The paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resort to their hypothesised value. By using estimates of the directional vectors obtained via blind identification, i.e. without knowing the array manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors etc., so that neither array calibration nor physical modelling is necessary. Rather suprisingly, ‘blind beamformers’ may outperform ‘informed beamformers’ in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption on which blind identification relies is the statistical independence of the sources, which is exploited using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalisation of fourth-order cumulant matrices; its implementation is described, and its performance is investigated by numerical experiments.

Blind beamforming for non-gaussian signals

Original Contribution: Blind separation of sources: A nonlinear neural algorithm

A myriad of applications require the extraction of a set of signals which are not directly accessible. Instead, this extraction must be carried out from another set of measurements which were generated as mixtures of the initial set. Since usually neither the original signals — called sources — nor the mixing transformation are known, this is certainly a challenging problem of multichannel blind estimation. One of the most typical examples is the socalled “ cocktail party” problem. In this situation, any person attending the party can hear the speech of the speaker they want to listen to, together with surrounding sounds coming from other ’ competing’ speakers, music, background noises, etc. Everybody has experienced how the human brain is able to separate all these incoming sound signals and to ’ switch’ to the desired one. Similar results can be achieved by adequately processing the output signals of an array of microphones, as long as the signals to be extracted fulfil certain conditions [62, 63] . Wireless communications is another usual application field of signal separation techniques. In a CDMA (Code Division Multiple Access) environment several users share the same radio channel by transmitting their signal after modifying it according to an appropriate code. Traditionally, the extraction of the desired signal at the receiving end requires the knowledge of the corresponding code.

Blind Source Separation

In the first part of this paper a global Kushner-Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can 'read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.

Convergence of stochastic algorithms: from the kushner-clark theorem to the lyapounov functional method

This paper deals with the problem of blind separation of sources (BSS). In the literature, one can find many Independent Component Algorithms (ICA) to solve the BSS. To demonstrate the performances of their algorithms, researchers often use different methods or performance indexes depending on their source signals and their applications. Many methods and performance indexes can not be used to compare two different algorithms applied to different signals. Most of the widely used performance indexes or methods are mentioned and discussed hereafter. We also give many examples to show limitations or drawbacks of some performance indexes or methods. keywords: Blind Separation of Sources, BSS, ICA, Crosstalk, SNR, SINR, Gap or Distance to Diagonal Matrix, Performance Indexes, Crosstalk Error, Rejection Level, Global Index, Symbol Error Rate, Scatter Plot, Error Signals, Real World Applications.

A survey of the performance indexes of ICA algorithms

The problem of sources discrimination, very classical in Signal Processing field, is also an actual problem in biological systems .
Biological sensors are sensitive to many sources, so the Central Nervous System processes typically multidimensional signais,
each component of which is an unknown mixture of unknown sources, assumed independent .
The neuromimetic solution, proposed in this paper, is based on a recursive and fully-interconnected network of operators. The
weight of the connections are varying according to an adaptation rule, which executes an independence test of the network
outputs . With regard to adaptation rudes used in adaptive filtering, here the adaptive increment is achieved necessarily by the
product of two non-linear functions .
Some experimental results, in Signal Processing and Image Processing fields, show the efficiency of this adaptive algorithm . We
proue also the possible generalization of this algorithm in the case of more complex (non-linear, degenerated, etc .) mixtures .
This algorithm points out a new concept of Independent Components Analysis, more powerful than this one of Principal
Components Analysis, and applicable in the general frame of data analysis.

Jutten

Papers

1 - Une solution neuromimétique au problème de séparation de sources