Une interface est une zone de l'espace qui sépare deux régions possédant des propriétés physiques différentes. La plupart des interfaces de la nature résultent d'un processus de croissance, mêlant une composante aléatoire et une dynamique déterministe régie par les symétries du problème. Le résultat du processus de croissance est un objet présentant des corrélations à longue portée. Dans cette thèse, nous nous proposons d'étudier la statistique d'extrême de différents types d'interfaces. Une première motivation est de raffiner la compréhension géométrique de tels objets, via leur maximum. Une seconde motivation s'inscrit dans la démarche plus générale de la statistique d'extrême de variables aléatoires fortement corrélées. A l'aide de méthodes analytiques d'intégrales de chemin nous analysons la distribution du maximum d'interfaces à l'équilibre, dont l'énergie es t purement élastique à courte portée. Nous attaquons ensuite le problème d'interfaces élastiques en milieu désordonné, principalement à l'aide de simulations numériques. Enfin nous étudierons une interface hors-équilibre dans son régime de croissance. L'équivalence de ce type d'interface avec le polymère dirigé en milieu aléatoire, un des paradigmes de la physique statistique des systèmes désordonnés, donne une portée étendue aux résultats concernant la statistique du maximum de l'interface. Nous exposerons les résultats que nous avons obtenus sur un modèle de mouvements browniens qui ne se croisent pas, tout en explicitant le lien entre ce modèle, l'interface en croissance et le polymère dirigé. / An interface is an area of space that separates two regions having different physical properties. Most interfaces in nature are the result of a growth process, mixing a random behavior and a deterministic dynamic derived from the symmetries of the problem. This growth process gives an object with extended correlations. In this thesis, we focus on the study of the extremum of different kinds of interfaces. A first motivation is to refine the geometric properties of such objects, looking at their maximum. A second motivation is to explore the extreme value statistics of strongly correlated random variables. Using path integral techniques we analyse the probability distribution of the maximum of equilibrium interfaces, possessing short range elastic energy. We then extend this to elastic interfaces in random media, with essentially numerical simulations. Finally we study a particular type of out-of-equilibrium interface, in its growing regime. Such interface is equivalent to the directed polymer in random media, a paradigm of the statistical mechanics of disordered systems. This equivalence reinforces the interest in the extreme value statistics of the interface. We will show the exact results we obtained for a non-intersecting Brownian motion model, explaining precisely the link with the growing interface and the directed polymer.

Das Ziel dieser Dissertation besteht darin, die Realisierbarkeit der Berechnungen der Niederenergie-Konstanten der chiralen Lagrangedichte zur Gewinnung physikalischer Informationen im epsilon--Regime der quenched QCD zu erforschen. Wir haben der Neuberger Operator und Overlap Hyperkubus Operator eingesetzt. Ein Hauptergebniss dieser Arbeit ist der Vergleich der Wahrscheinlichkeitsverteilungen einzelner Eigenwerte des Neuberger Operators in der QCD mit den analytischen Vorhersagen der Theorie der Zufallsmatritzen. Wir beobachten eine gute Übereinstimmung solange jede Seite des physikalischen Volumens größ er als etwa 1.12 fm ist. Dabei kann auch das chirale Kondensat Sigma abgeschätzt werden. Es ergab sich, daß diese untere Schranke von L allgemein gilt und die Größ e des physikalischen Volumens, auf dem der Axialkorrelator den Vorhersagen des chiralen Störungstheorie folgt, festlegt. Damit koennen wir die Pionzerfallskonstante bestimmen. Unsere Simulationen zeigen, daß wegen der groß en Wahrscheinlichkeit niedriger Eigenwerte die Messung des Axialkorrelators im topologischen neutralen Sektor extrem aufwändig ist. Doch reicht die Empfindlichkeit der Vorhersagen der chiralen Störungstheorie in höheren topologischen Sektoren bei der gegebenen