Spectrum Sensing Algorithms for Cognitive Radio Applications

Future wireless communications systems are expected to be extremely dynamic, smart and capable to interact with the surrounding radio environment. To implement such advanced devices, cognitive radio (CR) is a promising paradigm, focusing on strategies for acquiring information and learning. The first task of a cognitive systems is spectrum sensing, that has been mainly studied in the context of opportunistic spectrum access, in which cognitive nodes must implement signal detection techniques to identify unused bands for transmission. In the present work, we study different spectrum sensing algorithms, focusing on their statistical description and evaluation of the detection performance. Moving from traditional sensing approaches we consider the presence of practical impairments, and analyze algorithm design. Far from the ambition of cover the broad spectrum of spectrum sensing, we aim at providing contributions to the main classes of sensing techniques. In particular, in the context of energy detection we studied the practical design of the test, considering the case in which the noise power is estimated at the receiver. This analysis allows to deepen the phenomenon of the SNR wall, providing the conditions for its existence and showing that presence of the SNR wall is determined by the accuracy of the noise power estimation process. In the context of the eigenvalue based detectors, that can be adopted by multiple sensors systems, we studied the practical situation in presence of unbalances in the noise power at the receivers. Then, we shift the focus from single band detectors to wideband sensing, proposing a new approach based on information theoretic criteria. This technique is blind and, requiring no threshold setting, can be adopted even if the statistical distribution of the observed data in not known exactly. In the last part of the thesis we analyze some simple cooperative localization techniques based on weighted centroid strategies.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Statistical Physics and Modeling of Human Mobility

In this thesis, we extend some ideas of statistical physics to describe the properties of human mobility. By using a database containing GPS measures of individual paths (position, velocity and covered space at a spatial scale of 2 Km or a time scale of 30 sec), which includes the 2% of the private vehicles in Italy, we succeed in determining some statistical empirical laws pointing out "universal" characteristics of human mobility. Developing simple stochastic models suggesting possible explanations of the empirical observations, we are able to indicate what are the key quantities and cognitive features that are ruling individuals' mobility. To understand the features of individual dynamics, we have studied different aspects of urban mobility from a physical point of view. We discuss the implications of the Benford's law emerging from the distribution of times elapsed between successive trips. We observe how the daily travel-time budget is related with many aspects of the urban environment, and describe how the daily mobility budget is then spent. We link the scaling properties of individual mobility networks to the inhomogeneous average durations of the activities that are performed, and those of the networks describing people's common use of space with the fractional dimension of the urban territory. We study entropy measures of individual mobility patterns, showing that they carry almost the same information of the related mobility networks, but are also influenced by a hierarchy among the activities performed. We discover that Wardrop's principles are violated as drivers have only incomplete information on traffic state and therefore rely on knowledge on the average travel-times. We propose an assimilation model to solve the intrinsic scattering of GPS data on the street network, permitting the real-time reconstruction of traffic state at a urban scale.

Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.