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