Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 10, Pages 5057-5068Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2053362
Keywords
Blind source separation; independent component analysis; nonstationarity; second-order statistics; time-varying AR processes
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We consider the separation of Gaussian sources exhibiting general, arbitrary (not necessarily stationary) covariance structures. First, assuming a semi-blind scenario, in which the sources' covariance structures are known, we derive the maximum likelihood estimate of the separation matrix, as well as the induced Cramer-Rao lower bound (iCRLB) on the attainable Interference to Source Ratio (ISR). We then extend our results to the fully blind scenario, in which the covariance structures are unknown. We show that (under a scaling convention) the Fisher information matrix in this case is block-diagonal, implying that the same iCRLB (as in the semi-blind scenario) applies in this case as well. Subsequently, we demonstrate that the same semi-blind optimal performance can be approached asymptotically in the fully blind scenario if the sources are sufficiently ergodic, or if multiple snapshots are available.
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