Statistik nicht zur Bestimmung von Sigma aus. Als alternative Methode, gehen wir dazu über, allein den Beitrag der Nullmoden zu betrachten. Hier koennen wir Abschätzungen für die Pionzerfallskonstante und alpha gewinnen. Wir berechnen die topologische Suszeptibilität für den Neuberger und Overlap Hyperkubus Operator. Im letzten Fall ist der berechnete Wert näher beim Kontinuumslimes. Die Lokalisierung für den Overlap Hyperkubus Operator ist auch besser als für den Neuberger Operator. Unser anderes Ziel ist die Erforschung einer topologieerhaltenden Eichwirkung. / This thesis is dedicated to explore the feasibility of extraction of the low energy constants of the chiral Lagrangian in the epsilon--regime of quenched QCD. We apply two formulations of the Ginsparg-Wilson fermions, namely, the Neuberger operator and the hypercube overlap operator to compute the observables of interest. As a main result we present the comparison of the distributions of the leading individual eigenvalues of the Neuberger operator in QCD and the analytical predictions of chiral random matrix theory. We observe a good agreement as long as each side of the physical volume exceeds about 1.12 fm. At the same time the chiral condensate Sigma can also be estimated. It turns out that this bound for L is generic and sets the size of the physical volume where the axial correlator behaves according to chiral perturbation theory. This allows us to compute a value for the pion decay constant. The simulations also show that due to the high probability of the near-zero modes it is prohibitively difficult to sample the axial correlator in the neutral topological sector. In the higher sectors, however, we observe that the sensitivity of the analytical predictions for the axial correlator to extract Sigma is lost to a large extent. As an alternative procedure we only consider the contribution from the zero modes. Here we are able to obtain an estimate for the pion decay constant and alpha, where alpha is a low energy constant peculiar to quenching. We calculate the topological susceptibility, both for the Neuberger operator and for the overlap hypercube operator. It turns out that the result with the overlap hypercube operator is closer to the continuum limit. Also the locality properties are superior to those of the Neuberger fermions. As a theoretical development the Lüscher topology conserving gauge action is investigated. This enables us to sample the observables of interest in the epsilon--regime without recomputing the index.

O estudo de matrizes aleatórias na física tradicionalmente ocorre no contexto dos modelos de Wigner e na estatística por modelos de Wishart, que se conectam através do threefold way de Dyson para matrizes aleatórias reais, complexas e de quaternios indexadas respectivamente pelo índice B = 1; 2; 4 de Dyson. Estudos recentes mostraram o caminho para que estes modelos fossem generalizados para valores reais de B, permitindo o estudo de ensembles com índice arbitrário. Neste trabalho, estudamos as propriedades estatísticas destes sistemas e exploramos a física subjacente nos modelos de Wigner e Wishart e investigamos, através de cálculos numéricos, os efeitos de localização nos modelos de geral. Também introduzimos quebras na simetria desta nova forma e estudamos numericamente os resultados da estatística dos sistemas perturbados. / The study of random matrices in physics has traditionally occurred in the context of Wigner models and in statistics by Wishart models, which are connected through Dyson\'s threefold way for real, complex and quaternion random matrices index by the Dyson _ = 1; 2; 4 index, respectively. Recent studies have shown the way by which these models are generalized for real values of _, allowing for the study the ensembles with arbitrary index. In this work, we study the statistical properties of these systems and explore the underlying physics in Wigner\'s and Wishart\'s models through and investigate through numerical calculations the e_ects of localization in general _ models. We also introduce symmetry breaks in this new form and study numerically the results of the statistics of the disturbed systems.

