Cyclic spectrum reconstruction and cyclostationary detection from sub-Nyquist samples

In the context of Cognitive Radio (CR), opportunistic transmissions can exploit temporarily vacant spectral bands. Efficient and reliable spectrum sensing is a key in the CR process. CR receivers traditionally deal with wideband signals with high Nyquist rates and low Signal to Noise Ratios (SNRs). Thus, in this paper, we propose sub-Nyquist sampling and cyclostationary detection, which is robust to noise. We first reconstruct the cyclic spectrum or Spectral Correlation Function (SCF) of the signal, which is a characteristic function of cyclostationary signals such as communication signals, from sub-Nyquist samples and then 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 for perfect reconstruction of the signal's SCF in a noise-free environment and provide SCF recovery techniques. In the simulations, we show SCF recovery at the minimal rate in noise-free settings as well as the performance of our detector in the presence of noise.