Ukraine, Odessa, Odessа Polytechnic National University.

A method has been proposed for synchronizing modems that use a system of cyclic amplitude-phase keyed signals encoded by multi-level numerical sequences with an ideal periodic autocorrelation function to transmit information. The method is based on the invariance of the phase structure of the zero cyclic shift and the inverse zero cyclic shift of the coding sequence to the fast discrete Fourier transform. This makes it possible to detect a synchronization signal based on the analysis of only the phase structure of the signal at the output of the phase detector and to carry out fast automatic adjustment of the receiver gain under conditions of an unknown initial amplitude of the amplitude-phase manipulated signal. The amplitude structure of the clock signal is restored using a special case of the fast discrete Fourier transform — the fast discrete cosine transform. Due to the integer values of the amplitudes, the symmetry around the center, and taking into account the cyclicity property, a single matched filter is used to distinguish orthogonal cyclic signals in a system containing N signals with the number of multipliers equal to the number of discrete amplitude variations, less than N/2 for even N or N/2–1 for odd N.

Keywords: cyclic AFM signal, orthogonality, multilevel number sequence, receiver gain, frame synchronization, cyclic convolution, digital matched filter.

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