21 May 2015 Analysis of chaotic FM system synchronization for bistatic radar
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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 sr(t, x) = αst(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, xs, 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 xs and a scaled x. Since demodulation of sr(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 xs is high and that the self-noise in the correlation is negligible over long periods of time.
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Chandra S. Pappu, Chandra S. Pappu, Berenice Verdin, Berenice Verdin, Benjamin C. Flores, Benjamin C. Flores, James Boehm, James Boehm, Patrick Debroux, Patrick Debroux, "Analysis of chaotic FM system synchronization for bistatic radar", Proc. SPIE 9461, Radar Sensor Technology XIX; and Active and Passive Signatures VI, 94610Z (21 May 2015); doi: 10.1117/12.2177417; https://doi.org/10.1117/12.2177417

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