1. 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