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 - 09/30/00

Background - Message modulation and encoding using nonlinear chaotic signals is a contemporary research area of interest and growth because chaotic processes exhibit several natural characteristics beneficial to communications systems. Two key features of chaos include a noise-like time series, termed deterministically random motion, and a sensitive dependence on initial conditions, known colloquially as the butterfly effect. These items cause chaotic transmissions to have a low probability of detection as an information-bearing signal and a low probability of intercept.

The same features that are attractive to communications systems designers also 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 plagued such efforts, however, is the sensitivity of the chaotic processes to amplitude. This characteristic is related to sensitive dependence on initial conditions, and has historically served as the death knell for chaotic communications methods. The resulting intolerance of chaotic receivers to propagation path losses or transmitter amplification has prevented chaotic communications from moving beyond the status of laboratory curiosity.

Approach - The main 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 had also produced several interesting observations concerning 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 statistically optimal levels required 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 chip.

A final objective was the alignment of the bit decision boundaries in the receiver with the bit transition boundaries generated in the transmitter. Because 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 - All project technical goals were met. Chaotic communication was shown to be possible over arbitrarily large distances, data bit boundary alignment was achieved via matched filter techniques, and a data rate exceeding 10 kilobytes per second was achieved. A hardware demonstration was constructed to show the viability of chaos as a tool for secure communications, as well as the capabilities of the new digital signal-processing methods developed having application to chaotic and conventional communications systems.

Figure 1. Top level block diagram of Signal Amplitude Restorer

The most significant problem solved was the sensitivity of chaotic receivers to amplitude variation by a digital signal-processing algorithm called the Signal Amplitude Restorer. The prior development of a new chaotic receiver had produced a novel signal-to-noise ratio (SNR) estimator. When coupled with a received signal power estimator (signal-plus-noise) and a variable gain control in a feedback loop as seen in Figure 1, the necessary gain or attenuation was introduced to adjust the received signal amplitude to the statistically 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 between ±200 dB. Chaotic receivers can now handle any propagation loss or transmitter amplification resulting in a received signal within the dynamic range of the receiver front end. An example of the performance of the Signal Amplitude Restorer is shown in Figure 2 at 6-dB SNR.

(a) Signal level correction accuracy for 50-dB gain (-50-dB loss) through 200-dB loss 
  

(b) Top Trace: SNR estimation accuracy; Bottom Trace: Closeup of correction at 200-dB loss
  

Figure 2. Signal Amplitude Restorer performance at 6-dB Signal-to-Noise Ratio (Programmed levels - red, Corrections - blue)

A unique, previously unused digital data structure was implemented to address analog/digital conversion issues. This structure enabled minimum receiver data rate operation, obviated the need for the common technique of oversampling and the concomitant large received signal buffers, and provided the opportunity for received value corruption elimination via the digital technique of linear prediction. At the same time, it minimized transmit power requirements, resulting in longer battery life for unplugged applications. An example of the resulting decidedly noise-like chaotic baseband signal is shown in Figure 3.

Figure 3. Noise-like baseband chaotic signal

The amplitude restoration algorithm does not depend on chaotic characteristics, but rather exploits the probability density function of a signal. All signal and modulation methods possess probability densities, making the algorithm applicable to every known method of telecommunication. Because it accurately achieves statistically optimal receiver signal levels, it can improve the performance of existing receiver technology.

A proposed application of the Signal Amplitude Restorer to receivers with phase-locked-loops is the removal of noise from the received signal. Based on the results with chaotic signals, significant noise reduction is possible with concomitant improvements in:

  • Signal-to-noise ratio

  • Jam resistance

  • Stealth (less transmit power for same received fidelity)

  • Message bit error rate

  • Communications distance

  • Data rate

A second proposed use is the removal of tone interference without sacrificing the spectral content of the message signal, as occurs with contemporary techniques such as notch filters.

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