CHOCS: A Framework for Estimating Compressive Higher Order Cyclostationary Statistics

The framework of computing Higher Order Cyclostationary Statistics (HOCS) from an incoming signal has proven useful in a variety of applications over the past half century, from Automatic Modulation Recognition (AMR) to Time Difference of Arrival (TDOA) estimation. Much more recently, a theory known as Compressive Sensing (CS) has emerged that enables the efficient acquisition of high-bandwidth (but sparse) signals via nonuniform low-rate sampling protocols. While most work in CS has focused on reconstructing the high-bandwidth signals from nonuniform low-rate samples, in this work, we consider the task of inferring the modulation of a communications signal directly in the compressed domain, without requiring signal reconstruction. We show that the HOCS features used for AMR are compressible in the Fourier domain, and hence, that AMR of various linearly modulated signals is possible by estimating the same HOCS features from nonuniform compressive samples. We provide analytical support for the accurate approximation of HOCS features from nonuniform samples and derive practical rules for classification of modulation type using these samples based on simulated data.