Abstract
In a scenario where a cognitive radio unit wishes to transmit, it needs to know over which frequency bands it can operate. It can obtain this knowledge by estimating the power spectral density from a Nyquist-rate sampled signal. For wide-band signals sampling at the Nyquist rate is a major challenge and may be unfeasible. In this paper we accurately detect spectrum holes in sub-Nyquist frequencies without assuming wide sense stationarity in the compressed sampled signal. A novel extension to further reduce the sub-Nyquist samples is then presented by introducing a memory based compressed sensing that relies on the spectrum to be slowly varying.