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.

Date Published: 21 May 2015
PDF: 11 pages
Proc. SPIE 9461, Radar Sensor Technology XIX; and Active and Passive Signatures VI, 94610Z (21 May 2015); doi: 10.1117/12.2177417

Published in SPIE Proceedings Vol. 9461:
Radar Sensor Technology XIX; and Active and Passive Signatures VI
G. Charmaine Gilbreath; Kenneth I. Ranney; Armin Doerry; Chadwick Todd Hawley, Editor(s)