On Optimal Selection of Correlation Matrices for Matrix-Pencil-Based Separation

Abstract. The Matrix-Pencil approach to blind source separation estimates the mixing matrix from the Generalized Eigenvalue Decomposition (GEVD), or Exact Joint Diagonalization, of two “target-matrices”. In a Second-Order-Statistics framework, these target-matrices are two different correlation matrices (e.g., at different lags, taken over different time-intervals, etc.), attempting to capture the diversity of the sources (e.g., diverse spectra, different nonstationarity profiles, etc.). A central question in this context is how to best choose these target-matrices, given a statistical model for the sources. To answer this question, we consider a general paradigm for the target-matrices, viewed as two “generalized correlation” matrices, whose structure is governed by two selected “Association-Matrices”. We then derive an explicit expression (assuming Gaussian sources) for the resulting Interference-to-Source Ratio (ISR) in terms of the Association-Matrices. Subsequentl...

• Type: Conference
• Year: 2009
• Where: IDA
• Authors: Arie Yeredor
• Keywords: Artificial Intelligence, Blind Source Separation, Different Correlation Matrices, Exact Joint Diagonalization, IDA 2009