A Sub-Nyquist radar system based on optimized sensing matrices derived via sparse rulers

We consider practicable subsampling for sub- Nyquist radar systems based on a set of parallel bandpass filters for extracting range information of sparse target objects. Based on a compressed sensing framework, the corresponding measurement matrix composed of blockwise selected rows from a Fourier matrix is optimized, using sparse rulers known from combinatorial number theory. As an alternative cyclic difference sets are used to select individual rows of the Fourier matrix in a deterministic fashion which outperforms random selection. Simulations of the resulting sampling concepts with regard to recovery rates via orthogonal matching pursuit (OMP) illustrate the advantages of our designs.