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Design and Implementation of a Communications System Using Chaotic Transmissions That Operate Over a Noisy Channel at Significant Distances, 10-9134

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Principal Investigator
Arthur Fleming-Dahl
Business Development

Inclusive Dates: 04/01/99 - Current

Background - Message modulation and encoding using nonlinear chaotic signals is a research area of interest and growth because chaotic processes exhibit several natural characteristics beneficial to communications systems. Two key features of chaos are a noise-like time series, termed deterministically random motion, and a sensitive dependence on initial conditions, also known as the butterfly effect. The deterministically random motion causes chaotic transmissions to have a low probability of detection as an information-bearing signal and the butterfly effect results in a low probability of intercept. These features, although attractive to communications systems designers, complicate receiver design, especially from the standpoint of synchronizing a receiver to the transmitted waveform in the presence of random noise and signal-level variations. Several techniques for achieving chaotic synchronization, as well as various chaotic data modulation methods, have been investigated with some success. A fundamental limitation that has historically plagued such efforts is the sensitivity of the chaotic processes to amplitude, which is related to sensitive dependence on initial conditions and is a communications killer for chaotic methods. The resulting intolerance of chaotic receivers to propagation path losses or transmitter amplification has prevented chaotic communications from becoming more than a laboratory curiosity.

Approach - The primary purpose of this project was to develop an approach that overcomes the extreme sensitivity of chaos-based receivers to received signal amplitude. Prior work by the principal investigator that resulted in a new chaotic receiver design approach also produced several interesting observations about the properties of chaotic signals corrupted by noise. It was anticipated that this information could be exploited to estimate the noise content or the chaotic amplitude content of the received noisy chaotic signal. The amplitude of the received signal could then be adjusted to the optimal levels for the chaotic signal processing in the receiver. It was further desired to develop a hardware demonstration of the resulting system to physically prove the viability of fielding chaotic communications systems. This secondary goal required an initial conversion of the algorithms from the high-level mathematics language in which they were developed to the ubiquitous C programming language. The C-code could then be passed through a software translator to generate assembly language for a digital signal processing (DSP) chip. A final objective was the alignment of the bit decision boundaries in the receiver with the bit transition boundaries generated in the transmitter. Since multiple chaotic iterates represent a single data bit, it is necessary to determine the proper grouping of received iterates to process data bit decisions at the correct times. While the correct timing can be rigged to demonstrate the first two objectives, receiver operation with random active times requires the ability to achieve bit interval timing automatically.

Accomplishments - The sensitivity of chaotic receivers to amplitude variations has been solved by an innovation called the signal amplitude restorer. Its roots lie in a unique signal-to-noise ratio (SNR) estimator developed previously by the principal investigator for a new chaotic receiver architecture. When coupled with a running average received signal power estimator (signal-plus-noise) and a variable gain control, the necessary gain or attenuation was introduced to adjust the received signal amplitude to the optimal levels required by the receiver chaotic process algorithms. The receiver with uncorrected signal levels lost synchronization at +/- 3-dB signal level variation, while the augmented receiver retained synchronization at all levels tested between +200-dB and -200-dB signal level variation without exhibiting algorithmic limits. This capability was demonstrated down to 0-dB SNR, or equal signal power and noise power.

Note that 200-dB loss occurs over 147,000 miles at 1 gigahertz, which establishes the ability for chaotic communication beyond the moon. Chaotic receivers can now handle any propagation loss or transmitter amplification within the power-handling capability and sensitivity of the receiver front end. The conversion of the algorithms from the original high-level mathematics language to C-code is complete. The subsequent translation to assembly language by a special compiler and implementation in digital signal-processing hardware is underway.

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Signal amplitude restoration accuracy and consistency for 200-dB loss through 50-dB gain (-50-dB loss), at 3 dB SNR. The red dashed line shows programmed levels, with corrections shown by the blue traces.

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Top Trace: Signal-to-noise ratio estimate accuracy at 3-dB SNR. Bottom Trace: Close-up of correction at 200-dB loss in the presence of noise characterized by 3-dB SNR. The red dashed line shows programmed levels, with estimations and corrections shown by the blue traces.

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