Autocorrelation Function of Full-Response CPM Signals and Its Application to Synchronization

Two types of the autocorrelation functions of the full-response continuous phase modulation (CPM) signal are investigated in the paper, the autocorrelation functions are proven to be periodic functions when the modulation index of the CPM signal is h=1. Then the autocorrelation functions are expanded in the form of Fourier series, and two synchronization schemes are proposed to estimate the synchronization parameters from the coefficients of the Fourier series, including the carrier frequency offset, the carrier phase and the timing offset. The performances of the synchronization algorithms are shown by simulations and compared with the modified Cramer-Rao bounds (MCRB) and other synchronization schemes. The simulation results show that the first type of the proposed scheme has better synchronization performances than the available schemes.