Chaos could improve performance of wireless communication systems

May 13, 2013 by Lisa Zyga feature
Researchers have found that the information transmitted by a chaotic signal in a wireless communication system is not modified by the wireless channel as it is for non-chaotic signals. These figures show reconstructions of wireless signals traveling in different wireless channels. Credit: Hai-Peng Ren, et al. ©2013 American Physical Society

( —In today's wireless communication systems, the wireless signals are non-chaotic, meaning they have a well-defined period and frequency. Non-chaotic wireless signals are used in many applications, such as satellite communications, GPS navigation, cell phones, and Wi-Fi devices. However, as many people know first-hand, wireless systems usually have inferior performance compared to wired systems. The problem is due to physical impediments that the wireless signal faces in open space caused by the atmosphere, water, mountains, buildings, and other different media. Now in a new study, researchers have investigated how wireless communication could be implemented with chaotic signals, and found that chaotic signals could overcome some of these physical constraints and lead to superior performance.

The researchers, Hai-Peng Ren at Xi'an University of Technology in Xi'an, China, and the University of Aberdeen in Aberdeen, UK; Murilo S. Baptista at the University of Aberdeen; and Celso Grebogi at Freiburg University in Freiburg, Germany, have published their paper on with chaos in a recent issue of Physical Review Letters.

Although this is the first time that researchers have investigated how chaotic signals can be used in a wireless communication system, there has been a large amount of research on using chaotic signals in wired . The use of chaos in communication systems is appealing due to several intrinsic properties of chaos and the fact that chaotic signals can be generated by low-power, low-cost, small-area .

"A chaotic signal is generated by a non-linear system that has sensitivity dependence on initial conditions," Baptista, on behalf of his coauthors, told "Small perturbations in the system at a given time produce large changes at a later time—a property that is measured by the Lyapunov exponent. A chaotic signal has at least one positive Lyapunov exponent (two nearby initial conditions diverge exponentially fast from each other), but also negative ones. A chaotic signal is also aperiodic and broadband (it processes infinitely many frequencies). This last property is the consequence of the fact that a chaotic trajectory stays very close to an infinite set of periodic signals of infinitely many periods.

"A non-chaotic signal, such as a periodic one, is characterized by having a well-defined period (it always returns after completing one period; it is not aperiodic), it is generated by a system that does not have sensitivity to initial conditions, and it has only one well-defined frequency (not broadband)."

Scientists have previously shown that chaotic signals in wired communication systems can achieve higher bit rates (resulting in faster information transmission) in a commercial wired fiber-optic channel compared with non-chaotic signals.

In the new paper, the scientists' main result is that, although a chaotic signal itself is strongly modified by the wireless physical media through which it propagates, the information transmitted by the signal is not modified. That is, the information remains exactly the same when it is picked up at the receiver as it was when it was sent by the transmitter, despite having traveled through open space.

The researchers attribute this finding to the fact that chaotic signals preserve their spectra of positive Lyapunov exponents after being transmitted through wireless channels. The researchers also calculated that the amount of information in a transmitted chaotic signal is equal to its positive Lyapunov exponent, allowing them to determine a chaotic signal's information capacity.

"The fact that the positive Lyapunov exponent(s) of any chaotic signal is (are) preserved in the wireless channel means that the information transmitted arrives to the receiver and is available to be 'collected' (decoded)," Baptista said. "Decoding is possible because the negative Lyapunov exponents are also preserved, and allow us to use chaotic signals that, despite being modified, preserve their topological form (dimension)."

This capability of chaotic signals to propagate through open space while preserving their information is very different from the behavior of non-chaotic signals, where both the signal and the information it carries are modified by the physical media. One of the biggest causes of modification is multipath propagation, which occurs when a signal is disrupted so that it travels along many different paths and arrives many times at the receiving location. Interference and noise occur as a result, preventing information from being transmitted at a high bit rate. Multipath propagation is caused by reflection and refraction from the atmosphere, water, and terrestrial objects.

