Abstracts for the " Workshop on Transmission of Chaotic Signals " Nonlinear Communications Strategies (o) the Transmission of Chaotic Signals in a Multipath Channel (p)

s for the “Workshop on Transmission of Chaotic Signals” 1-3 August 2006, University of Bristol, UK Key: (O) – oral presentation; (P) poster presentation. Underlined author is oral presenter. The order is alphabetic according to the presenting author. Nonlinear Communications Strategies (O) Henry Abarbanel UCSD Knowledge of nonlinear physical systems has matured enough that application to practical problems is both feasible and welcome. We discuss some ideas in using nonlinear dynamics in addressing issues in communications. These include methods for modulating and demodulating information on carriers produced by nonlinear systems and methods for equalizing unwelcome nonlinearities in the communications channel, in transmitters and receivers. In an era with cheap, powerful computation, many of these strategies could compete with mainstream, typically linear, approaches, depending on the application. The Transmission of Chaotic Signals in a Multipath Channel (P) P. R. Atkins University of Birmingham The purpose of this work was to investigate the practicalities of transmitting a chaotic signal between two drifting surface buoys in a shallow water channel. Inevitably, the received signal would suffer from the problems of multipath, amplitude variations and Doppler spreads associated with surface buoys in bistatic scenarios. The experiment used multiple carriers to transmit signals with differing degrees of aperiodicity. An accurate replica of the transmitted signal was required at the receiver – this was conveyed using Phase Modulation techniques. Amplitude Modulated signals were analysed for detection of any non-linearities. The conclusions are that the multi-carrier approach successfully permitted the resolution of phase-ambiguities in the replica transfer process and that no nonlinearities were detected in a shallow-water channel (as expected). SONAR – Where Next? (O) P.R. Atkins University of Birmingham Sonar technologies have developed in differing ways for historical and geographical reasons. For example, the American and United Kingdom forces have traditionally concentrated on blue-water applications using passive techniques, whereas the Scandinavians have concentrated on coastal areas, requiring active techniques. In all application areas, traditional Fourier-based signal processing techniques have dominated, as a result of their robust and predictable behaviour. The need for precise control of frequency and amplitude characteristics will be demonstrated for systems used under typical operating conditions. The reverberation encountered as a result of a multitude of acoustic scatterers implies that continuous transmission sonar systems (as proposed by the chaotic signal proponents) find very few practical applications in sonar. However, the desired energy characteristics of a sonar transmission will be considered for underwater communication and picket-fence applications. Alternative target detection techniques such as DEMON processing will be briefly considered with a view to their exploitation by new transmission types. Finally, as it would appear that the majority of current military threats are land-based, consideration will be given to how sonar engineers might deploy their skills in urban environments. Chaotic signals in radar and sonar: impact of the embedding optimisation (P) Lanthao Benedikt, School of Computer Science, Cardiff University A number of recent studies have been focussed on applying chaotic signals to radar and sonar. Most of the proposed detection techniques are based on phase space reconstruction, using the Takens' time-delay embedding which is not optimal. In fact, this embedding often contains redundancies and uninformative elements; therefore the phase space reconstruction requires a large amount of data and a high computing cost. To overcome such drawbacks, we propose a method to determine the optimal embedding of the time series. We use a metric of determinism to quantify the extent to which an embedding is able to describe the underlying system, and thus we can eliminate the irrelevant elements. In this poster, we present three implementations of our method, based on three different metrics of determinism, e.g. mutual information, the continuity statistics and the Gamma statistics. Experiments are carried out on real-world data such as the Santa Fe Laser data, and also on artificially generated sonar data. Chaos in underwater acoustics and its application to sensing (O) Tamas Bodai, Alan Fenwick, and Marian Wiercigroch 1 Centre for Applied Dynamics Research, Department of Engineering, King's College, University of Aberdeen 2 QinetiQ Deep ocean sound propagation is studied to assist the design of a long range low frequency sonar [1]. Ray paths are refracted by sound speed variation in depth and range. In the deep ocean, a sound speed minimum in depth creates a wave guide, or duct, in which the stability of ray paths aspects the efficiency of signal transmission. When sound speed varies only with depth, the ray paths are governed by a 2D autonomous Hamiltonian system of equations, with range as the independent variable. The dependent variables are depth of ray path and the tangent of its angle to the