# Synchronization of Analog-Discrete Chaotic Systems for Wireless Sensor Network Design  
[PERSON]\({}^{\text{\textcircled{C}}}\)  
widely studied applications of chaotic systems include the development of new encryption schemes [5; 6] and random number generators [7; 8]. Another emerging application of chaos is its integration into communication by using the signals of chaotic sources to carry information. These systems can be classified as coherent and non-coherent. Due to the sensitivity to initial conditions, the identical chaos sources are asynchronous. Two coherent chaos-based systems require chaotic synchronization as they use the chaos waveform to detect the received information signal [9; 10]. The non-coherent chaotic systems do not require such synchronization, as the detection is conducted using the signal level [11] or using the delay, like in the differential chaos shift-keying (DCSK) case [12]. The non-coherent systems are simpler in implementation and have better noise immunity, but the coherent systems are more secure due to the presence of chaotic synchronization driven by the transmitting part. This development in chaos-based communication systems is not exclusive to IoT systems and includes radar communication applications [13; 14]. The various approaches to generating chaotic signals are divided into analog and discrete. The analog techniques mainly consist of continuous-time generators that exhibit chaotic behavior. Circuits like [15; 16], known as chaos oscillators or chaos generators, are specially designed for this purpose. Other circuits, like DC-DC converters [17], are not intended to generate chaotic signals yet can act as chaos sources under specific parameters. The discrete approaches mainly consist of chaotic maps--nonlinear functions that exhibit chaotic behavior. Another discrete approach is the digital implementation of chaotic circuits [18]. Chaotic oscillators are classically implemented as analog circuits using such elements as diodes, capacitors, coils, transistors, resistances, and operational amplifiers, which can ensure a cheap and simple source of chaos. Digital implementations of chaotic circuits are relatively novel, and have rapidly emerged in recent years. In many applications, those can provide significant advantages over analog circuits, such as determined behavior, control over the system's initial conditions, and lack of instabilities caused by the performance fluctuations and finite nominal tolerances of analog components. Previously, the proposed chaos-based communication systems used a single type of chaos source: a pair of chaos oscillators or chaotic maps. This approach is sufficient for a case of a small number of devices, but for developing a WSN, a more elaborate solution is desirable. This work proposes a hybrid analog-digital chaos approach for a star-topology WSN. Figure 1 introduces the WSN communication system's design that utilizes the analog chaos oscillator circuits in the individual SNs, and the discrete model of the chaos oscillator implemented as an FPGA or microprocessor-based embedded circuit in the gateway device. Chaos oscillators are simple analog circuits that are a cost-effective solution for implementing multiple SNs. The discrete implementation of the chaos oscillator in the gateway device is a more versatile approach since several discrete models can be implemented in a single chip and can synchronize and exchange information with multiple SNs using chaotic waveforms. The embedded implementation of the gateway also contributes to the security of information transfer. Figure 1: The proposed application of analog and discrete chaos oscillator-based communication in star-topology WSN. The most critical part of the given design is the ability of the discrete chaos oscillator to synchronize with the analog chaos oscillator and vice-versa. In terms of chaotic synchronization, two main techniques are commonly used.