HomeChair: Jean-Francois Cardoso, Dept. Signal Telecom Paris, France
HomeJitendra K. Tugnait, Auburn University (U.S.A.)
This paper is concerned with the problem of blind separation of independent signals (sources) from their linear convolutive mixtures. The various signals are assumed to be linear non-Gaussian but not necessarily i.i.d. Recently an iterative, normalized higher-order cumulant maximization based approach was developed using the fourth-order normalized cumulants of the ``beamformed'' data. A byproduct of this approach is a decomposition of the given data at each sensor into its independent signal components. In this paper an adaptive implementation of the above approach is developed using a stochastic gradient approach. Some further enhancements including a Wiener filter implementation for signal separation and adaptive filter reinitialization are also provided. A computer simulation example is presented.
ic981109.pdf (From Postscript)
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Shuichi Ohno, Shimane University (Japan)
Yujiro Inouye, Shimane University (Japan)
In order to attain multichannel blind deconvolution of linear time-invariant nonminimum-phase dynamic systems, Inouye and Habe proposed in 1995 a single-stage maximization criterion. The criterion function is the sum of squared forth-order cumulants of the equalizer outputs, and the coefficients of the equalizer are determined at once. On the other hand, one of possible approaches for multichannel blind deconvolution is to construct an equalizer based on the system identified by higher-order cumulant-matching. In this paper, it is shown that the single-stage maximization criterion is equivalent to a least-squares fourth-order cumulant-matching criterion after multichannel pre-whitening of channel outputs. This result provides us with an important interpretation of the single-stage maximization criterion.
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Zhengyuan Xu, Stevens Institute of Technology (U.S.A.)
Michail K. Tsatsanis, Stevens Institute of Technology (U.S.A.)
Constrained adaptive optimization techniques are employed in this paper to design direct blind equalizers. The method is based on minimizing the equalizer's output variance subject to appropriate constraints. The constraints are chosen to guarantee no desired signal cancellation and are also jointly and recursively optimized to improve performance. Our method provides adaptive solutions which directly optimize the equalizer's parameters, while its performance compares favorably to that of the linear prediction based approaches. Global convergence is established and comparisons with other blind and trained methods are presented.
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Carine Simon, UMLV (France)
Guy D'Urso, EDF/DER (France)
Christophe Vignat, UMLV (France)
Philippe Loubaton, UMLV (France)
Christian Jutten, UMLV (France)
In this paper, we consider the problem of blind separation of causal minimum phase convolutive mixtures of two sources. We study in detail the so-called decorrelation approach. It consists in finding a causal minimum phase filter which, driven by the observations, produces decorrelated outputs. It is well established that this approach allows to separate the sources if the mixing filter is a non static FIR filter. We show that this result is no longer true in the IIR case. We establish that it exists infinitely many causal minimum phase filters producing decorrelated outputs and provide a parameterisation of these filters. This clearly shows that the decorrelation approach is, in practice, non robust. In order to overcome this drawback, wepropose an alternative approach based on a linear prediction scheme, which, as the decorrelation approach, uses essentially the second order statistics of the observations.
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Eric Pite, Ecole Nationale Superieure des Telecommunications (France)
Pierre Duhamel, Ecole Nationale Superieure des Telecommunications (France)
Bilinear methods for jointly estimating the channel coefficients and the symbols emitted through these channels are very appealing. However, they can be trapped by local minima. This paper provides (i) a full characterization of the local minima, (ii) a simple criterion for checking whether the procedure has converged to the global minimum, (iii) a simple algorithm for obtaining this solution, with a proof of convergence.
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Gopal T Venkatesan, University of Minnesota (U.S.A.)
Mostafa Kaveh, University of Minnesota (U.S.A.)
Ahmed H. Tewfik, University of Minnesota (U.S.A.)
Kevin M. Buckley, Villanova University (U.S.A.)
In this paper we present a technique for the blind identification of single-input multiple-output (SIMO) pole-zero (PZ) systems using only the second order statistics of the system output data. The system input is treated as an unknown deterministic sequence, and hence, restrictive i.i.d. assumptions on the input sequence are not required. We estimate the poles and zeros of the channels in two steps : 1) estimate product of all permutations of a numerator and a denominator polynomial from two different channels, and 2) extract individual numerator and denominator polynomials for each channelfrom above estimate. Our technique performs well even with short records of data.
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Lang Tong, University of Connecticut (U.S.A.)
Qing Zhao, University of Connecticut (U.S.A.)
A linear least squares smoothing approach is proposed for the blind channel estimation. It is shown that the single-input multiple-output moving average process has the property that the error sequence of the least squ aressmoother, under certain conditions, uniquely determines the channel impulse response. The relationship among the dimension of the observation space, channel order and smoothing delay is presented. A new algorithm for channel estimation based on the least squares smoothing is developed. The proposed approach has the finite-sample convergence property in the absence of the channel noise. It also has a structure suitable for recursive implementations.
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Amir Sarajedini, University of California, San Diego (U.S.A.)
Paul M. Chau, University of California, San Diego (U.S.A.)
Blind Signal Separation (BSS) is a powerful technique for separation of mixed signals with weak assumptions on the incoming signals. The objectives of BSS are analogous to the objectives of Exploratory Projection Pursuit which is widely used in the statistical community for finding structure in high dimensional data sets. In this paper, we adapt Exploratory Projection pursuit for BSS. First, we introduce Exploratory Projection Pursuit and the associated projection pursuit index (PPI). We adapt the PPI for application to BSS. We also investigate the order of approximation required to achieve satisfactory separation using the PPI, and compare its performance to a maximum-likelihood BSS technique using a Gram-Charlier Expansion.
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