Gridless sparse reconstruction for the cyclic autocorrelation estimation

Abstract

In order to exploit the inherent cyclostationary properties which vary periodically in most man-made signals, one prerequisite is the knowledge of the signal's cyclic autocorrelation (CA) which can be estimated from finite time-domain samples. In this paper we concern about the sparse, periodic CA estimation and focus on recovering the CA using compressive sampling, i.e. a small amount of time-domain samples. Inspired by atomic norm based technology we model the CA estimation as a denoising problem with atomic norm, or equivalently an atomic norm soft thresholding (AST) problem, and propose a gridless version CA reconstruction which can locate the nonzero cyclic frequencies on an infinitely dense grid. The consequent convex optimization problem can be solved using semidefinite programming (SDP) via Alternating Direction Method of Multipliers (ADMM) in polynomial time. Numerical results demonstrate that the proposed method outperforms the traditional methods as well as the dictionary based CA estimator in terms of the mean square error (MSE) over a wide range of signal to noise ratios (SNR) case.