Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Equivariant Adaptive Separation via Independence) . The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions and interference rejection levels depend only on the (normalized) distributions of the source signals. Close form expressions of these quantities are given via an asymptotic performance analysis. This is completed by some numerical experiments illustrating the effectiveness of the proposed ap...

. Source separation consists in recovering a set of n independent signals from m n observed instantaneous mixtures of these signals, possibly corrupted by additive noise. Many source separation algorithms use second order information in a whitening operation which reduces the non trivial part of the separation to determining a unitary matrix. Most of them further show a kind of invariance property which can be exploited to predict some general results about their performance. Our first contribution is to exhibit a lower bound to the performance in terms of accuracy of the separation. This bound is independent of the algorithm and, in the i.i.d. case, of the distribution of the source signals. Second, we show that the performance of invariant algorithms depends on the mixing matrix and on the noise level in a specific way. A consequence is that at low noise levels, the performance does not depend on the mixture but only on the distribution of the sources, via a function which is charac...

In this article, the asymptotic properties of the empirical characteristic function are discussed. The residual of the joint and marginal empirical characteristic functions is studied and the uniform convergence of the residual in the wider sense and the weak convergence of the scaled residual to a Gaussian process are investigated. Taking into account of the result, a statistical test for independence against alternatives is considered.