In this thesis, the problem of quantifying the Pareto optimal boundary of the achievable rate region is considered over multiple-input single-output(MISO)interference channels, where the problem boils down to solving a sequence of convex feasibility problems after certain transformations. The feasibility problem is solved by two new distributed optimal beam forming algorithms, where the first one is to parallelize the computation based on the method of alternating projections, and the second one is to localize the computation based on the method of cyclic projections. Convergence proofs are established for both algorithms.

The capacity of multiuser wireless network, unclear for many years, has always been a hot research topic. Many different operation schemes and coding techniques have been proposed to enlarge the achievable rate region. And omnidirectional relay scheme is one of them. This thesis mainly works on the achievable region of the all-source all-cast network with omnidirectional relay scheme. In order to better understand this problem, we first describe the half-duplex model on the one-dimensional and two-dimensional regular networks. And we present an optimal operation scheme for them to have the maximum achievable rate. For the one-dimensional general network, we proposed an achievable region that indicates valued improvement compared to the previous results. In the full-duplex model of the one-dimensional general network, the maximum achievable rate is presented with a simpler proof in comparison with the previous results. In this thesis, we also show some discussions on more general networks.

The capacity of multiuser wireless network, unclear for many years, has always been a hot research topic. Many different operation schemes and coding techniques have been proposed to enlarge the achievable rate region. And omnidirectional relay scheme is one of them. This thesis mainly works on the achievable region of the all-source all-cast network with omnidirectional relay scheme. In order to better understand this problem, we first describe the half-duplex model on the one-dimensional and two-dimensional regular networks. And we present an optimal operation scheme for them to have the maximum achievable rate. For the one-dimensional general network, we proposed an achievable region that indicates valued improvement compared to the previous results. In the full-duplex model of the one-dimensional general network, the maximum achievable rate is presented with a simpler proof in comparison with the previous results. In this thesis, we also show some discussions on more general networks.

Dans cette thèse, on s'est intéressé à l'étude des canaux de diffusion avec des contraintes de transmission pratiques. Tout d'abord, on a étudié l'impact de la contrainte pratique de l'utilisation d'un alphabet fini à l'entrée du canal de diffusion Gaussien avec deux utilisateurs. Deux modèles de canaux de diffusion sont considérés lorsqu'il y a, en plus d'un message commun pour les deux utilisateurs, (i) un message privé pour l'un des deux utilisateurs sans contrainte de sécurité (ii) un message confidentiel pour l'un des deux utilisateurs qui doit être totalement caché de l'autre utilisateur. On a présenté plusieurs stratégies de diffusion distinguées par leur complexité d'implémentation. Plus précisément, on a étudié les régions des débits atteignables en utilisant le partage de temps, la superposition de modulation et le codage par superposition. Pour la superposition de modulation et le cas général du codage par superposition, les régions des débits atteignables maximales sont obtenues en maximisant par rapport aux positions des symboles dans la constellation et la distribution de probabilité jointe. On a étudié le compromis entre la complexité d'implémentation des stratégies de transmission et leurs efficacités en termes de gains en débits atteignables. On a étudié aussi l'impact de la contrainte de sécurité sur la communication en comparant les débits atteignables avec et sans cette contrainte. Enfin, on a étudié les performances du système avec des schémas d'accusés de réception hybrides (HARQ) pour un canal à écoute à évanouissement par blocs lorsque l'émetteur n'a pas une information parfaite sur l'état instantané du canal mais connait seulement les statistiques. On a considéré un schéma adaptatif pour la communication sécurisée en utilisant des canaux de retour à niveaux multiples vers l'émetteur pour changer la longueur des sous mots de code à chaque retransmission afin que le débit utile secret soit maximisé sous des contraintes d'"outages". / In this thesis, we aim to study broadcast channels with practical transmission constraints. First, we study the impact of finite input alphabet constraint on the achievable rates for the Gaussian broadcast channel with two users. We consider two models of broadcast channels, when there is in addition of a common message for two users, (i) a private message for one of them without secrecy constraint (ii) a confidential message for one of them which should be totally hidden from the other user. We present several broadcast strategies distinguished by their complexity of implementation. More precisely, we study achievable rate regions using time sharing, superposition modulation and superposition coding. For superposition modulation and superposition coding strategies, maximal achievable rate regions are obtained by maximizing over both symbol positions in the constellation and the joint probability distribution. We study the tradeoff between the complexity of implementation of the transmission strategies and their efficiency in terms of gains in achievable rates. We study also the impact of the secrecy constraint on communication by comparing the achievable rates with and without this constraint. Finally, we study the system performance using HARQ schemes for the block-fading wiretap channel when the transmitter has no instantaneous channel state information but knows channel statistics. We consider an adaptive-rate scheme for the secure communication by using multilevel feedback channels to change sub-codeword lengths at each retransmission, in order to maximize the secrecy throughput under outage probabilities constraints.

