Double Nonstationarity: Blind Extraction of Independent Nonstationary Vector/Component from Nonstationary Mixtures—Performance Analysis

Non-Gaussianity and non-stationarity are strong features on the basis of which blind source extraction (BSE) becomes a powerful signal processing tool. The recently proposed double nonstationarity model exploits both properties in the mixing and source models, which significantly broadens the class of identifiable signals. In this article, Cramér-Rao and performance analyses are presented, including the complex-valued case, non-circularity, joint extraction, and non-stationary mixing useful for moving source extraction. Besides identifiability conditions and achievable extraction accuracy, the results reveal the influence of a source model misspecification. Of particular interest is the case when the source of interest is Gaussian, which is not identifiable without taking into account source non-stationarity. The validity of the analyses is experimentally confirmed and compared with the empirical performance of the FastDIVA algorithm. It is shown that the closed-form expression obtained from the analysis can be used as information about the achieved interference-to-signal ratio without knowing the ground-truth signals.