Recovery of compressive samples from a randomly modulated converter

Many radar and communication signals tend to radio frequency (RF) signals of very high bandwidth. However, the information level of the signal is far lower than the actual bandwidth. Recently, there has been growing interest in nonlinear but structured signal models, in which signal lies in a shift-invariant space. In this paper, we introduce a randomly modulated converter to produce a low-rate set of digital measurements, and develop an efficient recovery of such signals from a given set of samples. More specifically, we treat the case in which signal lies in a shift-invariant spaces, chosen from a larger set of m possibilities. Our main result is an equivalence condition under which the proposed algorithm is guaranteed to recover the original signal. This result relies on the notion of restricted isometry property (RIP), which is a generalization of the standard RIP used extensively in the context of compressed sampling. Based on RIP we also prove stability of our approach in the presence of noise and modeling errors. Finally, we demonstrate the method by simulations, and show the proposed method yields better performance compared to over-sampling.