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The theory of Compressive Sensing (CS) has enabled the efficient acquisition of high-bandwidth (but sparse) signals via non-uniform low-rate sampling protocols. While most work in CS has focused on reconstructing the high-bandwidth signals from non-uniform low-rate samples, in this paper, the authors consider the task of inferring the modulation of a communications signal directly in the compressed domain, without requiring signal reconstruction. They show that the Nth 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 non-uniform compressive samples.
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