To meet the exponentially increasing traffic data driven by the rapidly growing mobile subscriptions, both industry and academia are exploring the potential of a new genera- tion (5G) of wireless technologies. An important 5G goal is to achieve high data rate. Small cells with spectrum sharing and multiple-input multiple-output (MIMO) techniques are one of the most promising 5G technologies, since it enables to increase the aggregate data rate by improving the spectral efficiency, nodes density and transmission bandwidth, respectively. However, the increased interference in the densified networks will in return limit the achievable rate performance if not properly managed. The considered setup can be modeled as MIMO interference networks, which can be classified into the K-user MIMO interference channel (IC) and the K-cell MIMO interfering broadcast channel/multiple access channel (MIMO-IBC/IMAC) according to the number of mobile stations (MSs) simultaneously served by each base station (BS). The thesis considers two physical layer (PHY) resource allocation problems that deal with the interference for both models: 1) Pareto boundary computation for the achiev- able rate region in a K-user single-stream MIMO IC and 2) grouping-based interference alignment (GIA) with optimized IA-Cell assignment in a MIMO-IMAC under limited feedback. In each problem, the thesis seeks to provide a deeper understanding of the system and novel mathematical results, along with supporting numerical examples. Some of the main contributions can be summarized as follows. It is an open problem to compute the Pareto boundary of the achievable rate region for a K-user single-stream MIMO IC. The K-user single-stream MIMO IC models multiple transmitter-receiver pairs which operate over the same spectrum simultaneously. Each transmitter and each receiver is equipped with multiple antennas, and a single desired data stream is communicated in each transmitter-receiver link. The individual achievable rates of the K users form a K-dimensional achievable rate region. To find efficient operating points in the achievable rate region, the Pareto boundary computation problem, which can be formulated as a multi-objective optimization problem, needs to be solved. The thesis transforms the multi-objective optimization problem to two single-objective optimization problems–single constraint rate maximization problem and alternating rate profile optimization problem, based on the formulations of the ε-constraint optimization and the weighted Chebyshev optimization, respectively. The thesis proposes two alternating optimization algorithms to solve both single-objective optimization problems. The convergence of both algorithms is guaranteed. Also, a heuristic initialization scheme is provided for each algorithm to achieve a high-quality solution. By varying the weights in each single-objective optimization problem, numerical results show that both algorithms provide an inner bound very close to the Pareto boundary. Furthermore, the thesis also computes some key points exactly on the Pareto boundary in closed-form. A framework for interference alignment (IA) under limited feedback is proposed for a MIMO-IMAC. The MIMO-IMAC well matches the uplink scenario in cellular system, where multiple cells share their spectrum and operate simultaneously. In each cell, a BS receives the desired signals from multiple MSs within its own cell and each BS and each MS is equipped with multi-antenna. By allowing the inter-cell coordination, the thesis develops a distributed IA framework under limited feedback from three aspects: the GIA, the IA-Cell assignment and dynamic feedback bit allocation (DBA), respec- tively. Firstly, the thesis provides a complete study along with some new improvements of the GIA, which enables to compute the exact IA precoders in closed-form, based on local channel state information at the receiver (CSIR). Secondly, the concept of IA-Cell assignment is introduced and its effect on the achievable rate and degrees of freedom (DoF) performance is analyzed. Two distributed matching approaches and one centralized assignment approach are proposed to find a good IA-Cell assignment in three scenrios with different backhaul overhead. Thirdly, under limited feedback, the thesis derives an upper bound of the residual interference to noise ratio (RINR), formulates and solves a corresponding DBA problem. Finally, numerical results show that the proposed GIA with optimized IA-Cell assignment and the DBA greatly outperforms the traditional GIA algorithm.

