Sub-Nyquist power spectrum reconstruction and support detection for cognitive radios

In order to respond to the ever-increasing demand for new spectral bands, the concept of Cognitive Radio (CR) has emerged, exploiting the spectrum sparsity. 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 should be reliable and efficient. Yet, CRs typically deal with wideband signals whose Nyquist rates are very high. In this paper, we propose to reconstruct the power spectrum of such signals from sub-Nyquist samples, rather than the signal itself as done in previous work, 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 power spectrum reconstruction in a noise-free environment and provide spectrum recovery techniques that achieve those rates. Simulations demonstrate spectrum recovery and support detection at the minimal rate in noise-free settings and show the impact of the signal-to-noise ratio (SNR) on the performance of our detector.