Automatic modulation recognition of PSK signals with Sub-Nyquist sampling based on high order statistics

Sampling rate required in the N
^th
Power Nonlinear Transformation (NPT) method is typically much greater than Nyquist rate, which causes heavy burden for the Analog to Digital Converter (ADC). Taking advantage of the sparse property of PSK signals' spectrum under NPT, we develop the NPT method for PSK signals with Sub-Nyquist rate samples. In this paper, combined the NPT method with Compressive Sensing (CS) theory, frequency spectrum reconstruction of the N
^th
power nonlinear transformation of PSK signals is presented, which can be further used for AMR and rough estimations of unknown carrier frequency and symbol rate.