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Wireless Communication Demonstration in Hardware Using an Exactly Solvable Chaotic System
Keywords: Chaos, Communcation, Oscillator
Initially, the area of chaos was primarily studied by mathematicians and physicist in order to help describe or model physical, chemical or naturally occurring phenomena. This motivation has now shifted towards taking advantage of the inherent properties found in chaos for various applications, such as communication systems, radar, random number generation (RNG), and noise signal generation. Some of the advantageous properties include continuous power spectral density for communication, radar and noise signal generation. In particular, communication systems can utilize the spread spectrum properties in order to minimize the detectability of the signal. This is because the transmitted power is spread out over a large range of frequencies, which gives the illusion of an increase in the noise floor. There is a large amount of theory involved in taking advantage of chaotic dynamics; however, there is room for applying these to real world systems. A wireless communication system based on an exact solvable chaotic equation has been demonstrated. The system consists of a data input section, a chaos oscillator controller, an exact solvable chaotic oscillator, an AM wireless communication system, a matched filter and a data output section. The information to be transmitted is typed via a keyboard from a desktop computer, which is provided the serial input on a ST microcontroller for the input data and the output data from the communication system. The exact solvable chaotic oscillator has a fundamental frequency of approximately 18.4 kHz. It produces a baseband chaotic signal using a single transistor sinusoidal oscillator circuit where the signum function based nonlinearity is generated using operational amplifiers (op amps), comparators, and digital logic devices. The oscillator is controlled into two distinct orbits, representing 1s and 0s, using proportional feedback control. This type of control compares the measured waveform with a desired waveform and applies a voltage pulse that is proportional to the magnitude of the difference between these two waveforms. This voltage pulse is then applied at regular intervals to the chaotic waveform in order to steer the trajectory to the desired waveform. A standard amplitude modulated (AM) transmitter up converts the chaos modulated signal onto a 2.3 GHz carrier for wireless transmission to a receiver that down converts it back to baseband. The required components include a voltage controlled oscillator (VCO), low noise amplifiers (LNA), mixers, active power detector, band pass filter (BPA), low pass filter (LPF), and an active 50Ω matching network. A matched filter for the exactly solvable system has been previously developed. The matched filter was previously developed utilizing the exact analytical solution, which is written as a linear convolution of a fixed basis function. This was shown that the matched filter could be written as a delay differential equation. The electronic matched filter was realized using a difference amplifier, analog integrator and utilizes all pass filters to generate the necessary delay circuit that to recovers the information from the received signal. This matched filter waveform is sampled by a ST microcontroller that communicates over a serial bus to recover the encoded information.
D. Aaron Whitney,
Auburn University
Auburn, Alabama

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