Sequential blind extraction of instantaneous mixtures with arbitrary rank

In this paper, we present new extractability conditions for blind source extraction of linear instantaneous mixtures. Two general conditions for source extraction of arbitrarily mixed nonzero sources are presented. A sufficient condition is provided to guarantee that sequential extraction can be continued. We also show an important property for inseparable mixtures; that is, any two extracted signals involving the same sources are proportional to each other. For sub-Gaussian or sup-Gaussian source signals with only mutual independence, cost functions based on fourth-order cumulants are introduced to sequentially extract all separable single sources and all inseparable mixtures. By minimizing the cost functions, gradient-based methods are developed. Our algorithms are guaranteed to converge. Finally, simulation results show the operation characteristics and the effectiveness of our methods