EE Seminar :Semi-Blind Separation of Complex-Valued Gaussian Sources
סמינר זה יחשב כסמינר שמיעה לתלמידי תואר שני ושלישי
Electrical Engineering Systems Seminar
Speaker: Roy Agmon
M.Sc. student under the supervision of Prof. Arie Yeredor
Monday, 29th July 2024, at 15:00
Room 011, Kitot Building, Faculty of Engineering
Semi-Blind Separation of Complex-Valued Gaussian Sources
Abstract
Blind Source Separation (BSS) is a well-known problem in signal processing which aims to recover unobserved statistically independent sources (signals) based on observations of their mixtures. The term ``blind" reflects the facts that the sources are not observed and that there is no prior information available about the mixture or about the distribution of each source. If prior information regarding the sources' joint distribution is available, the problem is termed ``semi blind". Independent Component Analysis (ICA) is a common technique to separate independent sources in a single set. If there are multiple sets such that each set contains independent sources but the sources are correlated across sets, the problem is termed Joint BSS (JBSS), or semi-blind JBSS, and the common separation technique is Independent Vector Analysis (IVA). As part of this work we show that using IVA we can exploit the correlation between sets in order to separate sources that are not necessarily separable in a single set using ICA. The quality of separation is quantified by the interference-to-signal ratio (ISR), which measures the residual energy of a source in the reconstruction of another source.
This work addresses the semi-blind JBSS of a particular type of sources, which are complex-valued and Gaussian distributed. Our interest in complex-valued sources requires us to address the two types of complex-valued distributions, “circular” and “non-circular”, and to examine their statistical properties, mainly their covariance and pseudo-covariance matrices. The prior knowledge regarding the sources' distributions, which are Gaussian with known (zero)-mean, covariance, and pseudo-covariance matrices, gives rise to a Maximum Likelihood Estimation (MLE) - based separation approach, which exploits the prior information regarding the sources' joint distribution.
We present the mathematical derivation of the MLE – based separation approach, including performance bounds analysis and a comparison of the resulting ISR to its lower bound, the induced Cramér Rao Lower Bound (iCRLB). We also demonstrate by our simulation results the ability to use IVA in order to separate sources that are not separable in a single set.
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