Results 1  10
of
36
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 520 (4 self)
 Add to MetaCart
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.
Blind Separation of Disjoint Orthogonal Signals: Demixing N Sources from 2 Mixtures
 In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP
, 2000
"... We present a novel method for blind separation of any number of sources using only two mixtures. The method applies when sources are (W)disjoint orthogonal, that is, when the supports of the (windowed) Fourier transform of any two signals in the mixture are disjoint sets. We show that, for anechoi ..."
Abstract

Cited by 125 (13 self)
 Add to MetaCart
We present a novel method for blind separation of any number of sources using only two mixtures. The method applies when sources are (W)disjoint orthogonal, that is, when the supports of the (windowed) Fourier transform of any two signals in the mixture are disjoint sets. We show that, for anechoic mixtures of attenuated and delayed sources, the method allows one to estimate the mixing parameters by clustering ratios of the timefrequency representations of the mixtures. The estimates of the mixing parameters are then used to partition the timefrequency representation of one mixture to recover the original sources. The technique is valid even in the case when the number of sources is larger than the number of mixtures. The general results are verified on both speech and wireless signals. Sample sound files can be found here: http://www.princeton.edu/~srickard/bss.html 1. INTRODUCTION Demixing noisy mixtures has been a goal of long standing in the field of blind source separation(...
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 ..."
Abstract

Cited by 125 (20 self)
 Add to MetaCart
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.
Optimization algorithms exploiting unitary constraints
 IEEE Trans. Signal Processing
, 2002
"... Abstract—This paper presents novel algorithms that iteratively converge to a local minimum of a realvalued function ( ) subject to the constraint that the columns of the complexvalued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained ..."
Abstract

Cited by 99 (13 self)
 Add to MetaCart
(Show Context)
Abstract—This paper presents novel algorithms that iteratively converge to a local minimum of a realvalued function ( ) subject to the constraint that the columns of the complexvalued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold. This significantly reduces the dimensionality of the optimization problem. Pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a Hermitian matrix. Index Terms—Constrained optimization, eigenvalue problems, optimization on manifolds, orthogonal constraints. I.
Multipacket Reception in Random Access Wireless Networks: From Signal Processing to Optimal Medium Access Control
, 2001
"... Recently, there has been considerable interest in the idea of crosslayer design of wireless networks. This is motivated by the need to provide a greater level of adaptivity to variations of wireless channels. This article examines one aspect of the interaction between the physical and medium access ..."
Abstract

Cited by 80 (13 self)
 Add to MetaCart
Recently, there has been considerable interest in the idea of crosslayer design of wireless networks. This is motivated by the need to provide a greater level of adaptivity to variations of wireless channels. This article examines one aspect of the interaction between the physical and medium access control layers. In particular, we consider the impact of signal processing techniques that enable multipacket reception on the throughput and design of random access protocols.
Identifiability Results for Blind Beamforming in Incoherent Multipath with Small Delay Spread
 IEEE TRANS. SIGNAL PROCESSING
, 2001
"... Several explicit identifiability results are derived for deterministic blind beamforming in incoherent multipath with small delay spread. For example, it is shown that if the sum of spatial and fractional sampling diversities exceeds two times the total number of paths, then identifiability can be g ..."
Abstract

