Recovery of High Order Statistics of PSK Signals Based on Low-Rank Matrix Completion

High order statistics are useful for automatic modulation recognition and parameter estimations. In this paper, we cast the problem of recovering high order statistics of PSK signals taken from nonuniform compressive samples as a one of recovering a low-rank matrix from missing or corrupted observations. This is a new model to describe the high order statistics of PSK signals. Unlike traditional uniformly Nyquist samples, our method uses the advanced optimization technique, which is guaranteed to find the low-rank matrix by simultaneously fixing the missing entries. Simulation results demonstrate that our method achieves accurate estimates of the major portion of the high order statistics. The new technique can be used to fulfil automatic modulation recognition (AMR) and rough estimations of parameters. More specifically, low-rank structure of PSK signals is studied. In contrast to the existing $l_{1}$ optimization criteria, our method proposed here is computationally more efficient and provides high accuracy.