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FIRB - RBAU01ZWXR, 2003-2005
The use of statistics in information engineering is traditionally linked to the analysis of critical events such as transmission errors, manufacturing process non-idealities, parameter perturbations, whose complete and deterministic characterization is difficult or even only too expensive. In this framework, even the most sophisticated methods mutuated from mathematical statistics are more often considered as analysis tools than as a way of obtaining synthesis models allowing performance optimization. The reason for this is that the engineering community often overlooks the systemistic aspects of statistic-based approaches that are invoked only to cope with lack of precision in an otherwise fully deterministic description. The recently developed methods of statistical dynamics allow this picture to be much enlarged since they show how, under suitable assumptions, some physical and possibly artificial systems exhibit an evolution that may be effectively anticipated and thus designed by means of stochastic methods. Providing that sufficiently flexible mathematical tools have been developed, we can foresee a general procedure for the design of the complex systems in which we are interested which consists of two preliminary steps that hopefully lead to a final optimization step. In the first step the target application is modeled to extract the dependencies between the system overall performance and the statistical features of the signals entailed in the processing. In the second step we may concentrate on these signals and identify what kind of (possibly chaotic) subsystems may be used for their generation/elaboration. The sum of these two steps should clarify a link between the design parameters of the previously mentioned subsystems and the final performance. Such a link can than be exploited for global optimization. Such a general scheme has already shown great potentials in few applicative fields such as spread-spectrum communications, switching power conversion, and cryptography. In particular, in the field of spread spectrum communication based on DS-CDMA, is has been possible to show that the adoption of chaos-based spreading sequences minimizes the multiple access interference as it is perceived by single-user correlation receivers. This is an OPTIMUM result in the sense that no other choice of sequence generation policy can result in a lower interference. Improvements with respect to classical sequences has been confirmed also by measurements. Noteworthy improvements can also be achieved when a slightly more complex, rake-based receiver is considered to cope with  multipath propagation condition. In this case the joint optimization of chaos-based sequences and the receiver filter leads to an improvement of up to three times in bit error rate with respect to conventional adaptation policies. Nonlinear dynamics can be also applied to the reduction of electromagnetic interference in power converters. This is due to the possibility of controlling the system so that the classical periodic switching (which causes high peaks in the spectral power density) is perturbed by a suitably designed jitter that may be mutuated from chaotic phenomena. The comprehension of some statistical properties of the quantized versions of chaotic trajectories allowed interesting advancements in fields related with the ever increasing needs of security in digital processing and transmission. For example, the availability of perfectly random bit generator paves the way to applications in the generation of key for criptographical systems. Furthermore, digital but chaos-based cryptography is moving from a pioneering stage to a more advanced understanding and promises to approach the performance obtained by conventional means. Finally, the same methodological tools allow the discovery of chaotic systems whose evolution exhibits a "strong burstiness". This is of extreme interest since, in general, strong burstiness has to do with polynomial statistical feature that can hardly be modeled by standard Poisson-based methods. Since these phenomena are often present in the data network traffic modeling field, their investigation is becoming a hot topic especially when it is related to the impact on queueing systems. The construction of simple conceptual model for such process can be surely regarded as a key contribution of statistical non-linear dynamics to his field. Moreover, chaotic maps from the same class considered in the traffic modeling problems, may lead to power spectrum that has the classical 1/f^a divergence in the origin, i.e. to the reproduction in the time-domain of a noise process that is often present in electronic devices and circuits. The availability of a time-domain generator has been recently proposed as a way to analyze those circuits without resort to unnecessary linearization or approximation in the frequency domain.

The project aims at the development of a general method for the analytical or semi-analytical investigation of higher-order statistics of stochastic processes generated by discrete-time chaotic systems. Based on this, it also aim at specializing some of the general tools within three cases of engineering interest: chaos-based frequency-modulation of clock signals to reduce their interfering potential; chaos-based frequency-modulation of PWM signals to reduce their interfering; chaos-based generation of self-similar signals to artificially reproduce traffic conditions that are usually met in LANs. In two of the above cases the project will produce a demonstrator. In particular: a switching power converter whose conducted/emitted interference spectrum features extremely attenuated peaks; a network terminal that is able to generate self-similar traffic of different kind depending on the software configuration.
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