One of the most popular ways to exploit the advantages of a multiple-input multiple-output (MIMO) system is using space time block coding. A space time block code (STBC) is a finite set of complex matrices whose entries consist of the information symbols to be transmitted. A linear STBC is one in which the information symbols are linearly combined to form a two-dimensional code matrix. A well known method of maximum-likelihood (ML) decoding of such STBCs is using the sphere decoder (SD). In this thesis, new constructions of STBCs with low sphere decoding complexity are presented and various ways of characterizing and reducing the sphere decoding complexity of an STBC are addressed. The construction of low sphere decoding complexity STBCs is tackled using irreducible matrix representations of Clifford algebras, cyclic division algebras and crossed-product algebras. The complexity reduction algorithms for the STBCs constructed are explored using tree based search algorithms. Considering an STBC as a vector space over the set of weight matrices, the problem of characterizing the sphere decoding complexity is addressed using quadratic form representations. The main results are as follows. A sub-class of fast decodable STBCs known as Block Orthogonal STBCs (BOSTBCs) are explored. A set of sufficient conditions to obtain BOSTBCs are explained. How the block orthogonal structure of these codes can be exploited to reduce the SD complexity of the STBC is then explained using a depth first tree search algorithm. Bounds on the SD complexity reduction and its relationship with the block orthogonal structure are then addressed. A set of constructions to obtain BOSTBCs are presented next using Clifford unitary weight designs (CUWDs), Coordinate-interleaved orthogonal designs (CIODs), cyclic division algebras and crossed product algebras which show that a lot of codes existing in literature exhibit the block orthogonal property. Next, the dependency of the ordering of information symbols on the SD complexity is discussed following which a quadratic form representation known as the Hurwitz-Radon quadratic form (HRQF) of an STBC is presented which is solely dependent on the weight matrices of the STBC and their ordering. It is then shown that the SD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization). It is also shown that the SD complexity is completely captured into a single matrix obtained from the HRQF. Also, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least SD complexity is presented using the HRQF matrix.

[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.

[pt] Com um número crescente de antenas em sistemas MIMO, o consumo de energia e os custos das interfaces de rádio correspondentes tornam-se relevantes. Nesse contexto, uma abordagem promissora é a utilização de conversores de dados de baixa resolução. Neste estudo, propomos dois novos pré-codificadores ótimos para a sinais de envelope constante e quantização de fase. O primeiro maximiza a distância mínima para o limite de decisão (MMDDT) nos receptores, enquanto o segundo minimiza o erro médio quadrático entre os símbolos dos usuários e o sinal de recepção. O design MMDDT apresetado nesse estudo é uma generalização de designs anteriores que baseiam-se em quantização de 1-bit. Além disso, ao contrário do projeto MMSE anterior que se baseia na resolução de 1-bit, a abordagem proposta emprega quantização de fase uniforme e a etapa de limite no método branch-and-bound é diferente em termos de considerar o relaxamento mais restritivo do problema não convexo, que é então utilizado para um design sub ótimo também. Além disso, três métodos diferentes de detecção suave e um esquema iterativo de detecção e decodificação que permite a utilização de codificação de canal em conjunto com pré-codificação de baixa resolução são propostos. Além de uma abordagem exata para calcular a informação extrínseca, duas aproximações com reduzida complexidade computacional são propostas. Os algoritmos propostos de pré-codificação branch-and-bound são superiores aos métodos existentes em termos de taxa de erro de bit. Resultados numéricos mostram que as abordagens propostas têm complexidade significativamente menor do que a busca exaustiva. Finalmente, os resultados baseados em um código de bloco LDPC indicam que os esquemas de processamento de recepção geram uma taxa de erro de bit menor em comparação com o projeto convencional. / [en] With an increasing number of antennas in multiple-input multiple-output (MIMO) systems, the energy consumption and costs of the corresponding front ends become relevant. In this context, a promising approach is the consideration of low-resolution data converters. In this study two novel optimal precoding branch-and-bound algorithms constrained to constant envelope signals and phase quantization are proposed. The first maximizes the minimum distance to the decision threshold (MMDDT) at the receivers, while the second minimizes the MSE between the users data symbols and the receive signal. This MMDDT design presented in this study is a generalization of prior designs that rely on 1-bit quantization. Moreover, unlike the prior MMSE design that relies on 1-bit resolution, the proposed MMSE approach employs uniform phase quantization and the bounding step in the branch-and-bound method is different in terms of considering the most restrictive relaxation of the nonconvex problem, which is then utilized for a suboptimal design also. Moreover, three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conjunction with low-resolution precoding are proposed. Besides an exact approach for computing the extrinsic information, two approximations with reduced computational complexity are devised. The proposed branch-and-bound precoding algorithms are superior to the existing methods in terms of bit error rate. Numerical results show that the proposed approaches have significantly lower complexity than exhaustive search. Finally, results based on an LDPC block code indicate that the proposed receive processing schemes yield a lower bit-error-rate compared to the conventional design.

