Super-Resolution of complex exponentials from modulations with known waveforms

In this paper, we investigate parametric estimation of complex exponentials from modulations with known waveforms. This problem arises naturally in radar systems and wireless communications, especially in applications which suffer from multipath effects. Viewing the problem as a group sparse recovery, we recast it naturally into an atomic norm minimization, which has an equivalent semidefinite program (SDP) characterization and thus can be solved efficiently. We experimentally demonstrate the advantage of our approach when compared with a super-resolution method that does not consider multipath effects.