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We have considered the problem of secure communication by means of chaotic carrier communication channels. Data protection is provided if the signal in the communication channel looks like a stochastic or noisy one, i.e., by the steganography property, and also by using advanced and secured approaches of mixing a useful signal into a chaotic carrier. The problem is to find effective and efficient techniques for useful signal reconstruction at the receiver side. We firstly use a synergetic nonlinear mathematical observer to recover the two useful signals transmitted simultaneously over a single communication channel. Compared to a known observer, the synergetic one operates with initial nonlinear models, i.e., it may be applied directly to chaotic systems. In that system structure, we consider the useful signals as unobservable variables and estimate them by the given model of a chaotic generator. A chaotic data transmission system with two channels is demonstrated; the presented mathematical procedure explains the steps of synergetic two-channel observer design. Computer simulation results prove the viability of our approach. The proposed data transmission scheme and the observer design procedure provide effective transmission and reconstruction of informational signals. Reconstruction error is up to approximately 25% but has a very short pulses shape and could be eliminated with further analog or digital filtering algorithms. As an example application, simulation of image transmission and recovery is demonstrated. The study's results may be used as a basis for further research into secure data transmission system design.Electronics 2020, 9, 497 2 of 24 Related Works and Methods OverviewThe overall issues and approaches of chaotic communications when using chaotic modulation schemes were briefly described by Riaz and Ali [21]. According to their study [21], the most common modulation schemes are: chaos shift keying (CSK); differential chaos shift keying (DCSK); additive chaos modulation (ACM); and multiplicative chaos modulation (MCM). CSK and DCKS provide secure communication by shifting between two identical or different chaotic generators. ACM and MCM provide mixing of the useful signal directly into the mathematical model of a chaotic generator in a linear (additive) or nonlinear (multiplicative) manner. In all of these schemes, one of the data secure factors is a chaotic carrier signal frequency ten times greater than the useful signal frequency or more. ACM with a combination of MCM was explored by Kevin Short in the 1990s [22] in several Electronics 2020, 9, 497 3 of 24 papers, where he proves that this kind of combined modulation does not provide security for a 3rd order system. In addition, we note that using only MCM is a more secure approach due to nonlinear mixing of the useful signal and MCM as a secure scheme is thus widely used in much research as indicated below. Different approaches and applications of chaotic data communication systems design have been illustrated in several recent papers [23][2...

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