[pt] IoT refere-se a um sistema de dispositivos de computação inter-relacionados que visa transferir dados através de uma rede sem exigir interação humanohumano ou humano-para-computador. Esses sistemas de comunicação modernos, exigem restrições de baixo consumo de energia e baixa complexidade no receptor. Nesse sentido, o conversor analógico-digital representa um gargalo para o desenvolvimento das aplicações dessas novas tecnologias, pois apresenta alto consumo de energia devido à sua alta resolução. A pesquisa realizada em relação aos conversores analógico-digitais com quantização grosseira mostrou que esses dispositivos são promissores para o projeto de futuros sistemas de comunicação. Para equilibrar a perda de informações, devido à quantização grosseira, a resolução no tempo é aumentada através da superamostragem. Esta tese considera um sistema com quantização de 1 bit e superamostragem no receptor com um canal de downlink MIMO multiusuário com banda ilimitada e apresenta, como principal contribuição, a nova modulação de cruzamento de zeros que implica que a informação é transmitida no instante de tempo zero-crossings. Este método é usado para a pré-codificação temporal através da otimização do design da forma de onda para dois pré-codificadores diferentes, a maximização temporal da distância mínima até o limiar de decisão com forçamento a zero espacial e a pré-codificação MMSE no espácio-temporal. Os resultados da simulação mostram que a abordagem de cruzamento de zeros proposta supera o estado da arte em termos da taxa de erro de bits para os dois pré-codificadores estudados. Além disso, essa nova modulação reduz a complexidade computacional, permite dispositivos de complexidade muito baixa e economiza recursos de banda em comparação com o método mais avançado. Análises adicionais mostram que a abordagem do cruzamento de zeros é benéfica em comparação com o método mais avançado em termos de maior distância mínima até o limiar de decisão e menor MSE para sistemas com limitações de banda. Além disso, foi desenvolvido um esquema de mapeamento de bits para modulação de cruzamento por zero, semelhante à codificação de Gray para reduzir ainda mais a taxa de erro de bits. / [en] The IoT refers to a system of interrelated computing devises which aims to transfer data over a network without requiring human-to-human or humanto- computer interaction. This Modern communication systems demand restrictions of low energy consumption and low complexity in the receiver. In this sense, the analog-to-digital converter represents a bottleneck for the development of the applications of these new technologies since it has a high energy consumption due to its high resolution. The research carried out concerning to the analog-to-digital converters with coarse quantization has shown that such devices are promising for the design of future communication systems. To balance the loss of information, due to the coarse quantization, the resolution in time is increased through oversampling. This thesis considers a system with 1-bit quantization and oversampling at the receiver with a bandlimited multiuser MIMO downlink channel and introduces, as the main contribution, the novel zero-crossing modulation which implies that the information is conveyed within the time instant of the zero-crossings. This method is used for the temporal precoding through the waveform design optimization for two different precoders, the temporal maximization of the minimum distance to the decision threshold with spatial zero forcing and the space-time MMSE precoding. The simulation results show that the proposed zero-crossing approach outperforms the state-of-theart in terms of the bit error rate for both precoders studied. In addition, this novel modulation reduces the computational complexity, allows very low complexity devices and saves band resources in comparison to the state-ofthe- art method. Additional analyses show that the zero-crossing approach is beneficial in comparison to the state-of-the-art method in terms of greater minimum distance to the decision threshold and lower MSE for systems with band limitations. Moreover, it was devised a bit-mapping scheme for zero-crossing modulation, similar to Gray-coding to further reduce the bit error rate.

Over a century since its inception, general relativity continues to lie at the heart of some of the most researched topics in theoretical physics. It seems likely that the coveted solutions to problems like quantum gravity are to be found in an extension of general relativity, one which may only be visible in an alternate formulation of the theory.  In this thesis we consider the possibility of casting general relativity in the form of an initial value problem where spacetime is seen as the evolution of space. This evolution is shown to be constrained and of Hamiltonian type.  Not all spacetimes are physically acceptable. To be compatible with particle physics, one would like spacetime to accommodate fermions. Here we can take comfort in Geroch’s theorem, which implies that any spacetime that admits a Hamiltonian formulation automatically supports the existence of fermions. We review the elements that go into the proof of this theorem. / Allmän relativitetsteori har i över hundra år legat i teoretiska fysikens framkant. Det är möjligt att lösningarna på öppna problem som kvantiseringen av gravitation går att finna i en utvidgning av allmän relativitetsteori – och kanske uppenbarar sig denna utvidgning bara ur en alternativ formulering av teorin. I den här uppsatsen formuleras allmän relativitetsteori och dess Einsteinekvationer som ett begynnelsevärdesproblem, genom vilket rumtiden kan betraktas som rummets historia. Vi visar att rummets rörelseekvationer är Hamiltons ekvationer med tvångsvillkor.  Enligt partikelfysiken bör fermioner kunna finnas till i rumtiden. Härom kan vi åberopa Gerochs sats, enligt vilken rumtider som har en Hamiltonsk formulering också medger fermioner. Vi redogör för huvuddragen i beviset av Gerochs sats.

Signal compression is daily-used tool for memory capacities reduction and for fast data communication. Methods based on wavelet transform seem to be very effective nowadays. Signal decomposition with a suitable bank filters following with coefficients quantization represents one of the available technique. After packing quantized coefficients into one sequence, run length coding together with Huffman coding are implemented. This thesis focuses on compression effectiveness for the different wavelet transform and quantization settings.

