Cyclostationary Detection from Sub-Nyquist Samples for Cognitive Radios: Model Reconciliation

Cognitive Radio (CR) challenges spectrum sensing into dealing with wideband signals in an efficient and reliable way. CR receivers traditionally deal with signals with high Nyquist rates and low Signal to Noise Ratios (SNRs). On the one hand, sub-Nyquist sampling of such signals alleviates the burden both on the analog and the digital side. On the other hand, cyclostationary detection ensures better robustness to noise. Cyclostationary detection from sub-Nyquist samples has been considered via two main signal models that seem inherently different. In this paper, we show that those two models can lead to similar relations between the cyclic spectrum we wish to recover and the correlation between the sub-Nyquist samples. We show that we can then derive the minimal sampling rate allowing for perfect reconstruction of the signal's cyclic spectrum in a noise-free environment for both models in a unified way. We consider both sparse and non sparse signals as well as blind and non blind detection in the sparse case. Simulations show that our detector outperforms energy detection at low SNRs.