Design and Implementation of a
Communications System Using Chaotic Transmissions That Operate Over a Noisy Channel at Significant Distances, 109134
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Principal Investigator
Arthur FlemingDahl
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 noiselike 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 informationbearing 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
signallevel 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 chaosbased 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 highlevel mathematics
language in which they were developed to the ubiquitous C programming language. The Ccode
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
signaltonoise 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 (signalplusnoise) 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 +/ 3dB signal level variation, while the augmented
receiver retained synchronization at all levels tested between +200dB and 200dB signal level variation without exhibiting algorithmic limits. This
capability was demonstrated down to 0dB SNR, or equal signal power and noise power.
Note that 200dB 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 powerhandling
capability and sensitivity of the receiver front end. The conversion of the algorithms
from the original highlevel mathematics language to Ccode is complete. The subsequent
translation to assembly language by a special compiler and implementation in digital
signalprocessing hardware is underway.
Signal amplitude restoration accuracy and
consistency for 200dB loss through 50dB gain (50dB loss), at 3 dB SNR. The red dashed
line shows programmed levels, with corrections shown by the blue traces.
Top Trace: Signaltonoise ratio estimate accuracy
at 3dB SNR. Bottom Trace: Closeup of correction at 200dB loss in the presence of noise characterized
by 3dB SNR. The red dashed line shows programmed levels, with estimations and corrections shown by the
blue traces.
Electronic Systems and
Instrumentation Program
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