horizontal. In such an environment all ray paths are regular, i.e. not chaotic. We are interested in range-dependent sound speed structures, especially in those with a transition from a singleto a double duct profile [2]. Often there is another type of range-dependence, namely, quasiperiodic range-dependent perturbation of the background sound speed. These are known as internal waves, and it has been shown that they allow ray chaos. Hamilton's equations obey KAM-theorem, which guarantees the existence of regular trajectories for a sufficiently small perturbation. In the case of transition, a ray which is regular before the transition zone may become chaotic after it. It is of general interest to relate the regular and chaotic sections of rays. For this, we numerically explore phase space and discover what state the rays have after transition, using the no transition case as a reference. We can ̄ nd a set of initial conditions called the launching basin, from which rays stay regular even after transition. Beside this direct analysis, we are developing new nonlinear dynamics tools to measure stability of wave propagation, to utilize it at sonar designing [3]. [1] Michael G Brown, John A Colosi, Steven Tomsovic, Anatoly L Virovlyansky, Michael AWolfson and George M. Zaslavsky, “Ray dynamics in long-range deep ocean sound propagation" J. Acoust. Soc. Am. 113 (5), 2533-2547 (2003) [2] M. Wiercigroch, A. H-D. Cheng, J. Simmen, M. Badiey, “Nonlinear behavior of acoustic rays in underwater sound channels" Chaos, Solitons & Fractals 9, 193-207 (1998) [3] Alexander Balanov, Natalia Janson, Charles Wang and Marian Wiercigroch, “Multiple delay differential systems in a sensing problem", study group report from the 43rd European Study Group with Industry, Lancaster 2002 UWB Communication Using Fractal Signals (P) V. N. Bolotov, Yu. V. Tkach Institute for Electromagnetic Research, Kharkov, Ukraine In recent years, the electromagnetic environment has radically changed worldwide because of numerous sources of high-power electromagnetic signals, which interfere with information-carrying signals and, thereby, considerably distort them. As a result, a wide-band background electromagnetic field is present in the environment, with its strength often much higher than that of natural electromagnetic fields. Such a situation places more stringent requirement on transmitting/receiving equipment and its operational maintenance. Therefore, of primary concern in the design of modern communications is to ensure a high immunity against different types of noise. A solution to this problem may lie in using those systems handling fractal wide band (FWB) signals. This type of UWB signals has multiband fractal spectra with exact top and lower boundaries. The maximum width of FWB signal spectrum is 640 MHz. FWB signals are not only ensuring a high protection of information against electromagnetic fields but also prevent unauthorized data detection. Fractal signals were generated and transmitted (in air or via 50 m cable) with a carrier at 2 GHz. Using FWB signals and recent advances in electronic technologies a new fractal communication system was created and successful experiments were carried out. Using a Phase Space Statistic to Identify Resonant Objects (O&P) Thomas L Carroll US Naval Research Labs. Conducting objects have natural resonances when driven by electromagnetic waves. The resonances occur when some dimension of the object is equal to a half integral number of wavelengths of the electromagnetic wave. Since the resonance frequencies depend on the size and shape of the object, they may be used to identify the object. The standard technique for finding these resonance frequencies is to emit a large electromagnetic impulse, which causes a transient ringing response from the object. There are problems with this method, which limit its practical application. I have developed a method based on the Kaplan-Glass phase space statistic that is sensitive to the phase shifts imposed by resonance, and has some practical advantages over the impulse technique. The phase space statistic works with a variety of different signals, which may be chaotic or non-chaotic. A Chaotic Radar Demonstration System (O&P) Josh Slater,Kawika Maunupau, Peter Paras, Amir Adibi, Matt Totino, Andrew Chin, Karl Janich, John Molinder; Samuel S. Osofsky, Albert M. Young, Christopher P. Silva; 1 Department of Engineering, Harvey Mudd College, Claremont, California, USA; 2 Communications and Networking Division, The Aerospace Corporation, El Segundo, California, USA Chaotically generated analog waveforms have certain properties that make them advantageous for use in a radar system. One such property is the noise-like nature of the signal. Using a chaotic signal that is spread over several hundred megahertz of bandwidth would make the transmitted signal difficult to detect by a target object. The Aerospace Corporation’s Harvey Mudd College Engineering Clinic Team has developed a proof-of-concept of a radar system that is based on the Young-Silva Chaotic Oscillator, which is capable of generating a chaotic waveform with approximately 200 MHz of bandwidth. Development of this radar system consisted of detailed spectral analysis of the chaotic signal, including the effects of different methods of signal conditioning on the autocorrelation of the chaotic signal, which is the