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89
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract

Cited by 1492 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
Fading Channels: InformationTheoretic And Communications Aspects
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... In this paper we review the most peculiar and interesting informationtheoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information ..."
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Cited by 289 (1 self)
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In this paper we review the most peculiar and interesting informationtheoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both singleuser and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.
Blind Identification and Equalization Based on SecondOrder Statistics: A Time Domain Approach
 IEEE Trans. Inform. Theory
, 1994
"... A new blind channel identification and equalization method is proposed that exploits the cyclostationarity of oversampled communication signals to achieve identification and equalization of possibly nonminimum phase (multipath) channels without using training signals. Unlike most adaptive blind equa ..."
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Cited by 166 (7 self)
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A new blind channel identification and equalization method is proposed that exploits the cyclostationarity of oversampled communication signals to achieve identification and equalization of possibly nonminimum phase (multipath) channels without using training signals. Unlike most adaptive blind equalization methods for which the convergence properties are often problematic, the channel estimation algorithm proposed here is asymptotically exact. Moreover, since it is based on secondorder statistics, the new approach may achieve equalization with fewer symbols than most techniques based only on higherorder statistics. Simulations have demonstrated promising performance of the proposed algorithm for the blind equalization of a threeray multipath channel.
A LeastSquares Approach to Blind Channel Identification
 IEEE Trans. Signal Processing
, 1995
"... Conventional blind channel idenffiication algorithm.q are based on channel outputs and knowledge of the probabilistic model of channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates ..."
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Cited by 122 (7 self)
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Conventional blind channel idenffiication algorithm.q are based on channel outputs and knowledge of the probabilistic model of channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates of certain statistics. In this paper, we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel FIR systems without requiring the knowledge of the input statistical model. A new blind idenffiieation algorithm based solely on the system outputs is proposed. Necessary and sufficient identifiability conditions in terms of the multichannel systems and the determhfistie input signal are also presented.
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 119 (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. I. INTRODUCTION A. Blind signal separation An elementary problem in the area of spatial si...
Equalization Using the Constant Modulus Criterion: A
 Review,” Proccedings of the IEEE, Invited
, 1997
"... This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help cata ..."
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Cited by 100 (21 self)
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This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.
Multichannel Blind Identification: From Subspace to Maximum Likelihood Methods
 Proc. IEEE
, 1998
"... this paper is to review developments in blind channel identification and estimation within the estimation theoretical framework. We have paid special attention to the issue of identifiability, which is at the center of all blind channel estimation problems. Various existing algorithms are classified ..."
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Cited by 79 (2 self)
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this paper is to review developments in blind channel identification and estimation within the estimation theoretical framework. We have paid special attention to the issue of identifiability, which is at the center of all blind channel estimation problems. Various existing algorithms are classified into the momentbased and the maximum likelihood (ML) methods. We further divide these algorithms based on the modeling of the input signal. If input is assumed to be random with prescribed statistics (or distributions), the corresponding blind channel estimation schemes are considered to be statistical. On the other hand, if the source does not have a statistical description, or although the source is random but the statistical properties of the source are not exploited, the corresponding estimation algorithms are classified as deterministic. Fig. 2 shows a map for different classes of algorithms and the organization of the paper.
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 74 (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...
Recent Developments in Blind Channel Equalization: From Cyclostationarity to Subspaces
 Signal Processing
, 1996
"... Since Tong, Xu and Kailath [1] demonstrated the feasibility of identifying possibly nonminimum phase channels using secondorder statistics, considerable research activity, both in algorithm development and fundamental analysis, has been seen in the area of blind identification of multiple FIR chan ..."
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Cited by 35 (1 self)
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Since Tong, Xu and Kailath [1] demonstrated the feasibility of identifying possibly nonminimum phase channels using secondorder statistics, considerable research activity, both in algorithm development and fundamental analysis, has been seen in the area of blind identification of multiple FIR channels. Many of the recently developed approaches invoke, either explicitly or implicitly, the algebraic structure of the data model, while some others resort to the use of cyclic correlation/spectral fitting techniques. The objective of this paper is to establish insightful connections among these studies and present recent developments of blind channel equalization. We also unify various representative algorithms into a common theoretical framework. 1 1
OnLine Blind Multichannel Equalization Based on Mutually Referenced Filters
 IEEE TRANS. SIGNAL PROCESSING
, 1997
"... This paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and timevarying communication channels. In the context of channel diversity, we introduce the concept of mutually referenced equalizers (MRE's) in which several filters are considered, the outputs of w ..."
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Cited by 32 (3 self)
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This paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and timevarying communication channels. In the context of channel diversity, we introduce the concept of mutually referenced equalizers (MRE's) in which several filters are considered, the outputs of which act as training signals for each other. A corresponding (constrained) multidimensional meansquare error (MSE) cost function is derived, the minimization of which is shown to be a necessary and sufficient condition for equalization. The links with a standard linear prediction problem are demonstrated. The proposed technique exhibits properties of important practical concern: 1) The proposed algorithm is globally convergent. 2)