# Synchronization of Monostatic Radar Using a Time-Delayed Chaos-Based FM Waveform
## 3 Chaos Radar Challenges  
There are some challenges and problems facing the chaos radar systems that can be summarized as follows:  
1. The key challenge is to build an easy, low cost, and more secure chaotic radar system, but this may result a complex behavior. The challenge for chaotic waveforms is whether these properties are adequate to provide unique and operant radar implementations.
2. The parameters mismatch in chaotic systems is still unavoidable in real situations of chaos synchronization. If the drive-response systems are not identical and there is a parameters mismatch, the synchronization error does not definitely converge to zero or it may lead to small fluctuations about zero; this is called quasi-synchronization or asymptotic synchronization [16]. Otherwise, loss of synchronization may occur in case of large parameters mismatch. Therefore, to design accurate synchronization with reasonable precision between the transmitter and the receiver, it is necessary to consider the role of parameters mismatch in the synchronization process.
3. Moreover, the relationship between chaos synchronization in time-delayed feedback systems and parameters mismatch is also another quite complex issue.  
To the best of our knowledge, some studies [17; 18] are only concerned with the coupled systems without time delay in the presence of parameters mismatch. Other significant reports have also been devoted on the adaptive-observer synchronization schemes to solve this problem using different time-delay chaotic systems [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Among these, [PERSON] et al. [16], [PERSON] et al. [19] and [PERSON] et al. [20] have discussed some approaches on synchronization of two coupled delayed systems with parameters mismatch under particular certain coupling strength for the delayed Lur'e systems.  
Upon these challenges, one of the solutions for the synchronization in the CBSR system is the Voltage-Control-Oscillator (VCO), which can be used for FM modulation in radar applications and by converting the frequencies of a base-band chaotic source system to microwave frequencies. The output frequencies are linearly changed with applied  
Figure 3: An example of a modern stealth Radar and IRST.  
input to VCO and the constant amplitude of the output microwave-signal. The frequency modulation method (FM) describes many characteristics such as the low eventuality of interception or detection in a radar system, the lower effect of jamming or noise, and less interjecting with other channels [4; 10]. The authors focused on microwave chaos signal practically created by the Colpitts oscillator and directly sent through a wide-band antenna without modulation, since direct (i.e., without modulation) chaotic radar remains a major system in the research field [3; 7].  
Referring to the essential design criteria for a chaotic radar system, the main contributions in this study are summarized as follows:  
* A new 0.3 GHz mono-static microwave chaotic radar is proposed based on a time-delay to generate and process frequency modulated (FM) waveforms. Tuning the right value for the loop gain (G) is carefully set in the Phase-Locked Loop (PLL) in order to reflect more reliable signal recovery.
* The finding indicates that such a radar system can be implemented with no need to complete self-synchronization or complex projective synchronization.
* Obtained results reveal the robustness of chaotic monostatic radar under various noise levels in terms of short-time cross-correlation of the transmitted and reconstructed waveforms.
* The proposed indirect mon-static chaotic radar system is considered as a state-of-the-art in a secure communication application.