Spectrum Reconstruction from Sub-Nyquist Sampling of Stationary Wideband Signals

In light of the ever-increasing demand for new spectral bands and the underutilization of those already allocated, the new concept of Cognitive Radio (CR) has emerged. Opportunistic users could exploit temporarily vacant bands after detecting the absence of activity of their owners. One of the most crucial tasks in the CR cycle is therefore spectrum sensing and detection which has to be precise and efficient. Yet, CRs typically deal with wideband signals whose Nyquist rates are very high. In this paper, we propose to reconstruct the spectrum of such signals from sub-Nyquist samples in order to perform detection. We consider both sparse and non sparse signals as well as blind and non blind detection in the sparse case. For each one of those scenarii, we derive the minimal sampling rate allowing perfect reconstruction of the signal spectrum in a noise-free environment and provide recovery techniques. The simulations show spectrum recovery at the minimal rate in noise-free settings.