Les futurs systèmes de communication sans fil devront utiliser des architectures cellulaires hétérogènes composées de grandes cellules (macro) plus performantes et de petites cellules (femto, micro, ou pico) très denses, afin de soutenir la demande de débit en augmentation exponentielle au niveau de la couche physique. Ces structures provoquent un niveau d'interférence sans précèdent à l'intérieur, comme à l'extérieur des cellules, qui doit être atténué ou, idéalement, exploité afin d'améliorer l'efficacité spectrale globale du réseau. Des techniques comme le MIMO à grande échelle (dit massive MIMO), la coopération, etc., qui contribuent aussi à la gestion des interférences, vont encore augmenter la taille des grandes architectures hétérogènes, qui échappent ainsi à toute possibilité d'analyse théorique par des techniques statistiques traditionnelles.Par conséquent, dans cette thèse, nous allons appliquer et améliorer des résultats connus de la théorie des matrices aléatoires à grande échelle (RMT) afin d'analyser le problème d'interférence et de proposer de nouveaux systèmes de précodage qui s'appuient sur les résultats acquis par l'analyse du système à grande échelle. Nous allons d'abord proposer et analyser une nouvelle famille de précodeurs qui réduit la complexité de calcul de précodage pour les stations de base équipées d'un grand nombre d'antennes, tout en conservant la plupart des capacités d'atténuation d'interférence de l'approche classique et le caractère quasi-optimal du précodeur regularised zero forcing. Dans un deuxième temps, nous allons proposer une variation de la structure de précodage linéaire optimal (obtenue pour de nombreuses mesures de performance) qui permet de réduire le niveau d'interférence induit aux autres cellules. Ceci permet aux petites cellules d'atténuer efficacement les interférences induites et reçues au moyen d'une coopération minimale. Afin de faciliter l'utilisation de l'approche analytique RMT pour les futures générations de chercheurs, nous fournissons également un tutoriel exhaustif sur l'application pratique de la RMT pour les problèmes de communication en début du manuscrit. / Future wireless communication systems will need to feature multi cellular heterogeneous architectures consisting of improved macro cells and very dense small cells, in order to support the exponentially rising demand for physical layer throughput. Such structures cause unprecedented levels of inter and intra cell interference, which needs to be mitigated or, ideally, exploited in order to improve overall spectral efficiency of the communication network. Techniques like massive multiple input multiple output (MIMO), cooperation, etc., that also help with interference management, will increase the size of the already large heterogeneous architectures to truly enormous networks, that defy theoretical analysis via traditional statistical methods.Accordingly, in this thesis we will apply and improve the already known framework of large random matrix theory (RMT) to analyse the interference problem and propose solutions centred around new precoding schemes, which rely on large system analysis based insights. First, we will propose and analyse a new family of precoding schemes that reduce the computational precoding complexity of base stations equipped with a large number of antennas, while maintaining most of the interference mitigation capabilities of conventional close-to-optimal regularized zero forcing. Second, we will propose an interference aware linear precoder, based on an intuitive trade-off and recent results on multi cell regularized zero forcing, that allows small cells to effectively mitigate induced interference with minimal cooperation. In order to facilitate utilization of the analytic RMT approach for future generations of interested researchers, we will also provide a comprehensive tutorial on the practical application of RMT in communication problems.

Partant du constat que dans plus en plus d'applications, la taille des données à traiter augmente, il semble pertinent d'utiliser des outils appropriés tels que la théorie des matrices aléatoires dans le régime en grandes dimensions. Plus particulièrement, dans les applications de traitement d'antenne et radar spécifiques STAP et MIMO-STAP, nous nous sommes intéressés au traitement d'un signal d'intérêt corrompu par un bruit additif composé d'une partie dite rang faible et d'un bruit blanc gaussien. Ainsi l'objet de cette thèse est d'étudier dans le régime en grandes dimensions la détection et le filtrage dit rang faible (fonction de projecteurs) pour le traitement d'antenne en utilisant la théorie des matrices aléatoires.La thèse propose alors trois contributions principales, dans le cadre de l'analyse asymptotique de fonctionnelles de projecteurs. Ainsi, premièrement, le régime en grandes dimensions permet ici de déterminer une approximation/prédiction des performances théoriques non asymptotiques, plus précise que ce qui existe actuellement en régime asymptotique classique (le nombre de données d'estimation tends vers l'infini à taille des données fixe). Deuxièmement, deux nouveaux filtres et deux nouveaux détecteurs adaptatifs rang faible ont été proposés et il a été montré qu'ils présentaient de meilleures performances en fonction des paramètres du système en terme de perte en RSB, probabilité de fausse alarme et probabilité de détection. Enfin, les résultats ont été validés sur une application de brouillage, puis appliqués aux traitements radar STAP et MIMO-STAP sparse. L'étude a alors mis en évidence une différence notable avec l'application de brouillage liée aux modèles de matrice de covariance traités dans cette thèse. / Nowadays, more and more applications deal with increasing dimensions. Thus, it seems relevant to exploit the appropriated tools as the random matrix theory in the large dimensional regime. More particularly, in the specific array processing applications as the STAP and MIMO-STAP radar applications, we were interested in the treatment of a signal of interest corrupted by an additive noise composed of a low rang noise and a white Gaussian. Therefore, the aim of this thesis is to study the low rank filtering and detection (function of projectors) in the large dimensional regime for array processing with random matrix theory tools.This thesis has three main contributions in the context of asymptotic analysis of projector functionals. Thus, the large dimensional regime first allows to determine an approximation/prediction of theoretical non asymptotic performance, much more precise than the literature in the classical asymptotic regime (when the number of estimation data tends to infinity at a fixed dimension). Secondly, two new low rank adaptive filters and detectors have been proposed and it has been shown that they have better performance as a function of the system parameters, in terms of SINR loss, false alarm probability and detection probability. Finally, the results have been validated on a jamming application and have been secondly applied to the STAP and sparse MIMO-STAP processings. Hence, the study highlighted a noticeable difference with the jamming application, related to the covariance matrix models concerned by this thesis.

