Communicating with chaos

Communicating with chaosChaos theory provides secure communication where signal transmissions are indistinguishable from background noise. Roy Rubenstein. Chaotic communications sounds like just the sort of activity the military would wish to avoid. Yet the US army has just awarded a research contract to investigate just that. Chaos theory promises the ultimate in secure communications, enabling signal transmissions which are indistinguishable from background noise (see Electronics Weekly, February 21, 1996). While the US military is interested in secure communications, the motivation for the research is more fundamental:to explore how non-linear dynamics, and chaotic techniques in particular, can be applied to common communication tasks like signal encoding, encryption and modulation. Moreover, the theory will also be practically applied in the form of a basestation demonstrator using chaotic techniques for wireless and optical communications. Shown is the circuit diagram of two coupled chaotic generators. Each circuit comprises a non-linear gain block and a linear feedback loop. If the circuit parameters in the two are matched, the two circuits evolve into perfect synchronisation. If the parameters differ slightly, as they will do in practice, the circuits remain synchronised in a general sense, with small chaotic deviations that are seen as system noise. Why does it work? Synchronisation between transmitter and receiver is key if a communications system – and a chaotic one at that – is to work. Otherwise all the careful signal encoding and modulation counts for nothing. Characterised by its irregular and unpredictable nature, chaos and synchronisation appears at first a contradiction. However, the essential feature is that chaotic oscillators are auto-synchronising. “There are directions in multidimensional space that are stable and those that are not,” said Professor Abarbanel. “Operation relies on the signal in the receive system being drawn back into synchronisation if it starts to drift. And when it is not drifting, it is inherently unstable. It is this instability that gives the wide bandwidth and offers the potential for enhanced security.” The suggested enhanced security is because instability implies non-periodicity and any noticeable pattern to a transmission helps in its uncovering. Also the combination of stable and unstable directions is unique to non-linear algorithms and no one has yet come up with ways of cracking them, claims Abarbanel. The research is being undertaken at the University of California, San Diego and University of California, Los Angeles and at California-based Stanford University. “Chaotic techniques promise low cost, low power transmitters and receivers, combined with more efficient use of available bandwidth,” said Henry Abarbanel, a physics professor involved in the research at the University of San Diego’s Institute of Non-linear Science. The low cost comes from feeding the data or analogue signals to be sent into a simple chaotic oscillator made from resistors, capacitors, inductors and a non-linear device such as a diode,” said Abarbanel. The more efficient bandwidth usage stems from the underlying broadband nature of chaotic signals. Like with code division multiple access (CDMA), the transmissions use all the channel’s bandwidth while the dynamic range is shared between the signals. Abarbanel describes chaotic signals as having a structure in ‘multidimensional space’. “Continuous wave signals have amplitude and phase; chaotic signals typically have three, four or five dimensions, but always more than two,” he said. A chaotic communication system requires that the receiver has an identical, or near-identical, structure to the transmitter. Communication is possible because the transmitter and receiver are auto-synchronising (see box) – the receiver adopts the state of the transmitter and follows deviations caused by the transmitted input message. Distortion on the received signal represents the modulation (ignoring channel distortion). The research project is a three-year one, with the option for a two-year extension.

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