Synchronization of Bistatic Radar Using Chaotic Amplitude and Frequency Modulated Signals

The purpose of this work is to develop a synchronization scheme for bistatic radar that uses a 3-D chaotic system to generate and process wideband AM and FM signals, which allows for the extraction of high range-resolution information from targets. For AM bistatic radar, the setup includes a drive oscillator at the transmitter and a response oscillator at the receiver. The challenge is synchronizing the response oscillator to the drive oscillator with a scaled version of the transmitted signal sr(t, x) = αs t(t, x), where x is a chaotic state variable and α is a scaling factor. Here, α accounts for space propagation losses and may not be known a priori. Improving upon a generalized projective synchronization reported elsewhere, it is shown mathematically and verified through simulations that synchronization is achievable. Furthermore, the short-time cross-correlation of the driver and response state variables is consistent over long time intervals. However, synchronization is highly susceptible to noise and is not deemed suitable for practical applications. For bistatic FM radar, the setup transmits a wideband chaos-based FM (CBFM) signal scbfm(t) that is reconstructed at the receiver using a conventional phase locked loop. Demodulation of s cbfm(t) is the first step in recovering the chaotic state variable x. However, the phase locked loop imposes a limit on the minimum error between the instantaneous frequency of the transmitter and the instantaneous frequency recovered by the receiver. Since the recovered frequency is a scaled version of the Lorenz variable x, the transmitted instantaneous and recovered frequencies are synchronized by utilizing either generalized projective synchronization or complete replacement synchronization with an appropriate scaling. The synchronized output is then utilized to reconstruct the FM signal. As a result, the short-time cross-correlation of the transmitted and reconstructed signals is high and the self-noise in the correlation is negligible. To assess the quality of the reconstructed FM signal, an entropy analysis of the cross-correlogram was performed. Although the performance of the cross-correlogram degrades with noise, the entropy of the correlogram is low. Comparatively, bistatic FM radar performs better than bistatic AM radar using complete replacement synchronization