We consider the problem of Adaptive Control of finite-dimensional, stable, Linear Time Invariant (LTI) plants. Amongst such plants, the subclass regarding which an upper bound on the order is not known or which are known to be nonminimum phase (zeros in the unstable region) pose formidable problems in their own right. On one hand, if an upper bound on the order of the plant is not known, adaptive control usually involves some form of order estimation. On the other hand, when the plant is allowed to be either minimum phase or nonminimum phase, the adaptive control problem, as is well-known, becomes considerably-less tractable. In this study, the class of unknown plants considered is such that no information is available on the upper bound of the plant order and, further, the plant may be either minimum phase or nonminimum phase. Albeit known to be stable, such plants throw myriads of challenges in the context of adaptive control. Adaptive control involving such plants has been addressed [79] in a Model Reference Adaptive Control (MRAC) framework. There, the inputs and outputs of the unknown plant are the only quantities available by measurement in terms of which any form of modeling of the unknown plant may be made. Inputs to the reference model have been taken from certain restricted classes of bounded signals. In particular, the three classes of inputs considered are piecewise continuous bounded functions which asymptotically approach • a nonzero constant, • a sinusoid, and • a sinusoid with a nonzero shift. Moreover, the control law is such that adaptation is carried out at specific instants separated by progressively larger intervals of time. The schemes there have been proved to be e-optimal in the sense of a suitably formulated optimality criterion. If, however, the reference model inputs be extended to the class of piecewise continuous bounded functions, that would compound the complexity of the adaptive control problem. Only one attempt [78] in adaptive control in such a setting has come to our notice. The problem there has been tackled by an application of the theory of Pade Approximations to time moments of an LTI system. Based on a time moments estimation procedure, a simple adaptive scheme for Single-Input Single-Output (SISO) systems with only a cascade compensator has been reported. The first chapter is essentially meant to ensure that the problem we seek to address in the field of adaptive control indeed has scope for research. Having defined Adaptive Control, we selectively scan through the literature on LTI systems, with focus on MRAC. We look out in particular for studies involving plants of which not much is known regarding their order and systems which are possibly nonminimum phase. We found no evidence to assert that the problem of adaptive control of stable LTI systems, not necessarily minimum phase and of unknown upper bound on the order, was explored enough, save two attempts involving SISO systems. Taking absence of evidence (of in-depth study) for evidence of absence, we make a case for the problem and formally state it. We preview the thesis. We set two targets before us in Chapter 2. The first is to review one of the existing procedures attacking the problem we intend to address. Since the approach is based on the notion of time moments of an LTI system, and as we are to employ Pade Approximations as a tool, we uncover these concepts to the limited extent of our requirement. The adaptive procedure, Plant Command Modifier Scheme (PCMS) [78], for SISO plants is reported in some detail. It stands supported on an algorithm specially designed to estimate the time moments of an LTI system given no more than its input and output. Model following there has been sought to be achieved by matching the first few time moments of the reference model by the corresponding ones of the overall compensated plant. The plant time moment estimates have been taken to represent the unknown plant. The second of the goals is to analyze PCMS critically so that it may serve as a forerunner to our work. We conclude the chapter after accomplishing these goals. In Chapter 3, we devise a time moment estimator for SISO systems from a perspective which is conceptually equivalent to, yet functionally different from, that appropriated in [78]. It is a recipe to obtain estimates of time moments of a system by computing time moment estimates of system input and output signals measured up to current time. Pade approximations come by handy for this purpose. The lacunae exposed by a critical examination of PCMS in Chapter 2 guide us to progressively refine the estimator. Infirmities in the control part of PCMS too have come to light on our probing into it. A few of these will be fixed by way of fabricating two exclusively cascade compensators. We encounter some more issues, traceable to the estimator, which need redressal. Instead of directly fine-tuning the estimator itself, as is the norm, we propose the idea of 'estimating' the lopsidedness of the estimator by using it on the fully known reference model. This will enable us to effect corrections and obtain admissible estimates. Next, we explore the possibility of incorporating feedback compensation in addition to the existing cascade compensation. With output error minimization in mind, we come up with three schemes in this category. In the process, we anticipate the risk of instability due to feedback and handle it by means of an instability preventer with an inbuilt instability detector. Extensive simulations with minimum and rionminimum phase unknown plants employing the various schemes proposed are presented. A systematic study of simulation results reveals a dyad of hierarchies of progressively enhanced overall performance. One is in the sequence of the proposed schemes and the other in going for matching more and more