Dans cette thèse, nous utilisons et contribuons à la théorie des produits de matrices aléatoires afin d'étudier des propriétés génériques des éléments et des sous-groupes des groupes linéaires. Notre premier résultat donne une version probabiliste de l'alternative de Tits : nous montrons que si M_n et M'_n sont deux marches aléatoires indépendantes sur un groupe linéaire de type fini non virtuellement résoluble alors presque sûrement les deux marches finiront par engendrer un sous-groupe libre non abélien à deux générateurs. Cela répond par l'affirmative à une question de Guivarc'h et de Gilman, Miasnikov et Osin. Plus précisément, nous montrons que la probabilité que M_n et M'_n n'engendrent pas un sous-groupe libre décroit exponentiellement vite vers zéro. Notre outil principal est la théorie des produits de matrices aléatoires. Durant la preuve, nous établissons de nouveaux théorèmes limites dans cette théorie, d'une part en généralisant des résultats connus dans le cadre des produits de matrices à valeurs dans les corps archimédiens à tout corps local, d'autre part en donnant des résultats qui sont nouveaux même sur R. Par exemple, nous montrons que sous des hypothèses naturelles sur la marche aléatoire, les composantes suivant K de M_n dans la décomposition KAK deviennent asymptotiquement indépendantes avec vitesse exponentielle. Dans la deuxième partie de la thèse, nous utilisons ces résultats pour étudier la transience des sous-variétés des groupes algébriques. Un de nos résultats peut être formulé comme suit: soient H un sous-groupe non élémentaire de SL_2(R), une probabilité adaptée sur H ayant un moment exponentiel, alors pour toute sous-variété algébrique propre V de SL_2(R), la probabilité que la marche aléatoire appartienne à V décroit exponentiellement vite vers zéro. Par conséquent, la sous-variété algébrique V est transiente pour la marche aléatoire. Nous généralisons cet énoncé au cas ou la marche aléatoire est adaptée sur un groupe Zariski dense des points réels d'un groupe algébrique défini et déployé sur R. Ces résultats sont à comparer avec des travaux récents de Kowalski et de Rivin. / In this thesis, we use and contribute to the theory of random matrix products in order to study generic properties of elements and subgroups of linear groups. Our first result gives a probabilistic version of the Tits alternative : we show that two independent random walks M_n and M'_n on a non virtually solvable finitely generated linear group will eventually generate a non abelian free subgroup. This answers a question of Guivarc'h and Gilman, Miasnikov and Osin. We show in fact that the probability that M_n and M'_n do not generate a free subgroup decreases exponentially fast to zero. Our methods rely deeply on random matrix products theory. During the proof we give some new limit theorems concerning this theory, some of them will be the generalization of known results for matrices taking value in archimedean fields to arbitrary local fields, others will be new even over R. For example, we show that under natural assumptions on the random walk, the K-parts of M_n in the KAK decomposition become asymptotically independent with exponential speed. Next, we use these properties to study the transience of algebraic subvarieties in algebraic groups. One of our results can be formulated as follows: let H be a non elementary subgroup of SL_2(R), a probability measure with an exponential moment whose support generates H, then for every proper algebraic subvariety V of SL_2(R), the probability that the random walk lies in V decreases exponentially fast to zero. This shows that every proper algebraic subvariety is transient for the random walk. We generalize this result to the case where the support of the probability measure generates a Zariski dense subgroup of the real points of an algebraic group defined and split over R. These results share common flavor with recent works of Kowalski and Rivin

