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.

中文翻译：

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复值独立向量分析的性能界限

独立向量分析（IVA）是一种多数据集联合盲源分离的方法，具有广泛的应用领域，包括音频源分离、生物医学数据分析等。对于涉及圆形和非圆形信号以及相关和不相关数据集的复值情况，可以得出可实现的精度。识别条件描述了何时可以以统计一致的方式将独立源与其线性混合物分开。CRLB 显示了数据集之间的非高斯性、非圆形性和统计依赖性如何影响可达到的分离精度。实验部分中的示例证实了 CRLB 的有效性。还，它们在可达到的精度和最先进算法的性能之间显示出一定的差距，尤其是在高度非圆形信号的情况下。因此，存在可能的改进空间。