High-resolution cyclic spectrum reconstruction from sub-Nyquist samples

In this paper, the problem of reconstruction of Spectral Correlation Function (SCF) from sub-Nyquist samples is studied. We will first propose a novel formulation for the problem and then employ two two-dimensional greedy like sparse signal recovery algorithms, namely Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Hard Thresholding (IHT), for the recovery of the sparse SCF. The achievable resolution of the proposed methods is shown to be significantly higher than the existing methods and therefore the methods can be applied to signals with fine frequency components. Comprehensive simulation results shows that the method can efficiently reconstruct the SCF of a signature-embedded OFDM signal, which has applications in cognitive radio systems.