Submitted by Mario BC (mario@bc.ufrpe.br) on 2017-02-07T13:36:07Z No. of bitstreams: 1 Thiago Conrado de Vasconcelos.pdf: 4646767 bytes, checksum: 61c228fc4590858e8ee056ac3909187e (MD5) / Made available in DSpace on 2017-02-07T13:36:07Z (GMT). No. of bitstreams: 1 Thiago Conrado de Vasconcelos.pdf: 4646767 bytes, checksum: 61c228fc4590858e8ee056ac3909187e (MD5) Previous issue date: 2016-02-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Throughout the latest years, the interest on Spintronics has increased. The principal purposes of the eld are to detect, manipulate, create and polarize spin currents. Within this topic, it is possible to emphasize the Spin Hall E ect(SEH) and the Inverse Spin Hall E ect(ISEH). In this dissertation, we analytically investigate the universal fluctuation of the conductance of the spin in a chaotic quantum point with chiral symmetry at low temperatures. We used random matrices theory and the expansion of the diagrammatic method for that purpose. We showed that when the chirality is broken, the universal fluctuation of the conductance dispersion is in the order of rms hGf sHi 0:18e=4 and that when there is the preservation of the chiral symmetry, the universal fluctuation of the conductance dispersion occurs in the order of rms [GqsH] 0:283e=4 which coincides with the literature. We also worked on ISEH, through the analytical analysis with the semi-classic expansion of the conductance and showed that in the semi-classic limit the relation rms [GqsH] = p2 rms hGf sHi is valid. / Ao longo dos últimos anos tem aumentado o interesse pelo estudo da spintrônica. O objetivo principal deste campo é detectar, manipular, criar e polarizar correntes de spin. Dentro deste tópico, se destaca o Efeito Hall (SHE) de Spin e Efeito Hall de Spin Inverso (ISHE). Neste trabalho investigamos analiticamente a flutuação universal da condutância de spin num ponto quântico caótico com simetria quiral a baixas temperaturas. Para isso, utilizamos a teoria de matrizes aleatória e a expansão do método diagramático. Mostramos que, quando a simetria de quiralidade é quebrada, a flutuação universal da condutância tem uma dispersão na ordem de na ordem de rms[GfsH] p2 0:18 e/4 e que, quando a simetria de quiralidade é preservada, a flutuação universal da condutância ocorre na ordem de rms[GqsH] 0.283 e/4 , o que está de acordo com a literatura. Em nosso trabalho também investigamos o (ISHE), por meio de uma análise analítica utilizamos a expansão semi-clássica da condutância e mostramos que no limite semi-clássico vale a relação rms[GqIsH] = p2 rms[GfIsH].

Advanced mobile communication systems are characterized by a dense deployment of different types of wireless access points. Since these systems are primarily limited by interference, multiple-input multiple-output (MIMO) techniques as well as coordinated transmission and detection schemes are necessary to mitigate this limitation. Thus, mobile communication systems become more complex which requires that also the mathematical tools for their theoretical analysis must evolve. These must be able to take the most important system characteristics into account, such as fading, path loss, and interference. The aim of this thesis is to develop such tools based on large random matrix theory and to demonstrate their usefulness with the help of several practical applications, such as the performance analysis of network MIMO and large-scale MIMO systems, the design of low-complexity polynomial expansion detectors, and the study of random beamforming techniques as well as multi-hop relay and double-scattering channels. The methods developed in this work provide deterministic approximations of the system performance which become arbitrarily tight in the large system regime with an unlimited number of transmitting and receiving devices. This leads in many cases to simple and close approximations of the finite-size system performance and allows one to draw relevant conclusions about the most significant parameters. One can think of these methods as a way to provide a deterministic abstraction of the physical layer which substantially reduces the system complexity. Due to this complexity reduction, it is possible to carry out a system optimization which would be otherwise intractable.

