# Synchronization of Monostatic Radar Using a Time-Delayed Chaos-Based FM Waveform
###### Abstract  
There is no doubt that chaotic systems are still attractive issues in various radar applications and communication systems. In this paper, we present a new 0.3 GHz mono-static microwave chaotic radar. It includes a chaotic system based on a time-delay to generate and process frequency modulated (FM) waveforms. Such a radar is designed to extract high-resolution information from the targets. To generate a continuous FM signal, the chaotic signal is first modulated using the voltage control oscillator (VCO). Next, the correct value for the loop gain (G) is carefully set when utilizing the Phase-Locked Loop (PLL) at the receiver, so that the instantaneous frequency that reflects a chaotic state variable can be reliably recovered. In this system, the PLL synchronization and radar correlation are enough to recover the echo signal and detect the target. The finding indicates that the system can be implemented with no need to use the complete self-synchronization or complex projective synchronization schemes as compared to the existing chaotic radar systems. The simulation results show that the short-time cross-correlation of the transmitted and reconstructed waveforms is good and satisfactory to detect the target under various signal-to-noise ratio (SNR) levels and with less complexity in the design. synchronization; chaotic time-delay; Phase-Locked Loop (PLL); mono-static radar; Chaotic FM Radar +
Footnote †: journal: remote sensing  
0000-0002-4198-42000-0000-0000-0000-0000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-00000-000000-00000-00000-00000-00000-00000-00000-000  
Typically, chaotic signal (CS) is characterized as a deterministic broadband signal, has a structure, and the maximum Lyapunov exponent is greater than zero; meanwhile the noise is expressed as a random and non-deterministic signal [3]. As CS has distinct characteristics of unsystematic phase variation and broadband of power spectrum, so chaos radars can easily offer the key characteristics:  
* Chaotic signal using simple and inexpensive deterministic systems. * CS has featureless low-probability of intercept/low probability of detection (LPI/LPD) characteristics, and therefore it is hidden or invisible signal. * CS is inherently anti-jamming signal and interference resistant. * CS is spectrally very efficient and can share spectral bands without any mutual interference. Then chaotic radar may utilize coherent signal processing schemes either by matched filter or correlation in order to reduce the noise in the echo signal and detect the target successfully. In general, in radar systems, there are a number of transmitter/receiver (antenna) nodes that are designed to make the system operate either as monostatic, bistatic, or multi-static radar. Each radar system depends on the type of waveform, whether continuous or non-continuous (i.e., pulse wave) [2]. The radar is called monostatic radar if the transmitter and receiver are placed in the same place; otherwise, the radar is a bistatic or multistatic type if both transmitter and receiver(s) are separately located over a distance [4]. Figure 1 depicts the three types of radar systems. Figure 1: A type of radar systems (**a**) Monostatic (**b**) Bistatic and (**c**) Multistatic radars. However, the major drawback in these passive bistatic radars mainly suffers from the lack of control on the transmitting waveform. Meanwhile, the conventional monostatic defense radars have a shortage in detecting low radar cross-section (L-RCS) targets. Figure 2 illustrates the fundamental operation of mono-static radar systems. In fact, the RCS metric is the crucial measure that defines the reflectivity of the target measure; thus, a larger RCS means easier target detection because the RCS of any target depends on the radar's transmitted frequency. Thus, the long-wave radars (below HF) have more precision, with large RCS compared to HF, VHF, and UHF radars. More details are presented in [2; 5; 6].