Chaotic Spreading Sequence for Linear Frequency Modulation

• Main Authors: Kateryna Serhiivna Osypenko, Valery Yakovych Zhuikov
• Format: Article
• Language: English
• Published: Igor Sikorsky Kyiv Polytechnic Institute 2018-08-01
• Series: Mìkrosistemi, Elektronìka ta Akustika
• Subjects: лінійно-частотна модуляція; розширююча послідовність; хаотичні процеси
• Online Access: http://elc.kpi.ua/article/view/134338

In the presented article the use of chaotic signals as spreading sequences for linear-frequency modulation is proposed. An example of a simplified block diagram for a chaotic signal generator constructed on the basis of linear and switching elements is given, as well as equations describing the operation of the circuit. The results of calculation and simulation of processes with specific specified parameters of the circuit are shown. The calculation of differential equations is carried out by a numerical method of Runge-Kutt of the fourth order of accuracy. It is shown that carrier frequency varies linearly, according to the scanning voltage. To maintain the full range of changes the beginning of each linear variable voltage function can be shifted for certain time interval. It is shown that when forming a range of frequency changes, it is necessary to take into account the presence of a "dead zone". The dependence of the transition from one frequency to another is random and depends on the values of correlation coefficient. A bifurcation diagram and display functions for processes with two and three attraction points are presented, The first zone of chaotic oscillations corresponds to the value of the coefficient, which is approximately in the range from 15 to 19. The second zone of chaotic oscillations correspond to the coefficient values from 40 to 59. The third zone of chaotic oscillations correspond to the coefficient values from 117 to 173. Between these zones regular oscillations are presented in the system. With an increase of correlation coefficient the number of attraction points and the corresponding display points can increase or decrease. The formulas for the calculation and the graph of the change in the correlation coefficient are given. It is shown that the correlation function is close to zero, some of its periodicity and the difference from zero is probably due to the existence of repeating areas of transient process. An example of an integer sequence for a process with two attraction points is given. For a process with two attraction points an example of integer sequences is given, which it is proposed to use to identify the type of chaotic process. The feature of generated chaotic sequences is shown – the sequence of integer function periods, which are enclosed between two attraction points is chaotic and unique. With using the deterministic equations with switching functions, a chaotic spreading sequence of linear frequency modulation is build, for identification of which it is proposed to use integer sequences of the number of periods that are enclosed between the points of generated frequencies. Ref. 7, fig. 4, table 1.