This work deals with the text-dependent speaker recognition in systems, where just a few training samples exist. For the purpose of this recognition, the voice imprint based on different features (e.g. MFCC, PLP, ACW etc.) is proposed. At the beginning, there is described the way, how the speech signal is produced. Some speech characteristics important for speaker recognition are also mentioned. The next part of work deals with the speech signal analysis. There is mentioned the preprocessing and also the feature extraction methods. The following part describes the process of speaker recognition and mentions the evaluation of the used methods: speaker identification and verification. Last theoretically based part of work deals with the classifiers which are suitable for the text-dependent recognition. The classifiers based on fractional distances, dynamic time warping, dispersion matching and vector quantization are mentioned. This work continues by design and realization of system, which evaluates all described classifiers for voice imprint based on different features.

This paper takes aim at creating a consistent form of study materials, supplemented with illustrative examples, for Signals and systems subject. The thesis starts with basic characteristics of acoustic, image, biological and communication signals. Characteristics of linear signals and AD&DA conversion has been added to the next part and to complete the submission, discrete signals follow. Diploma thesis as a whole contains basic theoretical description of problematics, which it tries to supplement with interesting examples, connections, graphs and matlab scripts for illustrative presentation of mentioned problematics.

This thesis is focused on subject of image compression using wavelet transform. The first part of this document provides reader with information about image compression, presents well known contemporary algorithms and looks into details of wavelet compression and following encoding schemes. Both JPEG and JPEG 2000 standards are introduced. Second part of this document analyzes and describes implementation of image compression tool including inovations and optimalizations. The third part is dedicated to comparison and evaluation of achievements.

Le projet de thèse comporte différentes directions possibles: a) Améliorer la compréhension des relations entre la théorie des structures de régularité développée par M. Hairer et la méthode des Distributions Paracontrolées développée par Gubinelli, Imkeller et Perkowski, et éventuellement fournir une synthèse des deux. C'est très spéculatif et, pour le moment, il n'y a pas de chemin clair vers cet objectif à long terme. b) Utiliser la théorie des Distributions Paracontrolées pour étudier différents types d'équations aux dérivés partiels: équations de transport et équations générales d'évolution hyperbolique, équations dispersives, systèmes de lois de conservation. Ces EDP ne sont pas dans le domaine des méthodes actuelles qui ont été développées principalement pour gérer les équations d'évolution semi-linéaire parabolique. c) Une fois qu'une théorie pour l'équation de transport perturbée par un signal irregulier a été établie, il sera possible de se dédier à l'étude des phénomènes de régularisation par le bruit qui, pour le moment, n'ont étés étudiés que dans le contexte des équations de transport perturbées par le mouvement brownien, en utilisant des outils standard d'analyse stochastique. d) Les techniques du Groupe de Renormalisation (GR) et les développements multi-échelles ont déjà été utilisés à la fois pour aborder les EDP et pour définir des champs quantiques euclidiens. La théorie des Distributions Paracontrolées peut être comprise comme une sorte d'analyse multi-échelle des fonctionnels non linéaires et il serait intéressant d'explorer l'interaction des techniques paradifférentielles avec des techniques plus standard, comme les "cluster expansions" et les méthodes liées au GR. / The thesis project has various possible directions: a) Improve the understanding of the relations between the theory of Regularity Structures developed by M.Hairer and the method of Paracontrolled Distributions developed by Gubinelli, Imkeller and Perkowski, and eventually to provide a synthesis. This is highly speculative and at the moment there are no clear path towards this long term goal. b) Use the theory of Paracontrolled Distributions to study different types of PDEs: transport equations and general hyperbolic evolution equation, dispersive equations, systems of conservation laws. These PDEs are not in the domain of the current methods which were developed mainly to handle parabolic semilinear evolution equations. c) Once a theory of transport equation driven by rough signals have been established it will become possible to tackle the phenomena of regularization by transport noise which for the moment has been studied only in the context of transport equations driven by Brownian motion, using standard tools of stochastic analysis. d) Renormalization group (RG) techniques and multi-scale expansions have already been used both to tackle PDE problems and to define Euclidean Quantum Field Theories. Paracontrolled Distributions theory can be understood as a kind of mul- tiscale analysis of non-linear functionals and it would be interesting to explore the interplay of paradifferential techniques with more standard techniques like cluster expansions and RG methods.

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.

Communications receivers that rely on 1-bit analogto-digital conversion are advantageous in terms of hardware complexity and power dissipation. Performance limitations due to the 1-bit quantization can be tackled with oversampling. This paper considers the oversampling gain from an information-theoretic perspective by analyzing the channel capacity with 1-bit quantization and oversampling at the receiver for the particular case of AWGN channels. This includes a numerical computation of the capacity and optimal transmit symbol constellations, as well as the derivation of closed-form expressions for large oversampling ratios and for high signal-to-noise ratios of the channel.

1-bit analog-to-digital conversion is very attractive for low-complexity communications receivers. A major drawback is, however, the small spectral efficiency when sampling at symbol rate. This can be improved through oversampling by exploiting the signal distortion caused by the transmission channel. This paper analyzes the achievable data rate of band-limited communications channels that are subject to additive noise and inter-symbol-interference with 1-bit quantization and oversampling at the receiver. It is shown that not only the channel noise but also the inter-symbol-interference can be exploited to benefit from oversampling.