The Spectral Method for the Synthesis of Integral H-sequences with an Ideal Periodic Autocorrelation Function

Abstract

In problems of signal discrimination, orthogonal cyclic sequences with good periodic autocorrelation functions (PACF) are most widely used. There are published studies on binary cyclic sequences with low PACF side lobes that do not possess the property of orthogonality for a length of N > 4. Hence, we propose the systems of orthogonal multilevel integer cyclic sequences of N = mn length, for which the cyclic convolution coincides with the m-convolution (H-sequence), which can be very effectively calculated. It is proposed to use amplitude phase shift keying (APSK) to transmit the Hsequence over the communication channel. The purpose of this study is to develop a regular algorithm for the synthesis of Hsequences of arbitrary length N = mn based on an analysis of their spectral properties. Studying the properties of the twiddle factors of the Fourier transform matrix in the basis of the Vilenkin-Chrestenson function allowed for developing a synthesis method in the frequency domain of multilevel integer H-sequences with ideal periodic autocorrelation functions.