Off-grid cyclic autocorrelation estimation from random measurements

The cyclic autocorrelation (CA), which only exist nonzero coefficients at the specific cycle frequencies, can exploit inherent cyclostationary properties which vary periodically in most man-made signals. However, the CA cannot usually be sparsely represented by the finite dictionary since the true cycle frequencies do not actually fall onto the discrete grid induced by the dictionary. Inspired by atomic norm based technology we concern about the sparse, off-grid CA estimation from compressive sampling. Unlike previous work we introduce the random measurement operator into atomic norm minimization and investigate the problems of locating the nonzero coefficients on an infinitely dense grid in the cycle frequency domain. The corresponding convex optimization problem can be solved using semidefinite programming (SDP) via Alternating Direction Method of Multipliers (ADMM). Numerical results demonstrate the effectiveness of the proposed method.