A Nonunitary Joint Block Diagonalization Algorithm for Blind Separation of Convolutive Mixtures of Sources

Ghennioui, Hicham; Mostafa, F. El; Thirion-Moreau, Nadège; Adib, Abdellah; Moreau, Éric

doi:10.1109/lsp.2007.903273

Cited by 40 publications

(26 citation statements)

References 15 publications

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“…At each run, the mixing system and the N e sources samples have been drawn randomly (according to a normal distribution). The quality of extraction is measured thanks to a performance index derived from [9] and defined by:…”

Section: Simulation Resultsmentioning

confidence: 99%

Cubic higher-order criterion and algorithm for blind extraction of a source signal

Dubroca

Luigi

Moreau

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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The paper deals with the problem of the blind extraction of a source signal after a MIMO convolutive mixture. The extraction is performed using a MISO equalizer. A contrast function based on high order statistics is first proposed. It is more general than the existing contrast in the same context and exhibits a cubic dependence w.r.t. the unknown equalizer parameters. This allows us to propose a new extraction algorithm based on a third order tensor decomposition. Computer simulations illustrate the good behavior and the usefulness of our algorithm.

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Section: Simulation Resultsmentioning

confidence: 99%

Cubic higher-order criterion and algorithm for blind extraction of a source signal

Dubroca

Luigi

Moreau

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…. F M from the matrices Y i given by (3.26) is called joint block diagonalization and it arises in some signal processing problems [78] [79]. Again, we can explain the method from another point of view.…”

Section: Signal Analysis Methodsmentioning

confidence: 99%

Localization of packet based radio transmitters in space, time, and frequency

Ivkovic

Spasojević

Seskar

2008

2008 42nd Asilomar Conference on Signals, Systems and Computers

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We consider the scenario where one or more sensors observe a frequency band potentially used by multiple radio transmitters forming packet based networks. Our goal is to develop algorithms for estimation of spectrum usage in space, time, and frequency. This estimation is obtained by performing some form of analysis of the received signals at the sensors. The proposed algorithms can be used for achieving efficient spectrum utilization by identifying unused portions of spectrum in space, time and frequency as well as for other applications requiring spectrum monitoring.The received signals consist of packets from multiple transmitters with possible timefrequency collisions. Each received signal consists of multiple statistically homogeneous segments where each combination of active transmitted signals creates one or more of such segments. In order to perform any form of statistical analysis using conventional methods for stationary or cyclostationary signals these segments must be first localized in time. In the first part of the thesis we propose a nonparametric algorithm for solving this problem. Initial segmentation is computed using a variant of mean shift algorithm, which is a clustering tool based on nonparametric estimate of the underlying probability distribution. We show that this type of mean shift algorithm is based on the modified Newton's method and provide a convergence analysis which explains how and why ii the algorithm works. Final segmentation results are obtained after applying a cluster validation procedure and impulse noise filtering on the initial segmentation results.In the second part of the thesis we propose a method for analysis of the segments localized in the first step. This method is useful if transmitted signals are linearly modulated or can be approximated as sums of linearly modulated signals. For each set of segments generated by the same combination of the transmitted signals we compute a certain two dimensional slice of the fourth order spectrum. These slices are arranged in a three way array. We show that under certain conditions it is possible to recover contributions of individual signals to the observed three way array by decomposing the array into low rank terms. Thus, for each received signal we can estimate its spectrum and the associated activity sequence in time. We discuss the uniqueness conditions, treat the nontrivial problem of fourth order spectrum estimation and propose a numerical algorithm for estimation of the spectra and the associated activity sequences of individual signals from the observed three way array.The algorithms for segmentation and fourth order spectrum based analysis require only one sensor. In the third part of the thesis we assume that multiple sensors are available. Using the algorithms mentioned above for each transmitter we can estimate its received spectrum at different sensors. From the received spectra of the same transmitted signal at different sensors it is possible to estimate the source signal spectrum and transfer functions of the ch...

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“…This can be done by existing algorithms for non-unitary JBD, e.g., [13]. Alternatively, this can also be done by the computation of the BCD-(L,L,·) [1] of the tensor M ∈ C LR×LR×N obtained by stacking the matrices Mn.…”

Section: Link Between the Bcd-(ll1) And Joint Block Diagonalizamentioning

confidence: 99%

A link between the decomposition of a third-order tensor in rank-(L,L,1) terms and Joint Block Diagonalization

Nion

Lathauwer

2009

2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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In this paper, we show that the Block Component Decomposition in rank-(L,L,1) terms of a third-order tensor, referred to as BCD-(L,L,1), can be reformulated as a Joint Block Diagonalization (JBD) problem, provided that certain assumptions on the dimensions are satisfied. This JBDbased reformulation leads to a new uniqueness bound for the BCD-(L,L,1). We also propose a closed-form solution to solve exact JBD problems. For approximate JBD problems, this closed-form solution yields a good starting value for iterative optimization algorithms. The performance of our technique is illustrated by its application to blind CDMA signal separation.

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A Nonunitary Joint Block Diagonalization Algorithm for Blind Separation of Convolutive Mixtures of Sources

Cited by 40 publications

References 15 publications

Cubic higher-order criterion and algorithm for blind extraction of a source signal

Cubic higher-order criterion and algorithm for blind extraction of a source signal

Localization of packet based radio transmitters in space, time, and frequency

A link between the decomposition of a third-order tensor in rank-(L,L,1) terms and Joint Block Diagonalization

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