  Cognitive radio aims at identifying unused radio-frequency (RF) bands with
the goal of re-using them opportunistically for other services. While
compressive sensing (CS) has been used to identify strong signals (or
interferers) in the RF spectrum from sub-Nyquist measurements, identifying
unused frequencies from CS measurements appears to be uncharted territory. In
this paper, we propose a novel method for identifying unused RF bands using an
algorithm we call least matching pursuit (LMP). We present a sufficient
condition for which LMP is guaranteed to identify unused frequency bands and
develop an improved algorithm that is inspired by our theoretical result. We
perform simulations for a CS-based RF whitespace detection task in order to
demonstrate that LMP is able to outperform black-box approaches that build on
deep neural networks.
