Automatic modulation recognition for spectrum sensing using nonuniform compressive samples

The theory of Compressive Sensing (CS) has enabled 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 N^th power nonlinear features used for Automatic Modulation Recognition (AMR) are compressible in the Fourier domain, and hence, that AMR of M-ary Phase-Shift-Keying (MPSK) modulated signals is possible by applying the same nonlinear transformation on nonuniform compressive samples. We provide analytical support for the accurate approximation of AMR features from nonuniform samples, present practical rules for classification of modulation type using these samples, and validate our proposed rules on simulated data.