Title: Statistical properties of a blind source separation estimator for complex-valued weakly stationary stochastic processes
Authors: Niko Lietzen - Aalto University School of Science (Finland) [presenting]
Lauri Viitasaari - Aalto University (Finland)
Pauliina Ilmonen - Aalto University School of Science (Finland)
Abstract: Novel asymptotic theory is presented for a blind source separation procedure, in the context of complex-valued signals. In particular, we provide a comprehensive mathematical foundation, applicable for a class of complex-valued blind source separation procedures, for scenarios when the blind source separation estimators have rates of convergence that differ from root-$n$ and when the corresponding estimators have limiting distributions that are not Gaussian. We further investigate the asymptotic behavior of the algorithm for multiple unknown signals extraction (AMUSE) procedure. Under general weakly stationary stochastic processes, obtaining central limit theorem type results is often challenging due to complicated dependency structures. To our knowledge, normalizations that differ from root-$n$ and limiting distributions that differ from the Gaussian distribution have not been previously considered in the blind source separation literature, neither in the real-valued nor the complex-valued case.