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