Adaptive resource allocation in wireless communication systems is crucial in order to support the diverse QoS needs of the services and optimize resource utilization. The design of resource allocation schemes should consider the service type for which it is intended. Moreover, due to feedback delay and channel estimation error, the Channel Quality Indicator (CQI) reported to the transmitter may not be a perfect measure of the channel quality and its use for resource allocation may severely degrade the systems performance. In this thesis, we study resource allocation and CQI reporting for wireless networks while taking the aforementioned factors into consideration. First, we consider resource allocation and adaptive modulation in uplink SC-FDMA systems. This is a combinatorial problem whose optimal solution is exponentially complex. We use canonical duality theory to derive a polynomial complexity resource allocation algorithm that provides a nearly optimal solution to the problem. Then, we focus on resource allocation for video streaming in wireless networks with time-varying interference. To this end, by using risk-sensitive control approach, we develop a cross-layer optimization framework that performs power control at the PHY/MAC layer and rate adaptation at the APPLICATION layer jointly and provides fairness among nodes. Finally, by using stochastic control and game theory, we design a robust best-M CQI reporting scheme for multi-carrier and multi-user systems which takes into account the impact of feedback delay and error in CQI computation. Performing resource allocation on the basis of the proposed CQI reporting can significantly improve the system performance.

This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space. The primary goal of this thesis is to apply the newly developed canonical duality theory to two non-convex variational problems: a modified version of Ericksen's bar and a problem of Landau-Ginzburg type. The canonical duality theory is investigated numerically and compared with classic methods of numerical nature. Both advantages and shortcomings of the canonical duality theory are discussed. A major component of this critical numerical investigation is a careful sensitivity study of the various approaches with respect to changes in parameters, boundary conditions and initial conditions. / Ph. D.

Au cours de cette thèse, nous nous sommes d'abord intéressés à l'optimisation des ressources et à la modulation adaptative dans les systèmes SC-FDMA (Single Carrier Frequency Division Multiple Access). Ce problème d'optimisation est combinatoire à complexité de calcul exponentielle. Afin de pallier à cette difficulté, nous avons utilisé la théorie de la dualité canonique, grâce à laquelle, la complexité du problème d'optimisation devient polynômiale et cela en constitue une amélioration remarquable. L'approche proposée est très proche de la solution optimale. Nous avons ensuite étudié la problématique complexe de l'allocation de ressources pour le "Streaming Vidéo" dans les réseaux sans fil, où il est nécessaire d'assurer une transmission vidéo de haute qualité en présence de canaux et de brouillages variables au cours du temps. Dans ce contexte, nous avons proposé une nouvelle méthode d'allocation de puissance conjointement à l'adaptation du débit vidéo. Pour ce faire, nous avons adopté une approche de la théorie de contrôle, intitulée "Risk-Sensitive Control". Nous avons dédié la troisième partie de la thèse à la conception d'une nouvelle stratégie "best-M" pour le renvoi du CQI (Channel Quality Indicator) pour les systèmes multi-utilisateurs et multi-porteuses. En générale, l'erreur d'estimation du CQI ainsi que son délai de renvoi sont gérés au niveau de la station de base. Notre nouvelle stratégie "best-M" suppose que la gestion de ces problèmes est confiée aux utilisateurs. De ce fait, la performance du système se trouve améliorée sans que son débit de signalisation ne soit augmenté en voix montante. / Adaptive resource allocation in wireless communication systems is crucial in order to support the diverse QoS needs of the services and optimize resource utilization. The design of resource allocation schemes should consider the service type for which it is intended. Moreover, due to feedback delay and channel estimation error, the Channel Quality Indicator (CQI) reported to the transmitter may not be a perfect measure of the channel quality and its use for resource allocation may severely degrade the systems performance. In this thesis, we study resource allocation and CQI reporting for wireless networks while taking the aforementioned factors into consideration. First, we consider resource allocation and adaptive modulation in uplink SC-FDMA systems. This is a combinatorial problem whose optimal solution is exponentially complex. We use canonical duality theory to derive a polynomial complexity resource allocation algorithm that provides a nearly optimal solution to the problem. Then, we focus on resource allocation for video streaming in wireless networks with time-varying interference. To this end, by using risk-sensitive control approach, we develop a cross-layer optimization framework that performs power control at the PHY/MAC layer and rate adaptation at the APPLICATION layer jointly and provides fairness among nodes. Finally, by using stochastic control and game theory, we design a robust best-M CQI reporting scheme for multi-carrier and multi-user systems which takes into account the impact of feedback delay and error in CQI computation. Performing resource allocation on the basis of the proposed CQI reporting can significantly improve the system performance.