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Blind Equalization Source Recovery

Dave Johson - Program Manager Blind Equalization Source Recovery - Michigan Aerospace Corporation
Program Manager
David K. Johnson, Ph.D.
734-975-8777 x140

MAC researchers have done significant work in Blind Equalization Source Recovery (BESR). The scenario is as follows: an unknown signal is sent on two different unknown channels; then, potentially noised receipts are collected. The goal is to recover the unknown signal as well as the unknown channels with the assumption that the channels are linear, i.e. convolution is the underlying operation. In addition, the following challenges are inherent in the problem:

  • Channels are believed to be sparse
    - Channel solutions should be "spiky" (multi-path)

  • Channel lengths are unknown
    - Unknown dimensionality forces ill-posedness

  • Signal and Channel taps do not naturally occur precisely on sample beats
Potential Applications
  • Multi-path Denoising for teleconferencing

  • Acoustic gunshot analysis in urban settings

Our approach to solving this problem is to apply L1 techniques to "discover" proper dimension and apply regularization to improve the system condition number.

The BESR Problem

These signals differ because they have taken different paths to the receiver

L2 result shows poor reconstruction

L1 Result provides excellent reconstruction

L1 Basis Pursuit can handle extremely challenging problems robustly


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