OMP with Unknown Filters for Multipath Channel Estimation

We study a modification of the orthogonal matching pursuit (OMP) for estimating sparse multipath channels. The reflectors that generate the multipath components are not ideal; rather, they act as filters, so that the returned pulses are reshaped and widened. To deal with this, we introduce unknown filters into the OMP, and then search for the best filtered set of atoms, together with the optimal set of filters. Our algorithm extends naturally to unknown pulses lying in any known subspace. We show how this observation allows us to reconstruct sums of Gaussians with unknown widths.