Cyclic spectrum reconstruction from sub-Nyquist samples

Communication signals are often cyclostationary, that is they have statistical characteristics that vary periodically in time. In the frequency domain, this translates into correlation between spectral components of the signal. As a result, the cyclic spectrum, a characteristic function of the second-order moment of such signals, exhibits spectral peaks at certain locations, called cyclic frequencies. Exploiting the cyclostationarity of communication signals allows to better model them and describe their properties. Moreover, it improves robustness to noise when processing such signals. The traditional signal processing task of spectrum sensing has been recently challenged by Cognitive Radios (CRs) into dealing with wideband signals in an efficient and reliable way. CR receivers 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, it increases the sensitivity to noise due to its aliasing. In this paper, we derive a method to reconstruct the cyclic spectrum of cyclostationary signals from sub-Nyquist samples rather than their spectrum or power spectrum, in order to better deal with noise. Any processing such as signal detection can then be performed on the reconstructed cyclic spectrum.