moments. Based on our experiments we pick one of the feedback schemes as the best. Chapter 4 is conceived of as a bridge between SISO and multivariable systems. A transition from SISO to Multi-Input Multi-Output (MIMO) adaptive control is not a proposition confined to the mathematics of dimension-enhancement. A descent from the MIMO to the SISO case is expected to be relatively simple, though. So to transit as smoothly and gracefully as possible, some issues have to be placed in perspective before exploring multivariable systems. We succinctly debate on the efforts in pursuit of the exact vis-a-vis the accurate, and their implications. We then set some notations and formulate certain results which serve to unify and simplify the development in the subsequent three chapters. We list a few standard results from matrix theory which are to be of frequent use in handling multivariable systems. We derive control laws for Single-Input Multi-Output (SIMO) systems in Chapter 5. Expectedly, SIMO systems display traits of observability and uncontrollability. Results of illustrative simulations are furnished. In Chapter 6, we formulate control laws for Multi-Input Single-Output (MISO) systems. Characteristics of unobservability and controllability stand out there. We present case studies. Before actually setting foot onto MIMO systems, we venture to conjecture on what to expect there. We work out all the cascade and feedback adaptive schemes for square and nonsquare MIMO systems in Chapter 7. We show that MIMO laws when projected to MISO, SIMO and SISO cases agree with the corresponding laws in the respective cases. Thus the generality of our treatment of MIMO systems over other multivariable and scalar systems is established. We report simulations of instances depicting satisfactory performance and highlight the limitations of the schemes in tackling the family of plants of unknown upper bound on the order and possibly nonminimum phase. This forms the culmination of our exercise which took off from the reported work involving SISO systems [78]. Up to the end of the 7th chapter, we are in pursuit of solutions for the problem as general as in §1.4. For SISO systems, with input restrictions, the problem has been addressed in [79]. The laws proposed there carry out adaptation only at certain discrete instants; with respect to a suitably chosen cost, the final laws are proved to be e>optimal. In Chapter 8, aided by initial suboptimal control laws, we finally devise two algorithms with continuous-time adaptation and prove their optimality. Simulations with minimum and nonminimum phase plants reveal the effectiveness of the various laws, besides throwing light on the bootstrapping and auto-rectifying features of the algorithms. In the tail-piece, we summarize the work and wind up matters reserved for later deliberation. As we critically review the present work, we decant the take-home message. A short note on applications followed by some loud thinking as a spin-off of this report will take us to finis.

Dans ce travail de thèse, on s'intéresse é l'emploi de techniques de traitement de signal de systèmes de communication MIMO (Multiple Input Multiple Output) pour des applications aux réseaux de capteurs sans fil. Les contraintes énergétiques de cette classe de réseau font appel à des topologies particulières et le réseau peut être perçu comme étant un ensemble de grappes de nœuds capteurs. Ceci ouvre la porte à des techniques avancées de communication de type MIMO. Dans un premier temps, les différents aspects caractérisant les réseaux de capteurs sans fil sont introduits. Puis, les efforts engagés pour optimiser la conservation de l'énergie dans ces réseaux sont résumés. Les concepts de base de systèmes MIMOs sont abordés dans le deuxième chapitre et l'exploration par voie numérique de différentes pistes de la technologie MIMO sont exposées. Nous nous intéressons à des techniques de diversité de polarisation dans le cadre de milieux de communication riches en diffuseurs. Par la suite, des méthodes de type beamforming sont proposées pour la localisation dans les réseaux de capteurs sans fil. Le nouvel algorithme de localisation est présenté et les performances sont évaluées. Nous identifions la configuration pour la communication inter-grappes qui permet pour les meilleurs compromis entre énergie et efficacité spectrale dans les réseaux de capteurs sans fil. Finalement, nous envisageons la technique de sélection de nœuds capteurs afin de réduire la consommation de l'énergie dans le réseau de capteur sans fil. / The aim of this work is to study from a signal processing point of view the use of MIMO (Multiple Input Multiple Output) communication systems for algorithms dedicated to wireless sensor networks. We investigate energy-constrained wireless sensor networks and we focus on cluster topology of the network. This topology permits for the use of MIMO communication system model. First, we review different aspects that characterize the wireless sensor network. Then, we introduce the existing strategies for energy conservation in the network. The basic concepts of MIMO systems are presented in the second chapter and numerical results are provided for evaluating the performances of MIMO techniques. Of particular interest, polarization diversity over rich scattering environment is studied. Thereafter, beamforming approach is proposed for the development of an original localization algorithm in wireless sensor network. The novel algorithm is described and performances are evaluated by simulation. We determine the optimal system configuration between a pair of clusters that permits for the highest capacity to energy ratio in the fourth chapter. The final chapter is devoted to sensor nodes selection in wireless sensor network. The aim of using such technique is to make energy conservation in the network.