# A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer
## 3 Methodology and the System Design Procedure  
### General Methodology  
We explored a nonlinear chaotic oscillations generator as a source of the carrier signal in a data secured communication system. Our goal was to transmit a useful signal over this chaotic carrier. To modulate our useful signal, we introduced it as a function directly into the structure of the generator of chaotic oscillations, so the output would be a highly-secured analog signal. Then this encoded signal entered the communication channel. To restore our useful signal on the receiver side we applied a known approach of synergetic nonlinear state observer design. To do so we treated our useful signal as an unknown variable and applied the designed observer for its estimation and reconstruction.  
The adaptive reception methods used in this work, including the work of mixing a useful signal directly into the structure of the chaotic generator model, have been considered in the works of Professor [PERSON] [13] and studied in several earlier papers [27; 28; 29; 30].  
Within the framework of these previous methods, in our work two of the constant coefficients of the chaotic generator model were replaced by functions whose arguments were the sum of the initial coefficient and the useful signal that varies over time. Thus, the useful signals were embedded directly into the structure of the chaotic generator itself and the resulting chaotic oscillations carried hidden information within these useful signals. This approach to mixing useful signals, not into the resulting chaotic oscillations, but directly into the generator itself in a nonlinear, multiplicative manner only, increased the stealth and security of the system. The innovation of this work was to restore the useful signals on the receiver side if there was information about the model of the chaotic carrier signal generator and its parameters, the modulated useful signal parameter, which non-linear mixing was performed, and what was considered an unobservable variable, that was subject to recovery by a synthesized state observer. To restore useful signals, we used a synergetic nonlinear observer of state variables, proposed in the works of the scientific school of Professor [PERSON] [38; 39; 40], to which the authors of this study belong; such an observer is able to work with a specific generator of deterministic chaos. The procedure for using a synergetic observer to reconstruct a signal with a chaotic carrier was presented earlier [39]. Our synergetic observer was based on the method of analytical design of an aggregated regulator (ADAR) that was first presented by [PERSON] [41] and later extended to many applications in several papers and studies (e.g., [38; 40]) within a framework of synergetic control theory. In previous research [42; 43], a synergetic observer application for a single-channel system with a chaotic carrier was shown. In this paper, a new design procedure is presented that works with a system employing two-channel transmission of useful signals.  
So, the communication system draft structure may be presented as in Figure 1. In the following subsections, we will specify each block of Figure 1 to build a communication system reflecting above mentioned general methodology.  
As an approach to building communication systems with a chaotic carrier, chaotic synchronization is used in many studies. On the contrary, our system will allow _not_ using chaotic synchronization and will provide a simpler circuit on the receiver's side.  
Figure 1: General block diagram of a chaotic communication system.