Blind Source Separation with a Time-Varying Mixing Matrix Marcus R. DeYoung and Prof. Brian L. Evans Embedded Signal Processing Laboratory Setup Applications BSS: Separate a mixture of n signals from m observations Sources must be independent Algorithms formulate an objective function attempting to measure independence Co-channel communication Separate multiple speakers Medical (EEG artifact removal) Interference separation and rejection Simulation Results Effects of Ill-Conditioned Mixing Matrix Problem What happens when the mixing matrix varies over time? Co-channel communications in Rayleigh fading as an example Standard Algorithms break down Ill-conditioned matrix leads to inability to stay at a local minimum Leads to re-ordering of the separated signals Condition Number Proposed Method Constant Mixing Matrix Rayleigh Fading Based on Equivariant Adaptive Separation via Independence (EASI) – a stochastic gradient approach Conclusions Iterative Update Equation: The adaptive step size helps achieve faster convergence with a constant mixing matrix With a time-varying mixing matrix, adaptive step size grows as the changes in the separating matrix become faster Higher complexity due to second gradient computation By allowing the stepsize ( ) to adapt, the separating matrix can adjust faster when the condition number is high, and slower for more accuracy when the matrix is well-conditioned. Use the EASI procedure, but let the step size vary: Essentially a second stochastic gradient descent Inter-Signal Interference TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAA