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44
Blind Signal Separation: Statistical Principles
, 2003
"... Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mut ..."
Abstract

Cited by 395 (4 self)
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Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem, to show how they stem from basic principles and how they relate to each other.
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 pro ..."
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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...
An Analytical Constant Modulus Algorithm
, 1996
"... Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of cochannel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all ..."
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Cited by 121 (31 self)
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Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of cochannel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel. In this paper, we show that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices. With this new, analytical approach, it is possible to detect the number of CM signals present in the channel, and to retrieve all of them exactly, rejecting other, nonCM signals. Only a modest amount of samples are required. The algorithm is robust in the presence of noise, and is tested on measured data, collected from an experimental setup.
Applications of Antenna Arrays to Mobile Communications, Part I: Performance Improvement, Feasibility, and System Considerations
 PROCEEDINGS OF THE IEEE
, 1997
"... The demand for wireless mobile... This paper is the first of a twopart study. It provides a comprehensive treatment, at a level appropriate to nonspecialists, of the use of an antenna array to enhance the efficiency of mobile communications systems. It presents an overview of mobile communications ..."
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Cited by 117 (0 self)
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The demand for wireless mobile... This paper is the first of a twopart study. It provides a comprehensive treatment, at a level appropriate to nonspecialists, of the use of an antenna array to enhance the efficiency of mobile communications systems. It presents an overview of mobile communications as well as details of how an array may be used in various mobile communications systems, including landmobile, indoorradio, and satellitebased systems. It discusses advantages of an array of antennas in a mobile communications system, highlights improvements that are possible by using multiple antennas compared to a single antenna in a system, and provides details on the feasibility of antenna arrays for mobile communications applications.
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
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Cited by 73 (0 self)
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Blind PARAFAC receivers for DSCDMA systems
 IEEE TRANS. SIGNAL PROCESSING
, 2000
"... This paper links the directsequence codedivision multiple access (DSCDMA) multiuser separationequalizationdetection problem to the parallel factor (PARAFAC) model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a deterministic blind PARAFAC ..."
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Cited by 70 (14 self)
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This paper links the directsequence codedivision multiple access (DSCDMA) multiuser separationequalizationdetection problem to the parallel factor (PARAFAC) model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a deterministic blind PARAFAC DSCDMA receiver with performance close to nonblind minimum meansquared error (MMSE). The proposed PARAFAC receiver capitalizes on code, spatial, and temporal diversitycombining, thereby supporting small sample sizes, more users than sensors, and/or less spreading than users. Interestingly, PARAFAC does not require knowledge of spreading codes, the specifics of multipath (interchip interference), DOAcalibration information, finite alphabet/constant modulus, or statistical independence/whiteness to recover the informationbearing signals. Instead, PARAFAC relies on a fundamental result regarding the uniqueness of lowrank threeway array decomposition due to Kruskal (and generalized herein to the complexvalued case) that guarantees identifiability of all relevant signals and propagation parameters. These and other issues are also demonstrated in pertinent simulation experiments.
Estimating Multiple CoChannel Digital Signals Using an Antenna Array
 IEEE SIGNAL PROCESSING LETTERS
, 1994
"... We propose a novel approach for separating and estimating multiple cochannel digital signals using an antenna array. The spatial response of the array is unknown. We exploit the temporal structure of the digital signals to simultaneously determine the array response and the bit sequence for each si ..."
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Cited by 67 (12 self)
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We propose a novel approach for separating and estimating multiple cochannel digital signals using an antenna array. The spatial response of the array is unknown. We exploit the temporal structure of the digital signals to simultaneously determine the array response and the bit sequence for each signal. Uniqueness of the estimates is established for signals with BPSK modulation format. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful in digital mobile communications. Simulation results demonstrate its promising performance.
Blind Separation of Synchronous CoChannel Digital Signals Using an Antenna Array. Part I. Algorithms
 IEEE Transactions on Signal Processing
, 1995
"... We propose a maximumlikelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet (FA) property of digital signals to simultaneou ..."
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Cited by 66 (6 self)
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We propose a maximumlikelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet (FA) property of digital signals to simultaneously determine the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for signals with linear modulation formats. We introduce a signal detection technique based on the FA property which is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful in wireless communication systems. Simulation results demonstrate its promising performance. Email: talwar@sccm.stanford.edu, Ph: (415) 7230061, Fax: (415) 7232411. This work was suppor...
Algebraic Methods for Deterministic Blind Beamforming
, 1998
"... Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using deterministic properties of the signals or the channels such as their constant modulus or directionsofarrival. Progress in this area has been abundant over the p ..."
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Cited by 31 (6 self)
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Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using deterministic properties of the signals or the channels such as their constant modulus or directionsofarrival. Progress in this area has been abundant over the past ten years and has resulted in several powerful algorithms. Unlike optimal or adaptive methods, the algebraic methods discussed in this review act on a fixed block of data and give closedform expressions for beamformers by focusing on algebraic structures. This typically leads to subspace estimation and generalized eigenvalue problems. After introducing a simple and widely used multipath channel model, the paper provides an anthology of properties that are available, and generic algorithms that exploit them.
Blind System Identification
, 1997
"... Blind system identification is a fundamental signal processing technology aimed to retrieve unknown information of a system from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation and blind image restoration. Th ..."
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Cited by 22 (1 self)
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Blind system identification is a fundamental signal processing technology aimed to retrieve unknown information of a system from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation and blind image restoration. This paper reviews a number of recently developed concepts and techniques for blind system identification which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input. Keywords: System identification, Blind techniques, Multichannels, Equalization, Source separation. This work has been supported by the Australian Research Council and the Australian Cooperative Research Center for Sensor Signal and Information Processing. y Currently with Motorola Australian Research Centre, 12 Lord Street, Botany 2019, ...