To meet the exponentially increasing traffic data driven by the rapidly growing mobile subscriptions, both industry and academia are exploring the potential of a new genera- tion (5G) of wireless technologies. An important 5G goal is to achieve high data rate. Small cells with spectrum sharing and multiple-input multiple-output (MIMO) techniques are one of the most promising 5G technologies, since it enables to increase the aggregate data rate by improving the spectral efficiency, nodes density and transmission bandwidth, respectively. However, the increased interference in the densified networks will in return limit the achievable rate performance if not properly managed. The considered setup can be modeled as MIMO interference networks, which can be classified into the K-user MIMO interference channel (IC) and the K-cell MIMO interfering broadcast channel/multiple access channel (MIMO-IBC/IMAC) according to the number of mobile stations (MSs) simultaneously served by each base station (BS). The thesis considers two physical layer (PHY) resource allocation problems that deal with the interference for both models: 1) Pareto boundary computation for the achiev- able rate region in a K-user single-stream MIMO IC and 2) grouping-based interference alignment (GIA) with optimized IA-Cell assignment in a MIMO-IMAC under limited feedback. In each problem, the thesis seeks to provide a deeper understanding of the system and novel mathematical results, along with supporting numerical examples. Some of the main contributions can be summarized as follows. It is an open problem to compute the Pareto boundary of the achievable rate region for a K-user single-stream MIMO IC. The K-user single-stream MIMO IC models multiple transmitter-receiver pairs which operate over the same spectrum simultaneously. Each transmitter and each receiver is equipped with multiple antennas, and a single desired data stream is communicated in each transmitter-receiver link. The individual achievable rates of the K users form a K-dimensional achievable rate region. To find efficient operating points in the achievable rate region, the Pareto boundary computation problem, which can be formulated as a multi-objective optimization problem, needs to be solved. The thesis transforms the multi-objective optimization problem to two single-objective optimization problems–single constraint rate maximization problem and alternating rate profile optimization problem, based on the formulations of the ε-constraint optimization and the weighted Chebyshev optimization, respectively. The thesis proposes two alternating optimization algorithms to solve both single-objective optimization problems. The convergence of both algorithms is guaranteed. Also, a heuristic initialization scheme is provided for each algorithm to achieve a high-quality solution. By varying the weights in each single-objective optimization problem, numerical results show that both algorithms provide an inner bound very close to the Pareto boundary. Furthermore, the thesis also computes some key points exactly on the Pareto boundary in closed-form. A framework for interference alignment (IA) under limited feedback is proposed for a MIMO-IMAC. The MIMO-IMAC well matches the uplink scenario in cellular system, where multiple cells share their spectrum and operate simultaneously. In each cell, a BS receives the desired signals from multiple MSs within its own cell and each BS and each MS is equipped with multi-antenna. By allowing the inter-cell coordination, the thesis develops a distributed IA framework under limited feedback from three aspects: the GIA, the IA-Cell assignment and dynamic feedback bit allocation (DBA), respec- tively. Firstly, the thesis provides a complete study along with some new improvements of the GIA, which enables to compute the exact IA precoders in closed-form, based on local channel state information at the receiver (CSIR). Secondly, the concept of IA-Cell assignment is introduced and its effect on the achievable rate and degrees of freedom (DoF) performance is analyzed. Two distributed matching approaches and one centralized assignment approach are proposed to find a good IA-Cell assignment in three scenrios with different backhaul overhead. Thirdly, under limited feedback, the thesis derives an upper bound of the residual interference to noise ratio (RINR), formulates and solves a corresponding DBA problem. Finally, numerical results show that the proposed GIA with optimized IA-Cell assignment and the DBA greatly outperforms the traditional GIA algorithm.