In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization problems efficiently while avoiding solutions with jagged fluence profiles. The last two papers concern optimization of step-and-shoot parameters with emphasis on generating treatment plans that can be delivered efficiently and accurately. In the first paper, the problem dimension of a fluence map optimization problem is reduced through a spectral decomposition of the Hessian of the objective function. The weights of the eigenvectors corresponding to the p largest eigenvalues are introduced as optimization variables, and the impact on the solution of varying p is studied. Including only a few eigenvector weights results in faster initial decrease of the objective value, but with an inferior solution, compared to optimization of the bixel weights. An approach combining eigenvector weights and bixel weights produces improved solutions, but at the expense of the pre-computational time for the spectral decomposition. So-called iterative regularization is performed on fluence map optimization problems in the second paper. The idea is to find regular solutions by utilizing an optimization method that is able to find near-optimal solutions with non-jagged fluence profiles in few iterations. The suitability of a quasi-Newton sequential quadratic programming method is demonstrated by comparing the treatment quality of deliverable step-and-shoot plans, generated through leaf sequencing with a fixed number of segments, for different number of bixel-weight iterations. A conclusion is that over-optimization of the fluence map optimization problem prior to leaf sequencing should be avoided. An approach for dynamically generating multileaf collimator segments using a column generation approach combined with optimization of segment shapes and weights is presented in the third paper. Numerical results demonstrate that the adjustment of leaf positions improves the plan quality and that satisfactory treatment plans are found with few segments. The method provides a tool for exploring the trade-off between plan quality and treatment complexity by generating a sequence of deliverable plans of increasing quality. The final paper is devoted to understanding the ability of the column generation approach in the third paper to find near-optimal solutions with very few columns compared to the problem dimension. The impact of different restrictions on the generated columns is studied, both in terms of numerical behaviour and convergence properties. A bound on the two-norm of the columns results in the conjugate-gradient method. Numerical results indicate that the appealing properties of the conjugate-gradient method on ill-conditioned problems are inherited in the column generation approach of the third paper. / QC 20100709

A programação paralela tem sido freqüentemente adotada para o desenvolvimento de aplicações que demandam alto desempenho computacional. Com o advento das arquiteturas multi-cores e a existência de diversos níveis de paralelismo é importante definir estratégias de programação paralela que tirem proveito desse poder de processamento nessas arquiteturas. Neste contexto, este trabalho busca avaliar o desempenho da utilização das arquiteturas multi-cores, principalmente o oferecido pelas unidades de processamento gráfico (GPUs) e CPUs multi-cores na resolução de um problema térmico inverso. Algoritmos paralelos para a GPU e CPU foram desenvolvidos utilizando respectivamente as ferramentas de programação em arquiteturas de memória compartilhada NVIDIA CUDA (Compute Unified Device Architecture) e a API POSIX Threads. O algoritmo do método do gradiente conjugado pré-condicionado para resolução de sistemas lineares esparsos foi implementado totalmente no espaço da memória global da GPU em CUDA. O algoritmo desenvolvido foi avaliado em dois modelos de GPU, os quais se mostraram mais eficientes, apresentando um speedup de quatro vezes que a versão serial do algoritmo. A aplicação paralela em POSIX Threads foi avaliada em diferentes CPUs multi-cores com distintas microarquiteturas. Buscando um maior desempenho do código paralelizado foram utilizados flags de otimização as quais se mostraram muito eficientes na aplicação desenvolvida. Desta forma o código paralelizado com o auxílio das flags de otimização chegou a apresentar tempos de processamento cerca de doze vezes mais rápido que a versão serial no mesmo processador sem nenhum tipo de otimização. Assim tanto a abordagem utilizando a GPU como um co-processador genérico a CPU como a aplicação paralela empregando as CPUs multi-cores mostraram-se ferramentas eficientes para a resolução do problema térmico inverso. / Parallel programming has been frequently adopted for the development of applications that demand high-performance computing. With the advent of multi-cores architectures and the existence of several levels of parallelism are important to define programming strategies that take advantage of parallel processing power in these architectures. In this context, this study aims to evaluate the performance of architectures using multi-cores, mainly those offered by the graphics processing units (GPUs) and CPU multi-cores in the resolution of an inverse thermal problem. Parallel algorithms for the GPU and CPU were developed respectively, using the programming tools in shared memory architectures, NVIDIA CUDA (Compute Unified Device Architecture) and the POSIX Threads API. The algorithm of the preconditioned conjugate gradient method for solving sparse linear systems entirely within the global memory of the GPU was implemented by CUDA. It evaluated the two models of GPU, which proved more efficient by having a speedup was four times faster than the serial version of the algorithm. The parallel application in POSIX Threads was evaluated in different multi-core CPU with different microarchitectures. Optimization flags were used to achieve a higher performance of the parallelized code. As those were efficient in the developed application, the parallelized code presented processing times about twelve times faster than the serial version on the same processor without any optimization. Thus both the approach using GPU as a coprocessor to the CPU as a generic parallel application using the multi-core CPU proved to be more efficient tools for solving the inverse thermal problem.

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.

