Compressed sensing, a method which relies on sparsity to reconstruct signals with relatively few measurements, provides a new approach to processing radar signals that is ideally suited to detailed imaging and identification of multiple targets. In this paper, we extend previously published theoretical work by investigating the practical problems associated with this approach. In deriving a discrete linear radar model that is suitable for compressed sensing, we discuss what the discrete model can tell us about continuously defined targets and show how sparsity in the latter translates to sparsity in the former. We provide details about how this problem can be solved when using large data sets. Through comparisons with matched filter processing, we validate our compressed sensing technique and demonstrate its application to meteors, where it has the potential to answer open questions about processes like fragmentation and flares. At the cost of computational complexity and an assumption of target sparsity, the benefits over pulse compression using a matched filter include no filtering sidelobes, noise removal, and higher possible range and Doppler frequency resolution.