As the researchers explain, wireless chaotic signals are not affected by multipath effects. This is because a chaotic signal that is used to communicate wirelessly has an information capacity (the amount of information per unit of time) that depends on the Lyapunov exponents of the signal—which is a property of the chaotic signal itself—but does not depend on the properties of the physical wireless channel, i.e., the multipath. It is as if multipath does not exist in the wireless channel. On the other hand, the amount of information per unit of time that can be transmitted wirelessly using non-chaotic signals depends on the properties of the multipath. As a result, chaos provides a natural way to create high-capacity communication systems.

The researchers are currently developing a prototype chaos-based wireless communication system based on the ability of wireless chaotic signals to preserve their Lyapunov exponents after transmission. They predict that it will possible to develop a large-scale -based that would have excellent performance by overcoming the interference and noise that negatively affect today's non-chaotic .

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More information: Hai-Peng Ren, et al. "Wireless Communication with Chaos." PRL 110, 184101 (2013). DOI: 10.1103/PhysRevLett.110.184101

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1 / 5 (4) May 13, 2013
The researchers are currently developing a prototype chaos-based wireless communication system based on the ability of wireless chaotic signals to preserve their Lyapunov exponents after transmission. They predict that it will possible to develop a large-scale chaos-based wireless communication system that would have excellent performance by overcoming the interference and noise that negatively affect today's non-chaotic wireless signals.

This is an amazing research in developing to improve quality in wireless (radio) communication since it was first done by changing from AM to FM system; anyway the theoretical basic concept is the same in which the working mechanism is still in mystery until …..
5 / 5 (2) May 13, 2013
You've got to be kidding me vacuum-mechanics. Do you believe that as long as you persist, someone will eventually listen? and it will make a magical and romantic story for the ages? get a life.
1.8 / 5 (5) May 13, 2013
This isn't a new technique. Back in the 1980's spread spectrum communication achieved similar results by similar means. (Except it used an analogue mixer/modulator back then) http://en.wikiped...nication
Using a pseudo-random number generator as your local oscillator you were effectively modulating wideband noise for transmission. It had the same benefits as this "chaotic" system: i.e. multipath and co-channel noise immunity. You could even transmit undetectably below the noise floor of conventional AM/FM signals. Only someone with the same pseudo random numbers generator could auto-correlate and demodulate the transmission.(So the Military were rumoured to be interested in its use.)
5 / 5 (1) May 13, 2013
Only someone with the same pseudo random numbers generator could auto-correlate and demodulate....
They were also rumored to be a lot harder to target with anti-radiation munitions.
1 / 5 (1) May 14, 2013
EyeNStein, you think this is equivalent to your fathers spread spectrum why?

1 / 5 (4) May 14, 2013
Don. If you look at the frequency spectrum of the spread spectrum signal, it too is a wideband chaotic white noise. Both swap a narrow single carrier with sidebands which is susceptible to coherent interference like multipath reflections or adjacent channels for an extremely wideband pseudo random chaotic signal.
Both are immune to interference because of the highly specific way the chaos is taken back out by the receiver to recover the signal..
not rated yet May 14, 2013
Direct Sequence Spread Spectrum.
Code Division Multiple Access.

It would have been nice if the authors included a discussion of what makes their different.
5 / 5 (1) May 14, 2013
Am I reading this wrong or are they trading off bandwith for better reception? Seems that using chaotic signals would mean a lot more crosstalk between neighboring channels.
5 / 5 (1) May 14, 2013
They hint at the noise having infinite bandwidth which makes it white noise with a delta function for its autocorrelation function.
This just means any segment of the white noise when correlated with another segment has a result that is expected to be zero in the statistical sense. If simultaneous channels use different wide band noise or chaos they can be recovered independently even while sharing the same spectrum.

And yes it is bandwidth traded for better reception, the signal power is spread out in frequency.
not rated yet May 14, 2013
Going ONLY from the title of this article, wifi transmission within the area of my home should have efficiencies far greater than 100%...
1 / 5 (1) Jun 11, 2013
Information carrier is the phase space of chaos - independent of energy or mass.