En la última década, la cooperación entre usuarios ha generado un gran interés por la posibilidad de mejorar la velocidad de transmisión en las redes de comunicaciones inalámbricas. El objetivo es formar un array con las antenas de todos los dispositivos y, de esta forma, aplicar técnicas de procesado espacio-temporal. El esquema de cooperación más sencillo es el canal con relays: todos los terminales que escuchen una comunicación entre dos puntos pueden ayudar a la fuente retransmitiendo lo que hayan recibido.En un sistema realista, los relays no disponen de información sobre el canal en trasmisión. En este escenario, los códigos espacio-temporales (STC, del inglés space-time coding) son la alternativa más eficiente para aprovechar la diversidad introducida por los relays. Sin embargo, los STC clásicos están diseñados para un número limitado y fijo de antenas transmisoras y no se adaptan bien a sistemas cooperativos donde el número de relays puede ser elevado y, sobretodo, puede variar en el tiempo, según los usuarios entren o salgan de la red. El problema principal es la necesidad de usar un código nuevo cada vez que cambie la configuración de la red, generando un importante tráfico de señalización.Esta tesis analiza un código espacio-temporal a bloques de dispersión lineal (LD-STBC, del inglés linear-dispersion space-time block coding), aleatorio y distribuido: a cada relay se le asigna una matriz aleatoria que aplica una transformación lineal al vector que contiene los símbolos de la fuente. Cada matriz se genera de forma independiente y sin ninguna relación con el número de usuarios involucrados. De esta manera, el número de nodos puede variar sin necesidad de modificar los códigos existentes.La forma más intuitiva de construir matrices de dispersión lineal independientes es que sus elementos sean variables aleatorias independientes e idénticamente distribuidas (i.i.d.). Por esta razón, se estudia primero la eficiencia espectral obtenida por este tipo de LD-STBC. Es importante remarcar que la eficiencia espectral es una cantidad aleatoria, ya que es una función de los códigos aleatorios anteriormente descritos. Sin embargo, cuando las dimensiones de las matrices crecen infinitamente pero manteniendo constante la tasa del código (relación entre número de símbolos de la fuente sobre el número de símbolos de los relays), la eficiencia espectral converge rápidamente hacia una cantidad determinista. Este resultado se demuestra usando la teoría de las matrices aleatorias. Por esta razón, el sistema se analiza aproximando la eficiencia espectral con su limite. Por ejemplo, la comparación con el canal directo entre fuente y destino permite definir unas condiciones suficientes en donde el sistema con relays es superior a la comunicación punto a punto.Posteriormente se debe analizar la probabilidad de outage, es decir la probabilidad de que, debido a la baja calidad del canal, la eficiencia espectral sea menor que la velocidad de transmisión solicitada por el sistema. Como ya se ha mencionado anteriormente, los relays se introducen para aumentar la diversidad del canal y, con ella, el número de caminos independientes entre la fuente y el receptor, reduciendo la probabilidad de outage. Para los LD-STBC i.i.d. las prestaciones en términos de outage dependen del tipo de relay (amplify and forward o decode and forward) y son función de la tasa del código, que debe ser cuidadosamente elegida para maximizar el orden de diversidad sin desperdiciar demasiados recursos.Finalmente, en el último capítulo de la tesis se considera otro tipo de LD-STBC, distinto del i.i.d. analizado hasta ahora. En este caso, las matrices de dispersión lineal siguen siendo independientes la una de la otra pero se añade la restricción de que cada una tenga columnas (o filas, según la tasa del código) ortogonales. Así, se consigue que el código siga siendo flexible con respecto a las variaciones en el número de usuarios, pero su estructura permite reducir la interferencia generada por cada relay, como se puede notar comparando su eficiencia espectral con la eficiencia espectral obtenida por el código i.i.d. Cabe destacar que el análisis asintótico de estos códigos (llamados isométricos) se basa en herramientas matemáticas más sofisticadas que las anteriores y, por lo tanto, es necesario un estudio más profundo para poder entender cómo se comporta en términos de outage. / In the last decade, cooperation among multiple terminals has been seen as one of the more promising strategies to improve transmission speed in wireless communications networks. Basically, the idea is to mimic an antenna array and apply distributed versions of well-known space-diversity techniques. In this context, the simplest cooperative scheme is the relay channel: all the terminals (relays) that overhear a point-to-point communication between a source and a destination may decide to aid the source by forwarding (relaying) its message.In a mobile system, it is common to assume that the relays do not have any information about the channel between them and the destination. Under this hypothesis, the best solution to exploit the diversity offered by multiple transmitting antennas is to use space-time coding (STC). However, classical STC's are designed for systems with a fixed and usually low number of antennas. Thus, they are not suitable for relaying in most mobile communications systems where the number of terminals is potentially large and may vary as users join or leave the network. For each new configuration, a new code has to be chosen and notified to the relays, introducing a set-up overhead of signaling traffic.In this dissertation we will propose and analyze a randomized distributed linear-dispersion space-time block code (LD-STBC): each relay is assigned a specific matrix which linearly transforms (left-multiplies) the column vector of source symbols. Each matrix is independently generated and does not depend on the total number of transmitters, which can thus change without interrupting data transmission for a new code--relay assignment.The more intuitive way to build independent linear-dispersion matrices is to fill them with independent and identically distributed (i.i.d.) random variables. Therefore, we will first consider these i.i.d. codes and characterize the resulting spectral efficiency. In order to analyze the performance achieved by the system, we consider a large-system analysis based on random matrix theory. We will show that the random spectral efficiency (function of the random linear-dispersion matrices) converges almost surely to a deterministic quantity when the dimensions of the code grow indefinitely while keeping constant the coding rate. Since convergence is very fast, the random spectral efficiency will be approximated by the deterministic limit in the subsequent analysis. By comparison with the direct link, sufficient conditions are derived for the superiority of relaying.Next, we will analyze the outage probability of the system, that is the probability that the spectral efficiency falls below a given target rate due to channel fading. The main purpose of diversity techniques is to introduce alternative paths from the source to the destination, so that data transmission does not fail when the direct link undergoes deep fading. We will show that the diversity behavior of LD-STBC relaying mainly depends on both the coding rate and the relaying strategy (amplify and forward or decode and forward). It is then important to choose the coding rate that maximizes the diversity order without wasting too many resources.To conclude the dissertation, we will consider a different code based on independent isometric Haar-distributed random linear-dispersion matrices. Thenew code maintains the flexibility of the previous one with respect to variations in the number of relays. However, the more complex structure of the codes allows a noticeable reduction of the interference generated by the relays. Unfortunately, isometric codes also require more sophisticated mathematical tools for their asymptotic analysis. For this reason, we simply introduce the problem by showing that it is possible to have some spectral-efficiency gain with respect to i.i.d. codes. The outage-probability analysis requires a more thorough understanding and will be the subject of future work.

Since direct-sequence code-division multiple-access (DS-CDMA) is an interference-limited random multiple-access scheme, the reduction of co-channel interference with either interference suppression or interference cancellation multiuser receivers and/or power control to prevent detrimental near-far situations is vital for improved performance. Up to date, some contributions investigated randomly-spread asymptotically - large number of users and large bandwidth - large CDMA systems with multiuser receivers and power control via random matrix theoretic and free probability theoretic tools especially over Gaussian and single-path fading channels. As complement within this thesis, we analyze also within the generalized random spreading framework but at finite system sizes and without power control the capacity achievable with linear multichannel multiuser receivers / i.e. RAKE, zero-forcing decorrelator, linear minimum mean-squared error (LMMSE) multiuser receivers, within a single-cell setting over generalized time-varying GWSSUS - Rayleigh/Ricean - fading channels via random matrix theoretic tools. Assuming maximal-ratio combining (MRC) of resolved frequency - multipath - diversity channels due to wideband transmission, the signal-to-interference ratios (SIRs) with multichannel multiuser receivers that set the basis for further derivations are statistically characterized. The information-theoretic ergodic and outage sum-rates spectral efficiencies are then derived and analyzed.