The cognitive radio-based wireless networks have been proposed as a promising technology to improve the utilization of the radio spectrum through opportunistic spectrum access. In this context, the cognitive radios opportunistically access the spectrum which is licensed to primary users when the primary user transmission is detected to be absent. For opportunistic spectrum access, the cognitive radios should sense the radio environment and allocate the spectrum and power based on the sensing results. To this end, in this thesis, I develop a novel cooperative spectrum sensing scheme for cognitive radio networks (CRNs) based on machine learning techniques which are used for pattern classification. In this regard, unsupervised and supervised learning-based classification techniques are implemented for cooperative spectrum sensing. Secondly, I propose a novel joint channel and power allocation scheme for downlink transmission in cellular CRNs. I formulate the downlink resource allocation problem as a generalized spectral-footprint minimization problem. The channel assignment problem for secondary users is solved by applying a modified Hungarian algorithm while the power allocation subproblem is solved by using Lagrangian technique. Specifically, I propose a low-complexity modified Hungarian algorithm for subchannel allocation which exploits the local information in the cost matrix. Finally, I propose a novel dynamic common control channel-based medium access control (MAC) protocol for CRNs. Specifically, unlike the traditional dedicated control channel-based MAC protocols, the proposed MAC protocol eliminates the requirement of a dedicated channel for control information exchange. / October 2015

Cette thèse est consacrée à l’étude de la stabilisation de certains systèmes distribués avec contrôle frontière de type dynamique. Nous considérons, d’abord, la stabilisation de l’équation de la poutre de Rayleigh avec un seul contrôle frontière dynamique moment ou force. Nous montrons que le système n’est pas uniformément (autrement dit exponentiellement) stable; mais par une méthode spectrale, nous établissons le taux polynomial optimal de décroissance de l’énergie du système. Ensuite, nous étudions la stabilisation indirecte de l’équation des ondes avec un amortissement frontière de type dynamique fractionnel. Nous montrons que le taux de décroissance de l’énergie dépend de la nature géométrique du domaine. En utilisant la méthode fréquentielle et une méthode spectrale, nous montrons la non stabilité exponentielle et nous établissons, plusieurs résultats de stabilité polynomiale. Enfin, nous considérons l’approximation de l’équation des ondes mono-dimensionnelle avec un seul amortissement frontière de type dynamique par un schéma de différence finie. Par une méthode spectrale, nous montrons que l’énergie discrétisée ne décroit pas uniformément (par rapport au pas du maillage) polynomialement vers zéro comme l’énergie du système continu. Nous introduisons, alors, un terme de viscosité numérique et nous montrons la décroissance polynomiale uniforme de l’énergie de notre schéma discret avec ce terme de viscosité. / This thesis is devoted to the study of the stabilization of some distributed systems with dynamic boundary control. First, we consider the stabilization of the Rayleigh beam equation with only one dynamic boundary control moment or force. We show that the system is not uniformly (exponentially) stable. However, using a spectral method, we establish the optimal polynomial decay rate of the energy of the system. Next, we study the indirect stability of the wave equation with a fractional dynamic boundary control. We show that the decay rate of the energy depends on the nature of the geometry of the domain. Using a frequency approach and a spectral method, we show the non exponential stability of the system and we establish, different polynomial stability results. Finally, we consider the finite difference space discretization of the 1-d wave equation with dynamic boundary control. First, using a spectral approach, we show that the polynomial decay of the discretized energy is not uniform with respect to the mesh size, as the energy of the continuous system. Next, we introduce a viscosity term and we establish the uniform (with respect to the mesh size) polynomial energy decay of our discrete scheme.