# A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer
## 3 Methodology and the System Design Procedure
### Building of the Data Transmission System Model and Overall System Computer Simulation  
In MATLAB/Simulink, we have built a model (Figure 12) reflecting a two-channel chaotic data transmission system (Figures 3 and 11) and provided a source and reconstructed signals as in Figure 13. Figure 6 presents the encoded signal into the communication channel  
In Figures 13 and 14, the simulation results of transmission and reconstruction of two piecewise-constant test signals are presented. In Figure 13a,b, the initial useful signals a and c are displayed as the blue lines, and the recovered signals are displayed via the red lines. We can see that the reconstructed signals had a form like the original ones but with an error. In order to illustrate the reconstruction error values, we displayed separate plots for reconstruction error values in Figure 14a,b. To compare the initial information signal with the transmitted one, we plotted the transmitted signal \(Z(\text{t})\) with rectangular pulses in the communication channel encoded by the chaotic system in Figure 6.  
To demonstrate the operability of the proposed algorithm, we perform additional simulation of the resulting closed-loop system with an observer in another computer mathematics package, Maple. Here we introduce a sinusoidal signal to the input of the system and provide simulations on a different time interval.  
Let us compare the simulation results in Figures 13 and 14 and Figures 15 and 16. When simulating the reconstruction of a sinusoidal signal, it can be seen that along with the cases of Figures 13 and 14, a smaller error was achieved for channel \(a\)'s signal transmission. In addition, at the initial time, the synergetic observer gave the largest recovery error.  
Figure 12: MATLAB/Simulink overall secure communication system block diagram with a two-channel synergetic observer. Here: _block 1_ is the useful signals source; _block 2_ is the transmitter with a chaotic generator; _block 4_ simulates errors in the communication channel; _block 3_ is the communication channel; and _block 5_ is the receiver (two-channel observer).  
Figure 13: Useful signal reconstruction with a two channel observer: (**a**) useful signal \(a\) (blue is the initial signal at the transmitter side; red is the reconstructed signal at the receiver side); (**b**) useful signal \(c\) (blue is the initial signal at the transmitter side; red is the reconstructed signal at the receiver side).  
Figure 16: Sinusoidal signal reconstruction error: (**a**) Signal \(a\) reconstruction error; and (**b**) Signal \(c\) reconstruction error.  
Figure 14: Transmitted signal reconstruction error: (**a**) Signal \(a\) reconstruction error; and (**b**) Signal \(c\) reconstruction error.  
Figure 15: Sinusoidal signal reconstruction with a two channel observer: (**a**) Useful signal \(a\) (blue is the initial signal at the transmitter side; red is the reconstructed signal at the receiver side); and (**b**) Useful signal \(c\) (blue is the initial signal at the transmitter side; red is the reconstructed signal at the receiver side).  
The overall block diagram illustrating the approach to communication system design is shown in Figure 17.  
An algorithm for our synergetic observer design procedure is presented in Table 2. According to the above example of chaotic carrier communication system design and two-channel synergetic observer design procedure for a Rossler chaotic generator, we provide this algorithm in detail to provide its possible implementation for systems with other chaotic generators.