Source separation when the input sources are discrete or have constant modulus

In this paper, we present a new method for the source separation problem when some prior information on the input sources is available. More specifically, we study the situation where the distributions of the input signals are discrete or are concentrated on a circle. The method is based on easy properties of Hankel forms and on the divisibility of Gaussian distributions. In both situations, we prove that the estimator converges in absence of noise or if we know the first moments of the noise up to its scale. Moreover, in the absence of noise, the estimate converges with a finite number of observations.