Riccardo Rovatti

Sequence synchronization in chaos-based DS-CDMA systems

The aim of this contribution is to consider a further step in the study of the impact of chaos-based techniques on classical DS-CDMA systems. The problem addressed here is the sequence phase acquisition and tracking which is needed to synchronize the spreading and despreading sequences of each link. An acquisition mechanism is proposed and analyzed in depth to identify parameters allowing the study of its performance when classical and chaos-based sequences are employed for spreading. Numerical results show that the adoption of chaos-based techniques may lead to an improvement in link startup delay and expected service availability.

A first experimental verification of optimal MAI reduction in chaos-based DS-CDMA systems

Recently, some of the authors derived a sufficient condition to obtain asynchronous DS-CDMA systems in which the MAI at the output of a classical correlation receiver is brought to its absolute minimum. Such a sufficient conditions constraints the autocorrelation function of the spreading sequences used to distinguish users to be real and of alternating sign. They also proved that such an autocorrelation profile can be almost perfectly matched by employing a properly designed family of chaotic systems and by using it to design real trajectories that are then quantized and periodically repeated to yield the users signatures. We report a preliminary experimental verifications of this theoretical prediction confirming that chaos-based spreading sequences outperform classical m- and Gold sequences when MAI is the dominant cause of error.

Control of Chaos Statistics for Optimization of DS-CDMA Systems

Results of recent theoretical investigations highlighted that the use of chaos in DS-CDMA systems may lead to non-negligible improvements in communication quality for several scenarios. We here briefly review the main steps in this derivation and report the corresponding theoretical prediction. In particular we show that the use of the so-called statistical approach to the study of a chaotic dynamical system allows to characterize and control the statistical features of the processes generated by it. By using such an approach, we highlight the path leading to the generation of chaos-based spreading sequences outperforming classical pseudo-random sequences in two important cases. Over non-selective channels, the ability of chaos-based spreading of minimizing multiple-access interference leads to an average improvement of 60% in Perr with respect to classical spreading. Over selective channels, the possibility of jointly optimizing chaos-based spreading and rake receiver profiles leads to improvements of up to 22% in Perr with respect to systems with either conventional spreading or conventional rake policies.

Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

The application of chaotic dynamics to signal processing tasks stems from the realization that its complex behaviors become tractable when observed from a statistical perspective. Here we illustrate the validity of this statement by considering two noteworthy problems—namely, the synthesis of high-electromagnetic compatibility clock signals and the generation of spreading sequences for direct-sequence code-division comunication systems, and by showing how the statistical approach to discrete-time chaotic systems can be applied to find their optimal solution. To this aim, we first review the basic mathematical tools both intuitively and formally; we consider the Perron–Frobenius operator, its spectral decomposition and its tie to the correlation properties of chaotic sequences. Then, by leveraging on the modeling/approximation of chaotic systems through Markov chains, we introduce a matrix/tensor-based framework where statistical indicators such as high-order correlations can be quantified. We underline how, for many particular cases, the proposed analysis tools can be reversed into synthesis methodologies and we use them to tackle the two above mentioned problems. In both cases, experimental evidence shows that the availability of statistical tools enables the design of chaos-based systems which favorably compare with analogous nonchaos-based counterparts.

Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications

With the aim of explaining the formal development behind the chaos-based modeling of network traffic and other similar phenomena, here we generalize the tools presented in the companion paper (Setti et al., 2002) to the case of piecewise-affine Markov maps with a possibly infinite, but countable number of Markov intervals. Since, in doing so, we keep the dimensionality of the space of the observables finite, we still obtain a finite tensor-based framework. Nevertheless, the increased complexity of the model forces the use of tensors of functions whose handling is greatly simplified by extensive z transformation. With this, a systematic procedure is devised to write analytical expressions for the tensors that take into account the joint probability assignments needed to compute any-order expectations. As an example of use, this machinery is finally applied to the study of self-similarity of quantized processes both in the analysis of higher order phenomena as well as in the analysis and design of second-order self-similar sources suitable for artificial network traffic generation.

Statistical approach to discrete-time chaotic systems: application of basic and advanced tools to DS-CDMA system optimization

Gives an introduction to DS-CDMA systems. Covers DS-CDMA principle (spreading, synchronization), performance overview, advanced receiver structure and classic versus chaotic spreading sequences. Performance on ideal channels is discussed. Cross-interference analysis, (n,t)-tailed shift performance, performance reformulation as a function of self-interference, performance optimization using the self-interference profile and chaotic optimum map search are all included. Performance on selective channels is also looked at.

Statistical approach to discrete-time chaotic systems: advanced tools for quantized chaotic trajectories

Classical tools for statistical analysis of chaotic maps can be generalized to express any-order joint probability of the state and thus any-order correlation functions of the trajectories. When trajectories are quantized correlations can be naturally expressed as combinations of tensors. These expressions feature noteworthy properties when,. piecewise-affine Markov maps are considered. The class of (n,t)-tailed shifts spans the range of maps producing exponentially vanishing correlation and allows the derivation of an analytical expression for any-order quantized correlation functions.