Réseaux et signal : des outils de traitement du signal pour l'analyse des réseaux

This thesis describes new tools specifically designed for the analysis of networks such as social, transportation, neuronal, protein, communication networks... These networks, along with the rapid expansion of electronic, IT and mobile technologies are increasingly monitored and measured. Adapted tools of analysis are therefore very much in demand, which need to be universal, powerful, and precise enough to be able to extract useful information from very different possibly large networks. To this end, a large community of researchers from various disciplines have concentrated their efforts on the analysis of graphs, well define mathematical tools modeling the interconnected structure of networks. Among all the considered directions of research, graph signal processing brings a new and promising vision : a signal is no longer defined on a regular n-dimensional topology, but on a particular topology defined by the graph. To apply these new ideas on the practical problems of network analysis paves the way to an analysis firmly rooted in signal processing theory. It is precisely this frontier between signal processing and network science that we explore throughout this thesis, as shown by two of its major contributions. Firstly, a multiscale version of community detection in networks is proposed, based on the recent definition of graph wavelets. Then, a network-adapted bootstrap method is introduced, that enables statistical estimation based on carefully designed graph resampling schemes.Cette thèse propose de nouveaux outils adaptés à l'analyse des réseaux : sociaux, de transport, de neurones, de protéines, de télécommunications... Ces réseaux, avec l'essor de certaines technologies électroniques, informatiques et mobiles, sont de plus en plus mesurables et mesurés ; la demande d'outils d'analyse assez génériques pour s'appliquer à ces réseaux de natures différentes, assez puissants pour gérer leur grande taille et assez pertinents pour en extraire l'information utile, augmente en conséquence. Pour répondre à cette demande, une grande communauté de chercheurs de différents horizons scientifiques concentre ses efforts sur l'analyse des graphes, des outils mathématiques modélisant la structure relationnelle des objets d'un réseau. Parmi les directions de recherche envisagées, le traitement du signal sur graphe apporte un éclairage prometteur sur la question : le signal n'est plus défini comme en traitement du signal classique sur une topologie régulière à n dimensions, mais sur une topologie particulière définie par le graphe. Appliquer ces idées nouvelles aux problématiques concrètes d'analyse d'un réseau, c'est ouvrir la voie à une analyse solidement fondée sur la théorie du signal. C'est précisément autour de cette frontière entre traitement du signal et science des réseaux que s'articule cette thèse, comme l'illustrent ses deux principales contributions. D'abord, une version multiéchelle de détection de communautés dans un réseau est introduite, basée sur la définition récente des ondelettes sur graphe. Puis, inspirée du concept classique de bootstrap, une méthode de rééchantillonnage de graphes est proposée à des fins d'estimation statistique

Characterisation and Modelling of Indoor and Short-Range MIMO Communications

Over the last decade, we have witnessed the rapid evolution of Multiple-Input Multiple-Output (MIMO) systems which promise to break the frontiers of conventional architectures and deliver high throughput by employing more than one element at the transmitter (Tx) and receiver (Rx) in order to exploit the spatial domain. This is achieved by transmitting simultaneous data streams from different elements which impinge on the Rx with ideally unique spatial signatures as a result of the propagation paths’ interactions with the surrounding environment. This thesis is oriented to the statistical characterisation and modelling of MIMO systems and particularly of indoor and short-range channels which lend themselves a plethora of modern applications, such as wireless local networks (WLANs), peer-to-peer and vehicular communications. The contributions of the thesis are detailed below. Firstly, an indoor channel model is proposed which decorrelates the full spatial correlation matrix of a 5.2 GHzmeasuredMIMO channel and thereafter assigns the Nakagami-m distribution on the resulting uncorrelated eigenmodes. The choice of the flexible Nakagami-m density was found to better fit the measured data compared to the commonly used Rayleigh and Ricean distributions. In fact, the proposed scheme captures the spatial variations of the measured channel reasonably well and systematically outperforms two known analytical models in terms of information theory and link-level performance. The second contribution introduces an array processing scheme, namely the three-dimensional (3D) frequency domain Space Alternating Generalised Expectation Maximisation (FD-SAGE) algorithm for jointly extracting the dominant paths’ parameters. The scheme exhibits a satisfactory robustness in a synthetic environment even for closely separated sources and is applicable to any array geometry as long as its manifold is known. The algorithm is further applied to the same set of raw data so that different global spatial parameters of interest are determined; these are the multipath clustering, azimuth spreads and inter-dependency of the spatial domains. The third contribution covers the case of short-range communications which have nowadays emerged as a hot topic in the area of wireless networks. The main focus is on dual-branch MIMO Ricean systems for which a design methodology to achieve maximum capacities in the presence of Line-of-Sight (LoS) components is proposed. Moreover, a statistical eigenanalysis of these configurations is performed and novel closed-formulae for the marginal eigenvalue and condition number statistics are derived. These formulae are further used to develop an adaptive detector (AD) whose aim is to reduce the feasibility cost and complexity of Maximum Likelihood (ML)-based MIMO receivers. Finally, a tractable novel upper bound on the ergodic capacity of the above mentioned MIMO systems is presented which relies on a fundamental power constraint. The bound is sufficiently tight and applicable for arbitrary rank of the mean channel matrix, Signal-to-Noise ratio (SNR) and takes the effects of spatial correlation at both ends into account. More importantly, it includes previously reported capacity bounds as special cases