Sub-Nyquist sampling for power spectrum sensing in cognitive radios: A unified approach

In light of the ever-increasing demand for new spectral
bands and the underutilization of those already allocated, the
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 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 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 scenarios, we derive the minimal sampling
rate allowing perfect reconstruction of the signal’s power
spectrum in a noise-free environment and provide power spectrum
recovery techniques that achieve those rates. The analysis is performed
for two different signal models considered in the literature,
which we refer to as the analog and digital models, and shows that
both lead to similar results. Simulations demonstrate power spectrum
recovery at the minimal rate in noise-free settings and the impact
of several parameters on the detector performance, including
signal-to-noise ratio, sensing time and sampling rate.