Blind Source Separation with a Time-Varying Mixing Matrix

1
Blind Source Separation with a Time-Varying
Mixing Matrix
Marcus R. DeYoung and Prof. Brian L.
Evans Embedded Signal Processing Laboratory
Applications
Setup

• 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

• 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

Iterative Update Equation
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
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