This article addresses the problem of the blind identification of the mixing matrix in the case of a possibly under-determined instantaneous linear mixture of sources. The considered input signals are cyclo-stationary processes with unknown cyclic frequencies. We propose a new method consisting of the application of a particular linear operator on the correlation matrix of the observations. Then, taking advantage of the properties of the above transformed matrix, a set of rank-one matrices can be built. Combined with a classification procedure, it makes it possible to estimate the different columns of the wanted mixing matrix. This approach is also compared with the classical PARAFAC decomposition approach. Finally, computer simulations are provided in order to illustrate the behavior and the usefulness of the two proposed approaches in the context of digital communications.