# A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer
## 1 Introduction  
Dynamic chaos as a phenomenon has attracted researchers' attention since the well-known works of [PERSON] [1, 2]. Chaotic systems have found application in the study of chemical reactions, phenomena in medicine, biology, economics, sociology, engineering, etc. [2, 3, 4, 5, 6, 7, 8]. Chaotic systems and the phenomena of dynamic chaos are also used in the development of communication systems [9, 10, 11, 12]. Development of new methods of data protection is always a state-of-the-art problem. Traditional approaches aredigital and/or analog signals hardware and software encryption with various algorithms. Another advanced approach is use of chaotic oscillation generators instead of a van der Pol oscillator as a carrier oscillation generator in data transmission systems. In such a case the unpredictable nature of a chaotic carrier to an external listener becomes a protective tool itself. It should be noted that the chaotic carrier dramatically complicates a communication system, producing a lot of engineering problems. The most important problems are: (i) introduction of the informational signal into the chaotic carrier at the transmitter side while providing a sufficient security level; and (ii) successful recovery/reconstruction of the information signal at the receiver side. Secondary problems may include transmitter and receiver systems synchronization, signal reconstruction accuracy, etc.  
There are various methods for protecting a useful signal with chaotic oscillations [12]. These methods differ both in the way of introducing a useful signal into a chaotic one in a communication channel and in the way of recovering a useful signal on the receiver side. The most promising methods are nonlinear mixing (or chaotic generator parameter nonlinear modulation) of a useful signal into the structure of a chaotic generator and adaptive methods of signal reception [12; 13].  
In our study, we combine these advanced approaches and explore a chaotic carrier two-channel data transmission system using nonlinear parametric modulation at the transmitter side and a two-channel observer for useful signal estimation at the receiver side.  
The main contributions of this study are summarized as follows:  
* Here we firstly present a design procedure for a two-channel nonlinear synergetic observer that we used as an adaptive method of signal reception in chaotic carrier communication system;
* The presented design procedure is implemented for Rossler generator;
* We built a chaotic communication system viable structure based on the combination of chaotic generator nonlinear parametric modulation, method of global reconstruction of a dynamic system and nonlinear synergetic observer;
* Application of synergetic observer chaotic carrier communication system for image transmission.  
The article is organized as follows. Section 2 presents an overview of various methods of secured signal transmission using the chaotic generator as a signal carrier including ones that use parametric modulation and various techniques of signal reconstruction on the receiver side including observer design methods. Section 3 presents the methodology of our approach considered here (Section 3.1), security analysis of the encoded transmission system (Section 3.3), a system design procedure algorithm with a design example (Sections 3.4 and 3.5) as well as an overall system computer simulation (Section 3.6). To compare the obtained results, the chaotic system was estimated using the least squares method in Section 3.7. In Section 4.1, some hardware system implementation options on an Arduino, Raspberry Pi and FPGAs are discussed based on examples from other studies described earlier [14; 15; 16; 17; 18; 19; 20]. Besides Section 4 provides examples of system software implementation, including an example of digital data software transmission (Section 4.2) and secured image transmission via the designed system in Section 4.3. Discussion and conclusions as well as the study's future directions are presented in Sections 5 and 6.