Blind Source Separation with a TimeVarying Mixing Matrix
Blind Source Separation with a Time-Varying Mixing Matrix Marcus R. De. Young and Prof. Brian L. Evans Embedded Signal Processing Laboratory Setup Applications • BSS: Separate a mixture of n signals from m observations • Co-channel communication • Separate multiple speakers • Medical (EEG artifact removal) • Interference separation and rejection • Sources must be independent • Algorithms formulate an objective function attempting to measure independence 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 Based on Equivariant Adaptive Separation via Independence (EASI) – a stochastic gradient approach Iterative Update Equation: Inter-Signal Interference 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 Constant Mixing Matrix Rayleigh Fading Conclusions • 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
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