Cited by 26 (9 self)
 Add to MetaCart
(Show Context)
Several explicit identifiability results are derived for deterministic blind beamforming in incoherent multipath with small delay spread. For example, it is shown that if the sum of spatial and fractional sampling diversities exceeds two times the total number of paths, then identifiability can be guaranteed even for one symbol snapshot. The tools come from the theory of lowrank threeway array decomposition (commonly referred to as parallel factor analysis (PARAFAC) and data smoothing in one and two dimensions. New results regarding the Kruskalrank of certain structured matrices are also included, and they are of interest in their own right.
Complex ICA by negentropy maximization
 IEEE Trans. Neural Netw
, 2008
"... Abstract—In this paper, we use complex analytic functions to achieve independent component analysis (ICA) by maximization of nonGaussianity and introduce the complex maximization of nonGaussianity (CMN) algorithm. We derive both a gradient–descent and a quasiNewton algorithm that use the full sec ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we use complex analytic functions to achieve independent component analysis (ICA) by maximization of nonGaussianity and introduce the complex maximization of nonGaussianity (CMN) algorithm. We derive both a gradient–descent and a quasiNewton algorithm that use the full secondorder statistics providing superior performance with circular and noncircular sources as compared to existing methods. We show the connection among ICA methods through maximization of nonGaussianity, mutual information, and maximum likelihood (ML) for the complex case, and emphasize the importance of density matching for all three cases. Local stability conditions are derived for the CMN cost function that explicitly show the effects of noncircularity on convergence and demonstrated through simulation examples. Index Terms—Complexvalued data, independent component analysis (ICA), quasiNewton algorithm. I.
Adaptive Algorithms to Track the PARAFAC Decomposition of a ThirdOrder Tensor
"... Abstract—The PARAFAC decomposition of a higherorder tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode—both serious drawbacks for online applications. When ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
Abstract—The PARAFAC decomposition of a higherorder tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode—both serious drawbacks for online applications. When the data are serially acquired, or the underlying model changes with time, adaptive PARAFAC algorithms that can track the sought decomposition at low complexity would be highly desirable. This is a challenging task that has not been addressed in the literature, and the topic of this paper. Given an estimate of the PARAFAC decomposition of a tensor at instant t, we propose two adaptive algorithms to update the decomposition at instant t +1, the new tensor being obtained from the old one after appending a new slice in the ’time ’ dimension. The proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of stateofart batch algorithms, at orders of magnitude lower complexity. The effectiveness of the proposed algorithms is illustrated using a MIMO radar application (tracking of directions of arrival and directions of departure) as an example. Index Terms—Adaptive algorithms, DOA/DOD tracking, higherorder tensor, MIMO radar, PARAllel FACtor (PARAFAC).
Lathauwer: Block component modelbased blind DSCDMA receiver
 IEEE Trans. Signal Process
, 2008
"... Abstract—In this paper, we consider the problem of blind multiuser separationequalization in the uplink of a wideband DSCDMA system, in a multipath propagation environment with intersymbolinterference (ISI). To solve this problem, we propose a multilinear algebraic receiver that relies on a new t ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
Abstract—In this paper, we consider the problem of blind multiuser separationequalization in the uplink of a wideband DSCDMA system, in a multipath propagation environment with intersymbolinterference (ISI). To solve this problem, we propose a multilinear algebraic receiver that relies on a new thirdorder tensor decomposition and generalizes the parallel factor (PARAFAC) model. Our method is deterministic and exploits the temporal, spatial and spectral diversities to collect the received data in a thirdorder tensor. The specific algebraic structure of this tensor is then used to decompose it in a sum of user’s contributions. The socalled Block Component Model (BCM) receiver does not require knowledge of the spreading codes, the propagation parameters, nor statistical independence of the sources but relies instead on a fundamental uniqueness condition of the decomposition that guarantees identifiability of every user’s contribution. The development of fast and reliable techniques to calculate this decomposition is important. We propose a blind receiver based either on an alternating least squares (ALS) algorithm or on a LevenbergMarquardt (LM) algorithm. Simulations illustrate the performance of the algorithms. Index Terms—Blind signal extraction, block component model
Synchronization and packet separation in wireless ad hoc networks by known modulus algorithms
 IEEE J. Sel. Commn
, 2005
"... Abstract—In mobile asynchronous ad hoc networks, multiple users may transmit packets at the same time. If a collision occurs, then in current systems both packets are lost and need to be retransmitted, reducing the overall throughput. To mitigate this, we consider to extend the receiver with a small ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
Abstract—In mobile asynchronous ad hoc networks, multiple users may transmit packets at the same time. If a collision occurs, then in current systems both packets are lost and need to be retransmitted, reducing the overall throughput. To mitigate this, we consider to extend the receiver with a small antenna array, so that it can suppress interfering signals. To characterize the signal of interest, we propose to modulate it at the symbol rate by a known amplitude variation. This allows the corresponding multichannel receiver to estimate the beamformer weights that will suppress the interfering sources. We introduce “known modulus algorithms” to achieve this. We also derive synchronization algorithms to estimate the offset of the desired packet in an observation window, among interfering data packets. The algorithms are illustrated via simulations. Index Terms—Ad hoc networks, blind source separation, known modulus algorithm (KMA), packet offset estimation, synchronization. I.