Abstract
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.
Highlights
Continuous phase modulation (CPM) is a bandwidth efficient digital modulation scheme used for data transmission over band-limited channels [1]
The synchronization procedure includes carrier frequency and phase estimation, timing recovery, which are necessary in the CPM receiver and there are many research works on the issues [5]
We investigate the characteristics of the autocorrelation function of the CPM signal with h = 1
Summary
Continuous phase modulation (CPM) is a bandwidth efficient digital modulation scheme used for data transmission over band-limited channels [1]. Since the statistical parameters of the CPM signals do not contain the transmitted symbol information, the statistical characteristics of the CPM signals could be used to estimate the modulation parameters and synchronization parameters. Among the feedforward schemes in the available literatures, the common viewpoint that all the algorithms use the characteristics of the CPM signals with h = 1. The statistical characteristics of the CPM signal with h = 1 are not investigated in those literatures. In [4], some statistics are discussed and used to design the synchronization algorithm, but the autocorrelation functions of the CPM signal are not considered. We investigate the characteristics of the autocorrelation function of the CPM signal with h = 1.
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