Analysis of chaotic FM system synchronization for bistatic radar

Abstract

We propose a scheme for bistatic radar that uses a chaotic system to generate a wideband FM signal that is reconstructed at the receiver via a conventional phase lock loop. The setup for the bistatic radar includes a 3 state variable drive oscillator at the transmitter and a response oscillator at the receiver. The challenge is in synchronizing the response oscillator of the radar receiver utilizing a scaled version of the transmitted signal s r (t, x) = αs t (t, x) where x is one of three driver oscillator state variables and α is the scaling factor that accounts for antenna gain, system losses, and space propagation. For FM, we also assume that the instantaneous frequency of the received signal, x s , is a scaled version of the Lorenz variable x. Since this additional scaling factor may not be known a priori, the response oscillator must be able to accept the scaled version of x as an input. Thus, to achieve synchronization we utilize a generalized projective synchronization technique that introduces a controller term -μe where μ is a control factor and e is the difference between the response state variable x s and a scaled x. Since demodulation of s r (t) is required to reconstruct the chaotic state variable x, the phase lock loop imposes a limit on the minimum error e. We verify through simulations that, once synchronization is achieved, the short-time correlation of x and x s is high and that the self-noise in the correlation is negligible over long periods of time.

Synchronization of Monostatic Radar Using a Time-Delayed Chaos-Based FM Waveform

“…Regardless of the target's altitude, they can identify stealthy and small targets at very long ranges. Although such radars have disadvantages, such as massive antennas, immobility, and a large quantity of clutter, they are nonetheless highly effective against stealth ships and stealth aircraft when deployed on the ground [9,10,14].…”

“…However, most conventional radars are basically designed to operate on the microwave frequency band between 300 MHz (1 m) and 300 GHz (1 mm). On the other hand, several chaos radar systems have been designed and implemented for various secure communications [7][8][9][10]; they may employ coherent signal processing schemes either by matched filter or correlation to reduce the noise and eventually obtain the highest improvement in Signal-to-Noise Ratio (SNR) [7,11]. Another issue in chaotic based radar systems (CBRS) is choosing the type of chaos synchronization between the transmitter and the receiver nodes.…”

“…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, Liu et al [16], He et al [19] and Huang 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.…”

“…The output frequencies are linearly changed with applied 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].…”

Synchronisation of bistatic radar using chaotic AM and chaos‐based FM waveforms

“…This includes a mixer, a low‐pass filter (LPF), an amplifier and a voltage control oscillator (VCO) [30]. The output of the VCO is proportional to the instantaneous frequency of the transmitted FM waveform [31]. Thus, the recovered frequency is an estimate of the chaotic state variable x ( t ) and is represented as .…”