Study of correlation functions of ensembles of orthogonal multiphase code sequences obtained on the basis of hermitian matrices

This study addresses the challenge of enhancing the structural secrecy of information transmission systems employing code-division multiplexing. To increase the structural secrecy of information transmission systems with coded channel separation, the necessity of increasing the number of used ensembles of orthogonal code sequences is proved. One of the possible ways to expand the number of orthogonal code sequences is the use of eigenvectors of Hermitian matrixes. Due to the complex component, multiphase orthogonal code sequences are obtained, the expansion of the number of which can be achieved by changing both the modules and arguments of the Hermitian matrix coefficients. However, not all multiphase orthogonal code sequences obtained from the eigenvectors of the Hermitian matrix will have the established requirements for correlation characteristics. The objectives of the paper are to determine the constraints for 4-th order Hermitian matrices at which ensembles of orthogonal multiphase code sequences described by their eigenvectors satisfy the first and second "condition of L. E. Varakin" by their correlation functions. The possible values of side peaks of correlation functions for different values of arguments of Hermitian matrix coefficients are calculated. Establishment of the ranges of changes in the side peaks of autocorrelation DR_j and cross-correlation DR_jk functions of ensembles of orthogonal multiphase code sequences have been established, which respectively lie within the limits from R_jmin = 0.25 to R_jmax = 0.75 and from R_jkmin = 0.5 to R_jkmax = 0.75.