Wireless Communication of a Chaotic Waveform

Abstract

Over the past couple of decades, mathematical equations have been developed that successfully model natural phenomena that occur in various fields such as chemistry, biology, and fluid mechanics. These equations, however simple, produce complicated solutions with occasional unpredictable behavior. Analysis and research of these models and other models that exhibit such response has been deemed ``chaos theory". One of the requirements for a system to be considered chaotic is that the system must be sensitive to initial conditions. The term ``chaos theory" implies that an exact outcome is incomprehensible, leading to a common assumption that an analytic solution is unattainable for chaotic systems. This expectation has since been refuted as an exact solution has been derived for some chaotic systems. This unlocked the potential for a chaotic system to be implemented in practical applications. One such novel technique has arisen in the form of an electronic circuit. This circuit has been designed to oscillate in a chaotic manner and possess an exact solution that can be calculated.

Due to sensitivity intrinsic to all chaotic systems, small perturbations can be used to control the chaotic oscillation. Because the chaotic oscillation can be controlled and its response determined, a circuit can be employed as a form of a modulator in encoding and encryption in communication systems. Common communication systems, subsystems and circuits are discussed along with analog modulation and demodulation techniques. A transmitting and receiving is circuit are detailed that successfully presents the transmission of a chaotic waveform in a wireless medium.