Performance Analysis of the Strong Uncorrelating Transformation in Blind Separation of Complex-Valued Sources

The strong uncorrelating transformation (SUT) is an effective tool for blind separation of complex-valued independent sources, commonly applied to the (spatial) sample autocovariance and pseudo-autocovariance matrices of the observed mixtures. In this work we analyze the performance (in terms of the resulting interference to source ratio (ISR)) of SUT-based blind separation of general wide-sense stationary complex-valued sources. Based on a small-errors analysis, we derive explicit expressions for the attainable ISR in terms of the temporal correlations and pseudo-correlations of the sources. We demonstrate by simulation that the empirical performance closely follows our analytic prediction at moderate to long observation lengths. An important implication ensuing from our analysis is that a rectilinear (“maximally improper”) source can be perfectly separated from all the other (nonrectilinear) sources.