By encoding a signal in a randomly chosen subspace before transmission, this transmitted signal proves robust to sparse errors in the channel. In this talk, we will further demonstrate the robustness of such signals to unknown convolutive channels. In particular, we show that if the channel is not especially resonant at any given frequency (e.g., the channel is sparse or random), we are able to simultaneously recover both the transmitted signal and the channel characteristics by solving a rank minimization in X, the rank-1 outer product of the two unknown vectors, subject to the receiver observations. We demonstrate favorable simulated performance for sparse and random channels. Using a parallel approach to classical compressed sensing theory, we prove a restricted isometry property about our linear operator that guarantees a high probability of recovery when the number of observations is at least linear with the dimension of the message and the length of the channel.