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Phase modulation is a commonly used modulation mode in digital communication,which usually brings phase sparsity to digital signals. It is naturally toconnect the sparsity with the newly emerged theory of compressed sensing (CS),which enables sub-Nyquist sampling of high-bandwidth to sparse signals. For thepresent, applications of CS theory in communication field mainly focus onspectrum sensing, sparse channel estimation etc. Few of current researches takethe phase sparse character into consideration. In this paper, we establish thenovel model of phase modulation signals based on phase sparsity, and introduceCS theory to the phase domain. According to CS theory, rather than thebandwidth, the sampling rate required here is scaling with the symbol rate,which is usually much lower than the Nyquist rate. In this paper, we provideanalytical support for the model, and simulations verify its validity.

Automatic Modulation Recognition of PSK Signals Using Nonuniform Compressive Samples Based on High Order Statistics