An Electronic Implementation of Lorenz Chaotic Oscillator Synchronization for Bistatic Radar Applications

The authors report the simulation and actual implementation of chaotic oscillator synchronization for a pair of three-state variable Lorenz systems. The first oscillator performs as a driver (transmitter), while the second system is made to respond the received waveform. Specifically, one of the state variables of the driver circuit is judiciously selected to generate an RF waveform. This waveform is transmitted through a noisy channel and is used to drive the response system until both the systems of all three state variables achieve complete replacement synchronization. It is known that this synchronization is sensitive to changes in received power. To overcome this, a technique hereon called generalized projective synchronization is employed to accept an attenuated version of the transmitted waveform. A sensitivity analysis reveals that generalized projective synchronization is robust with respect to deviations in the control parameter values of the response system due to tolerances of electronic components. The potential of the generalized projective synchronization is illustrated for a bistatic radar system case, where synchronization is necessary to obtain the range-Doppler information of a moving target. In this instance, the cross correlation, short-time cross-correlogram and cross ambiguity surface of the transmitted and synchronized waveforms are of high quality as indicated by their entropy measures.