Compressed Sensing of digital signals with finite alphabets

We investigate the Compressed Sensing (CS) of digital signals with finite alphabets. More specifically, multiple-phase-shift-keying (M-PSK) alphabet is studied. Exploring the finite alphabets character, the sampling procedure can be achieved at Sub-Nyquist rate. Considering the modulation procedure, the model can also serve to a joint demodulation model. Furthermore, the sampling rate required here scales with the symbol rate, which is much lower than the Nyquist rate. Numerical simulations verify its validity.