backbone calculation for range determination. Steps have been taken to narrow the width of the main autocorrelation peak and to lower the levels of adjacent peaks, which will help to improve the range resolution of the system. Development of the proof-of-concept system has required significant hardware design to achieve modulation, pulsing, and amplification of signals. Modulation and demodulation are achieved through the use of phase-locked loops built up around high bandwidth voltage controlled oscillators centered at 2.4 GHz. The transmitted and received signals are acquired via a high speed digital oscilloscope and processed by a PC running LabView, which performs post processing, calculates the cross correlation between transmitted and received signals, and determines the target’s range. Modelling and Simulation by Scicos: On Chaotic signal generation from a simple hybrid system (P) Fatima El Guezar, Hassane Bouzahir, INSA-Toulouse (France) & University of Agadir (Morocco) We explore some modeling capabilities of Scicos. Our aim is to generate chaos from a simple hybrid dynamical system. We give the chaotic dynamics of the current-programmed boost converter in open-loop circuit as a case study. By considering two bifurcation parameters the current reference and the voltage input, we observe that the obtained Scicos simulations show that the book converter is prone to subharmonic behavior and chaos. We also present the corresponding bifurcation diagrams. Enhanced performance through Bifurcation? (O) A.J. Fenwick Air Division, QinetiQ, Farnborough UK (on attachment to Centre for Applied Dynamics Research, University of Aberdeen, UK) Research in radar and sonar aims to enhance performance by improving detectability, accuracy of localisation, classification or processing efficiency. If the transmission is chaotic a natural question to ask is whether it is possible to achieve any of these through bifurcation. The hope is that through interactions with the environment or the target, the dynamics of a class of chaotic signals is altered in an advantageous way. Enhanced performance will result if the presence of the modified dynamics can be detected more easily, i.e. with higher probability, lower processing load or both. Some standard target and environmental models are selected from a brief survey of radar and sonar scenarios, and it is shown what scope there is for the occurrence of bifurcations. Whether the occurrence of a bifurcation will provide a performance advantage is discussed. Attractor Reconstruction from Sonar Data (P) A.J. Fenwick Air Division, QinetiQ, Farnborough UK (on attachment to Centre for Applied Dynamics Research, University of Aberdeen, UK) As part of a three year programme to investigate the use of chaotic signals in sonar sponsored by the UK MoD, a trial was conducted in 2004 at the Waterlip outdoor acoustic test facility. The measurements were organised into four experiments, designed to provide data on different aspects of the use of chaotic signals in a practical sonar system. After an outline of the sonar problem and how chaotic signals can help, the experimental set up will be presented. So far the analysis has been restricted to linear and non-linear analysis of the echoes from a hard target, which produces a replica of the signal. Attempts to reconstruct the attractor of the echo by standard methods show a lower dimensionality than might be expected when the effect of the transducers is accounted for. A selection of the results will be presented. Chaotic radar: problems, benefits and applications (O) Stephen Harman QinetiQ This presentation will discuss the fundamental limitations of using chaotic/noise waveforms in practical radar systems. In addition, the benefits and potential benefits will be discussed that will give the radar system designer impetus to using these, to date, little used waveform in radar. Finally potential radar applications will be discussed based on conclusions obtained from assessment of the benefits and limitations. Chaos without Nonlinear Dynamics (O&P) Ned J. Corron, Scott T. Hayes, Shawn D. Pethel, and Jonathan N. Blakely U. S. Army RDECOM Recently, it has been shown that chaos can be synthesized by the linear superposition of certain pulse basis functions. Here, we extend this result and show that a linear, second-order filter driven by a random signal can generate a waveform that is chaotic under time reversal. That is, the waveform exhibits determinism and a positive Lyapunov exponent when viewed backward in time. We demonstrate the filter using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. We also explore variations of this filter to generate other attractor topologies, including folded band and higher-order Lorenz waveforms. From a practical point of view, this method for generating chaotic waveforms may be well suited for potential applications using the transmission of chaotic signals, including chaos radar, communications, and nondestructive testing. For example, encoding information in the symbolic dynamics of a chaotic waveform is accomplished simply by replacing the random drive with the message signal. The existence of such filters also demonstrates that chaos may be connected to physical theories beyond those described by a deterministic nonlinear dynamical system. Fundamental Properties of Chaos Signals (O) Scott T. Hayes