Blind Equalization Source Recovery
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:
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Channels are believed to be sparse
- Channel solutions should be "spiky" (multi-path)
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Channel lengths are unknown
- Unknown dimensionality forces ill-posedness
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Signal and Channel taps do not naturally occur precisely on sample beats
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Potential Applications
- Multi-path Denoising for teleconferencing
- Acoustic gunshot analysis in urban settings
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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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