THE STUDY OF THE CROSS-CORRELATION PROPERTIES OF COMPLEX SIGNALS ENSEMBLES OBTAINED BY FILTERED FREQUENCY ELEMENTS PERMUTATIONS
Authors: Lysechko V. P. , Kulagin D. O. , Indyk S. V. , Zhuchenko О. S. , Kovtun І. V. 
Published: July 2022

Context. The relevance is to study the cross-correlation properties of the developed complex signals ensembles of large volume with a low level of multiple access interference, thereby increasing the efficiency of using a limited radio frequency range. The Object of Research is a method of bandpass filtering with permutations, which allows forming complex signals ensembles of large volume.
Objective. The Objective is to determine the optimal cross-correlation properties for the formation of complex signals ensembles of large volume with a low level of multiple access interference.
Method. The work has the study results of cross-correlation properties of complex signals ensembles obtained by applying the filtered elements permutation method. The formation of complex signals ensembles is based on pseudo-random sequences with improved cross-correlation properties in the time domain. Bandpass filtering is applied to such sequences, and the number of filter bands is determined based on the calculation of the frequency spectrum utilization coefficient. The filter band optimal width determination is based on a comparison of the maximum emissions of the side lobes values of the of cross-correlation function of signals from the elements number in the involved sequences. The signals obtained by frequency bands allocating are characterized by a difference in form in the minimal similarity condition. In order to reduce the multiple access interference impact, the frequency components transfer obtained by spectral filtering to the common frequency range is carried out. After that, the signals are transferred using the full search method. As a result, it was obtained all possible combinations of signal pairs permutations. The use of permutations in the complex signals ensemble formation can significantly increase the ensemble volume. The signals generated by frequency filtering, to which the transfer to the common frequency band and their subsequent permutation was applied, are subjected to correlation analysis based on the calculation of the maximum emissions values of the side lobes of the cross-correlation function.
Comparative characteristic of cross-correlation properties of developed signals with known signals prove that signals generated based on pseudo-random sequences with improved cross-correlation properties have a much larger ensembles volume, are formed on the basis of simple algorithms that don’t require significant computing resources and have satisfactory cross-correlation characteristics. The use of bandpass filtering method with permutation allows the formation of large-volume ensembles whose signals differ inform, and the combination of different frequency bands reduces the vulnerability to multiple access interference.
Results. Due to the software implementation of the bandpass filtering method with permutations, the comparison of crosscorrelation properties of nonlinear sequences, M-sequences, multiphase signals and developed signals based on sequences with improved cross-correlation properties was performed.
In estimating the levels of maximum emissions of side lobes of the cross-correlation function, it was found that the generated signals obtained by bandpass filtering with permutations deteriorate cross-correlation characteristics by increasing the pulse duration proportional to the decrease in signal frequency band, but their value satisfies the minimal similarity condition, used in cognitive telecommunications systems.
Conclusions. The study of the signals cross-correlation properties proves the effectiveness of the developed bandpass filtering with permutations method. The generated signals have cross-correlated characteristics no worse than ensembles based on known signals. At this level of maximum emissions of the side lobes of the cross-correlation function of the developed signals is 7–12% less than the known signals. Thus, the method of bandpass filtering with permutations can be used to increase the efficiency of radio frequency resource use of both existing and advanced cognitive telecommunication networks of wireless access based on systems with code division multiplexing.