Sub-Nyquist Sampling for Power Spectrum Sensing in Cognitive Radios: A Unified Approach

TL;DR

This paper introduces a unified sub-Nyquist sampling method for power spectrum sensing in cognitive radios, enabling efficient detection of wideband signals at rates below Nyquist, with theoretical minimal sampling rates and practical recovery techniques.

Contribution

It proposes a unified framework for reconstructing power spectra from sub-Nyquist samples, deriving minimal sampling rates for various scenarios, and demonstrating effective detection in noise-free environments.

Findings

Power spectrum can be reconstructed at minimal rates in noise-free conditions.

The proposed methods perform well across different signal models.

Simulation results highlight the impact of SNR, sensing time, and sampling rate.

Abstract

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 scenarii, 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 show the impact of several parameters on the detector performance, including signal-to-noise ratio (SNR), sensing time and sampling rate.