Non-uniform sampling for compressive cyclic spectrum reconstruction

We introduce a new cyclic spectrum estimation method for wide-sense cyclostationary (WSCS) signals sampled at sub-Nyquist rate using non-uniform sampling. We exploit the block Toeplitz structure of the WSCS signal correlation matrix and write the linear relationship between this matrix and the correlations of the sub-Nyquist rate samples as an overdetermined system. We find the condition under which the system matrix has full column rank allowing for least-squares reconstruction of the WSCS signal correlation matrix from the correlations of the compressive measurements. We also evaluate the case when the support of the WSCS signal correlation is limited and look at a special case where each selection matrix is restricted to either an identity matrix or an empty matrix. In the latter case, we can connect the full column rank condition of the system matrix with a circular sparse ruler.