A new composite criterion for adaptive and iterative blind source separation

When n independent random signals are mixed by an unknown m n matrix, the task of recovering the original signals from their mixtures is called blind source separation. This contribution introduces two simple source sep-artion algorithms. The rst one is adaptive, the second is iterative. Both work indiierently with complex or real signals and use an estimation equation involving 2nd-order and higher-order information. A key feature is that resulting performance is independent of the mixing matrix in the noiseless case. Simulations also indicate the absence of ill convergence. Source separation consists in recovering a set of n independent signals from m n observed instantaneous mixtures of these signals. Denoting x(t) the m 1 vector of observations (sensor outputs) at time t, possibly corrupted by additive noise n(t), the model is x(t) = As(t) + n(t) (1) where the mn matrix A is called thèmixing matrix' and where the n independent signals are collected in a n 1 vector denoted s(t). The purpose of source separation is to nd a separating matrix, i.e. a n m matrix B such that ^ s(t) = Bx(t) is an estimate of the source signals. Note-s(t) A m n B n m-x(t)-z(t) = ^ s(t) 6 n(t) Figure 1. Mixing and separation. that in the complex case, model equation (1) is the familiar linear model used in narrow band array processing. In this context, it is usually assumed that the columns of A depend on very few location parameters (such as DOAs) and that this dependence is known via the array manifold. In contrast , we address here a problem of blind array processing in the sense that the matrix A is assumed to be full rank but otherwise unstructured. This approach is strongly motivated when (i) one is interested in recovering the source signals (like in communication applications) but not in locating the emitting sources and whenever (ii) the array manifold is unavailable or is expected to signiicantly depart from its model. Source separation is calibration-free and, by essence, insensitive to modelling uncertainties. Such a `blind array processing' is possible assuming independent and non Gaussian sources, a strong but often plausible assumption , which may be exploited using higher-order statistics or non-linearities. Various techniques have been designed to identify the mixing matrix A from observations only. Block-oriented algorithms developped so far use identiication criteria based on 2nd-and 4th-order cumulants 1, 2, 3, 4], making …