Chaotic communications that are difficult to detect

Chaos Based Frequency Modulation for Joint Monostatic and Bistatic Radar-Communication Systems

In this article, we propose the utilization of chaos-based frequency modulated (CBFM) waveforms for joint monostatic and bistatic radar-communication systems. Short-duration pulses generated via chaotic oscillators are used for wideband radar imaging, while information is embedded in the pulses using chaos shift keying (CSK). A self-synchronization technique for chaotic systems decodes the information at the communication receiver and reconstructs the transmitted waveform at the bistatic radar receiver. Using a nonlinear detection scheme, we show that the CBFM waveforms closely follow the theoretical bit-error rate (BER) associated with bipolar phase-shift keying (BPSK). We utilize the same nonlinear detection scheme to optimize the target detection at the bistatic radar receiver. The ambiguity function for both the monostatic and bistatic cases resembles a thumbtack ambiguity function with a pseudo-random sidelobe distribution. Furthermore, we characterize the high-resolution imaging capability of the CBFM waveforms in the presence of noise and considering a complex target.

Fast high-quality numerical shadowing of chaotic maps using synchronization

For a chaotic, dynamical system, a typical noisy trajectory diverges exponentially from the true trajectory with the same initial conditions. Nonetheless, the noisy trajectory, as representative of the dynamical system, may have credibility if there exists a true trajectory, corresponding to a slightly different initial condition, that stays close to the noisy trajectory for long periods of time. For finding such shadowing trajectories, a synchronization based method is presented. We call it the synchronize-and-pullback algorithm. Several numerical examples are shown illustrating the method. Finally, an application of the proposed shadowing technique for noise filtration in the context of communication is presented.

Synchronizing chaotic maps using an arbitrary scalar signal

A method we call the slide-and-match algorithm is presented whereby any transmitter-receiver pair of identical, chaotic maps may be synchronized using almost any scalar function of the driving transmitter state, transmitted to the receiver as the synchronizing signal. No prior investigation of either the map or the signal generating function is required. In order to illustrate the concepts, numerical simulations of applications are presented.

Chaotic system for self-synchronizing Doppler measurement

In a radar system, it is necessary to measure both range and velocity of a target. The movement of the target causes a Doppler shift of the radar signal, and the size of the Doppler shift is used to measure the velocity of the target. In this work, a chaotic drive-response system is simulated that detects a Doppler shift in a chaotic signal. The response system can detect Doppler shifts in more than one signal at a time.

Chaotic control and synchronization for system identification

Research into applications of synchronized chaotic systems assumes that it will be necessary to build many different drive-response pairs, but little is known in general about designing higher dimensional chaotic flows. In this paper, I do not add any design techniques, but I show that it is possible to create multiple drive-response pairs from one chaotic system by applying chaos control techniques to the drive and response systems. If one can design one chaotic system with the desired properties, then many drive-response pairs can be built from this system, so that it is not necessary to solve the design problem more than once. I show both numerical simulations and experimental work with chaotic circuits. I also test the response systems for ability to overcome noise or other interference.