4 September 2009 Multiple channel estimation using spectrally random probes
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Abstract
We consider the problem of estimating the channel response between multiple source receiver pairs all sensing the same medium. A different pulse is sent from each source, and the response is measured at each receiver. If each source sends its pulse while the others are silent, estimating the channel is a classical deconvolution problem. If the sources transmit simultaneously, estimating the channel requires "inverting" an underdetermined system of equations. In this paper, we show how this second scenario relates to the theory of compressed sensing. In particular, if the pulses are long and random, then the channel matrix will be a restricted isometry, and we can apply the tools of compressed sensing to simultaneously recover the channels from each source to a single receiver.
© (2009) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Justin Romberg, Justin Romberg, } "Multiple channel estimation using spectrally random probes", Proc. SPIE 7446, Wavelets XIII, 744606 (4 September 2009); doi: 10.1117/12.829895; https://doi.org/10.1117/12.829895
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