 1997
"... Separation of sources consists in recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: the linear mixture should be `blindly' processed. This typically occurs in narrowband array processi ..."
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Cited by 201 (6 self)
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Separation of sources consists in recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: the linear mixture should be `blindly' processed. This typically occurs in narrowband array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast to other previously reported techniques, the proposed approach relies only on stationary secondorder statistics, being based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method. I. Introduction I N many situations of practical interest, one has to process multidimensional observations of the form: x(t) = y(t) + n(t) = As(t) + n(t); (1) i.e. x...
Adaptive Source Separation With Uniform Performance
 In Proc. EUSIPCO
, 1994
"... . This paper presents a family of adaptive algorithms for the blind separation of independent signals. Source separation consists in recovering a set of independent signals from some linear mixtures of them, the coefficients of the mixtures being unknown. In the noiseless case, the `hardness' of the ..."
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Cited by 32 (2 self)
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. This paper presents a family of adaptive algorithms for the blind separation of independent signals. Source separation consists in recovering a set of independent signals from some linear mixtures of them, the coefficients of the mixtures being unknown. In the noiseless case, the `hardness' of the blind source separation problem does not depend on the mixing matrix (see the companion paper [1]). It is then reasonable to expect adaptive algorithms to exhibit convergence and stability properties that would also be independent of the mixing matrix. We show that this desirable uniform performance feature is simply achieved by considering `serial updating' of the separating matrix. Next, generalizing from the gradient of a standard cumulantbased contrast function, we present a family of adaptive algorithms called `PFS', based on the idea of serial updating. The stability condition and the theoretical asymptotic separation levels are given in closed form and, as expected, depend only on ...
Maximum Likelihood Source Separation for Discrete Sources
 in Proc. EUSIPCO
, 1994
"... . This communication deals with the source separation problem which consists in the separation of a noisy mixture of independent sources without a priori knowledge of the mixture coefficients. In this paper, we consider the maximum likelihood (ML) approach for discrete source signals with known prob ..."
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Cited by 28 (11 self)
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. This communication deals with the source separation problem which consists in the separation of a noisy mixture of independent sources without a priori knowledge of the mixture coefficients. In this paper, we consider the maximum likelihood (ML) approach for discrete source signals with known probability distributions. An important feature of the ML approach in Gaussian noise is that the covariance matrix of the additive noise can be treated as a parameter. Hence, it is not necessary to know or to model the spatial structure of the noise. Another striking feature offered in the case of discrete sources is that, under mild assumptions, it is possible to separate more sources than sensors. In this paper, we consider maximization of the likelihood via the ExpectationMaximization (EM) algorithm. 1. Introduction When an array of m sensors samples the fields radiated by n narrow band sources its output is classically modeled as an instantaneous spatial mixture of a random vector made of ...
EURASIP Journal on Applied Signal Processing 2003:11, 1157–1166 c ○ 2003 Hindawi Publishing Corporation Equivalence between FrequencyDomain Blind Source Separation and FrequencyDomain Adaptive Beamforming for Convolutive Mixtures
, 2002
"... Frequencydomain blind source separation (BSS) is shown to be equivalent to two sets of frequencydomain adaptive beamformers (ABFs) under certain conditions. The zero search of the offdiagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the A ..."
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Frequencydomain blind source separation (BSS) is shown to be equivalent to two sets of frequencydomain adaptive beamformers (ABFs) under certain conditions. The zero search of the offdiagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the ABFs. The unmixing matrix of the BSS and the filter coefficients of the ABFs convergetothesamesolutionifthetwosourcesignalsareideallyindependent. If they are dependent, this results in a bias for the correct unmixing filter coefficients. Therefore, the performance of the BSS is limited to that of the ABF if the ABF can use exact geometric information. This understanding gives an interpretation of BSS from a physical point of view.