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20
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 ..."
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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
FourthOrder Cumulant Structure Forcing. Application to Blind Array Processing
, 1992
"... In blind array processing, the array manifold is unknown but, under the signal independence assumption, the signal parameters can be estimated by resorting to higherorder information. We consider the 4thorder cumulant tensor and show that sample cumulant enhancement based on rank and symmetry prop ..."
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Cited by 11 (8 self)
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In blind array processing, the array manifold is unknown but, under the signal independence assumption, the signal parameters can be estimated by resorting to higherorder information. We consider the 4thorder cumulant tensor and show that sample cumulant enhancement based on rank and symmetry properties yields cumulant estimates with the exact theoretical structure. Any identification procedure based on enhanced cumulants is then equivalent to cumulant matching, bypassing the need for initialization and optimization. 1. INTRODUCTION This paper deals with a linear data model where a m dimensional complex vector x(t) is assumed to be the superposition of n linear components, possibly corrupted by additive noise. An observation can then be written as: x(t) = X p=1;n sp(t) ap +N(t) (1) where each sp(t) is a complex stationary scalar process, each ap is a deterministic m21 vector, and the m21 vector N(t) represents additive noise. This is the standard model in narrow band array p...
SecondOrder Versus FourthOrder Music Algorithms: An Asymptotical Statistical Analysis
 in Proc. Int. Sig. Proc. Workshop on HigherOrder Stat
, 1991
"... Direction finding techniques are usually based on the 2ndorder statistics of the received data. In this paper, we propose a MUSIClike direction finding algorithm which uses a matrixvalued statistic based on the contraction of the 4thorder cumulant tensor of the array data (42 MUSIC). We then deri ..."
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Cited by 8 (4 self)
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Direction finding techniques are usually based on the 2ndorder statistics of the received data. In this paper, we propose a MUSIClike direction finding algorithm which uses a matrixvalued statistic based on the contraction of the 4thorder cumulant tensor of the array data (42 MUSIC). We then derive, in a unified framework, the asymptotic covariance of estimation errors for both 2ndorder and 4thorder based MUSICs, and show that the 4thorder method can perform equally well or even better than the 2ndorder method, even when the noise spatial structure is known. 1. INTRODUCTION Current array processing techniques are based on the secondorder statistics of the received signals. In many situations, in particular in digital communications, received signals are nonGaussian so that they contain valuable statistical information in their moments of order greater than two. In these circumstances, it makes sense to develop array processing techniques that exploit higherorder information...
HigherOrder NarrowBand Array Processing
 Proc. Int. Sig. Proc. Work. on HOS, pp 121130, Chamrousse
, 1991
"... This communication deals with narrowband array processing using higherorder cumulants. A versatile tensor formalism is presented and adopted throughout to handle higherorder statistics of complex multivariates. We essentially focus on the use 4thorder cumulants for source localization in the spi ..."
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Cited by 7 (4 self)
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This communication deals with narrowband array processing using higherorder cumulants. A versatile tensor formalism is presented and adopted throughout to handle higherorder statistics of complex multivariates. We essentially focus on the use 4thorder cumulants for source localization in the spirit of the modern "subspace" techniques. We discuss "full cumulant tensor" solutions and their "downsized" versions in matrix form. Higherorder cumulants are usually advocated for in presence of additive Gaussian noise, but other potential advantages often are overlooked : nonGaussian sensor noise cancellation, "more sources than sensors" ability, blind identification. This is discussed via the notion of fourthorder signal subspace. The paper is not intended as being a review, but other related approaches based on higherorder statistics are briefly reported. 1. INTRODUCTION The recent renewal of interest for higherorder statistics has been mainly oriented towards time series processi...
Compressive MUSIC: revisiting the link between compressive sensing and array signal processing
 IEEE Trans. on Information Theory
, 2012
"... Abstract—The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems have been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sen ..."
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Cited by 5 (3 self)
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Abstract—The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems have been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS) due to its capability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees the accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the probabilistic CS and deterministic sensor array signal processing has not been fully understood. The main contribution of the present article is a unified approach that revisits the link between CS and array signal processing first unveiled in the mid 1990s by Feng and Bresler. The new algorithm, which we call compressive MUSIC, identifies the parts of support using CS, after which the remaining supports are estimated using a novel generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and that it can approach the optimalbound with finite number of snapshots even in cases where the signals are linearly dependent. Index Terms—Compressive sensing, multiple measurement vector problem, joint sparsity, MUSIC, SOMP, thresholding. I.
Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom
, 2010
"... A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide ( 2) degrees of freedom using only physical sensors when the secondorder st ..."
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Cited by 5 (3 self)
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A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide ( 2) degrees of freedom using only physical sensors when the secondorder statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimuminput–minimumoutput (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested coarray, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourthorder cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations.
An Objective Function for Independence
 In Proc. International Conference on Neural Networks
, 1996
"... The problem of separating a linear or nonlinear mixture of independent sources has been the focus of many studies in recent years. It is well known that the classical principal component analysis method, which is based on second order statistics, performs poorly even in the linear case, if the sourc ..."
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Cited by 5 (3 self)
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The problem of separating a linear or nonlinear mixture of independent sources has been the focus of many studies in recent years. It is well known that the classical principal component analysis method, which is based on second order statistics, performs poorly even in the linear case, if the sources do not have Gaussian distributions. Based on this fact, several algorithms take in account higher than second order statistics in their approach to the problem. Other algorithms use the KullbackLeibler divergence to find a transformation that can separate the independent signals. Nevertheless the great majority of these algorithms only take in account a finite number of statistics, usually up to the fourth order, or use some kind of smoothed approximations. In this paper we present a new class of objective functions for source separation. The objective functions use statistics of all orders simultaneously, and have the advantage of being continuous, differentiable functions that can be c...
Asymptotic Performance Analysis Of Direction Finding Algorithms Based On FourthOrder Cumulants.
 IEEE Trans. on SP
, 1999
"... In the narrow band array processing context, the use of higherorder statistics has been often advocated because consistent and asymptotically unbiased parameter estimates can be obtained without it being necessary to know, to model or to estimate the spatial covariance of the noise as long as it is ..."
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Cited by 2 (1 self)
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In the narrow band array processing context, the use of higherorder statistics has been often advocated because consistent and asymptotically unbiased parameter estimates can be obtained without it being necessary to know, to model or to estimate the spatial covariance of the noise as long as it is normally distributed. However, experimentation shows that this `noise insensitivity' is traded for increased variability of the parameter estimates. The main purpose of this contribution is to derive and work out closed form expressions of the asymptotic covariance of MUSIClike directionofarrival estimates based on two fourthorder cumulant matrices: the diagonal slice and the contracted quadricovariance. This is compared to the standard covariance based MUSIC estimate establishing on a rational basis the domain of applicability of higherorder statistics for DOA estimation. In particular, the actual impact of the noise variance and of the dynamic range of the sources is investigated. T...
Direction Finding Algorithms Using Fourth Order Statistics. Asymptotic Performance Analysis
 in Proc. ICASSP
, 1992
"... This communication deals with highresolution direction finding using higherorder cumulants of the array data. Two 4thorder cumulantbased matrices are considered : the diagonal cumulant slice and the contracted quadricovariance. They are evaluated in the context of DOA estimation using "subspace" ..."
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Cited by 2 (2 self)
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This communication deals with highresolution direction finding using higherorder cumulants of the array data. Two 4thorder cumulantbased matrices are considered : the diagonal cumulant slice and the contracted quadricovariance. They are evaluated in the context of DOA estimation using "subspace" techniques. To this purpose, we introduce an original methodology to derive the closed form of asymptotical performance. This analysis is applied to the cumulant based DOA estimation problem, establishing on a rational basis the domain of applicability of HOS in DOA estimation which is larger than usually believed. It is also shown that the contracted quadricovariance outperforms the diagonal slice in all respects. Some numerical evaluations illustrate the results. INTRODUCTION Current narrowband array processing techniques are based on the secondorder statistics of the received signals. In many situations, the received signals are nonGaussian, so that they contain valuable statistical...
A Novel Array Structure for DirectionsofArrival Estimation with Increased Degrees
 of Freedom,” International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2010
, 2010
"... A novel array structure for significantly increasing the degrees of freedom of linear arrays is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N 2) degrees of freedom using only O(N) physical sensors. It is possible to provide close ..."
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Cited by 2 (2 self)
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A novel array structure for significantly increasing the degrees of freedom of linear arrays is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N 2) degrees of freedom using only O(N) physical sensors. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than sensors. A novel spatial smoothing based technique is also proposed to exploit the increased degrees of freedom offered by the array to perform DOA estimation of more sources than sensors, using only second order statistics of the received data. This method does not suffer from inherent weaknesses of techniques employing higher order statistics or quasi stationarity of sources. The validity of all the proposed methods is verified through numerical examples.