Performance Bounds for Complex-Valued Independent Vector Analysis

Independent Vector Analysis (IVA) is a method for joint Blind Source Separation of multiple datasets with wide area of applications including audio source separation, biomedical data analysis, etc. In this paper, identification conditions and Cramér-Rao Lower Bound (CRLB) on the achievable accuracy are derived for the complex-valued case involving circular and non-circular signals and correlated and uncorrelated datasets. The identification conditions describe when independent sources can be separated from their linear mixture in the statistically consistent manner. The CRLB shows how non-Gaussianty, non-circularity of sources and statistical dependence between datasets influence the attainable separation accuracy. Examples presented in the experimental part confirm the validity of the CRLB. Also, they show certain gap between the attainable accuracy and performance of state-of-the-art algorithms, especially, in case of highly non-circular signals. Hence, there is a room for possible improvements.