La performance d'un algorithme sur une architecture donnée dépend à la fois de la vitesse à laquelle le processeur effectue des opérations à virgule flottante (flops) et de la vitesse d'accès à la mémoire et au disque. Etant donné que le coût de la communication est beaucoup plus élevé que celui des opérations arithmétiques, celle-là forme un goulot d'étranglement dans les algorithmes numériques. Récemment, des méthodes de sous-espace de Krylov basées sur les méthodes 's-step' ont été développées pour réduire les communications. En effet, très peu de préconditionneurs existent pour ces méthodes, ce qui constitue une importante limitation. Dans cette thèse, nous présentons le préconditionneur nommé ''Communication-Avoiding ILU0'', pour la résolution des systèmes d’équations linéaires (Ax=b) de très grandes tailles. Nous proposons une nouvelle renumérotation de la matrice A ('alternating min-max layers'), avec laquelle nous montrons que le préconditionneur en question réduit la communication. Il est ainsi possible d’effectuer « s » itérations d’une méthode itérative préconditionnée sans communication. Nous présentons aussi deux nouvelles méthodes itératives, que nous nommons 'multiple search direction with orthogonalization CG' (MSDO-CG) et 'long recurrence enlarged CG' (LRE-CG). Ces dernières servent à la résolution des systèmes linéaires d’équations de très grandes tailles, et sont basées sur l’enrichissement de l’espace de Krylov par la décomposition du domaine de la matrice A. / The performance of an algorithm on any architecture is dependent on the processing unit’s speed for performing floating point operations (flops) and the speed of accessing memory and disk. As the cost of communication is much higher than arithmetic operations, and since this gap is expected to continue to increase exponentially, communication is often the bottleneck in numerical algorithms. In a quest to address the communication problem, recent research has focused on communication avoiding Krylov subspace methods based on the so called s-step methods. However there are very few communication avoiding preconditioners, and this represents a serious limitation of these methods. In this thesis, we present a communication avoiding ILU0 preconditioner for solving large systems of linear equations (Ax=b) by using iterative Krylov subspace methods. Our preconditioner allows to perform s iterations of the iterative method with no communication, by applying a heuristic alternating min-max layers reordering to the input matrix A, and through ghosting some of the input data and performing redundant computation. We also introduce a new approach for reducing communication in the Krylov subspace methods, that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration, based on the domain decomposition of the graph of A. The enlarged Krylov projection subspace methods lead to faster convergence in terms of iterations and to parallelizable algorithms with less communication, with respect to Krylov methods. We discuss two new versions of Conjugate Gradient, multiple search direction with orthogonalization CG (MSDO-CG) and long recurrence enlarged CG (LRE-CG).

L'objectif de cette thèse est l'accélération des solveurs de Gradient Conjugué avec déflation utilisés pour la résolution de l'équation de Poisson pour la pression, dans le cas de la simulation d'écoulements à faible nombre de Mach sur des maillages non structurés. Une méthode de redémarrage basée sur une estimation de l'effet des erreurs numériques a été mise en œuvre et validée. Par la suite, une méthode à trois niveaux de maillage a été créée, et deux techniques ont dû être développées pour réduire le nombre d'itérations sur les niveaux grossiers : l'une permet la création de solutions initiales grâce à une méthode de projection adaptée, l'autre consiste en une adaptation du critère de convergence sur les niveaux grossiers. Les résultats numériques sur des simulations massivement parallèles montrent entre autres une réduction considérable du temps de calcul global. D'autres pistes de recherche sont introduites, notamment concernant l'équilibrage dynamiques de charge de calcul. / The main objective of this thesis is to accelerate deflated Conjugate Gradient solvers used for solving the pressure Poisson equation, for the simulation of low-Mach number flows on unstructured meshes. A restart method based on an estimation of the effect of numerical errors has been implemented and validated. Then, a three-level deflation method has been created, and two techniques are developed in order to reduce the number of iterations on the coarse levels : one of them is the creation of initial guesses thanks to a well-suited projection method, the other one consists in adapting the convergence criterion on the coarse grids. Numerical results on massively parallel simulations show, among others, a drastic reduction of the computational times of the solver. Other lines of research are introduced, especially regarding dynamic load balancing.

<p>U disertaciji su posmatrani projektivni postupci tipa konjugovanih gradijenata za re&scaron;avanje nelinearnih monotonih sistema velikih dimenzija. Ovi postupci kombinuju projektivnu metodu sa pravcima pretraživanja tipa konjugovanih gradijenata. Zbog osobine monotonosti sistema, projektivna metoda omogućava jednostavnu globalizaciju, a pravci pretraživanja tipa konjugovanih gradijenata zahtevaju malo<br />računarske memorije pa su pogodni za re&scaron;avanje sistema velikih dimenzija. Projektivni postupci tipa konjugovanih gradijenata ne koriste izvode niti funkciju cilja i zasnovani su samo na izračunavanju vrednosti funkcije sistema, pa su pogodni i za re&scaron;avanje neglatkih monotonih sistema. Po&scaron;to se globalna konvergencija dokazuje bez pretpostavki o regularnosti, ovi postupci se mogu koristiti i za re&scaron;avanje sistema sa singularnim re&scaron;enjima. U disertaciji su definisana tri nova tročlana pravca pretraživanja<br />tipa Flečer-Rivs i dva nova hibridna pravca tipa Hu-Stori. Formulisani su projektivni postupci sa novim pravcima pretraživanja i dokazana je njihova globalna konvergencija. Numeričke performanse postupaka testirane su na relevantnim primerima i poređene sa poznatim postupcima iz literature. Numerički rezultati potvrđuju da su novi postupci robusni, efikasni i uporedivi sa postojećim postupcima.</p> / <p>Projection based CG methods for solving large-scale nonlinear monotone systems are considered in this thesis. These methods combine hyperplane projection technique with conjugate gradient (CG) search directions. Hyperplane projection method is suitable for monotone systems, because it enables simply globalization, while CG directions are efficient for large-scale nonlinear systems, due to low memory. Projection based CG methods are funcion-value based, they don&rsquo;t use merit function and derivatives, and because of that they are also suitable for solving nonsmooth monotone systems. The global convergence of these methods are ensured without additional regularity assumptions, so they can be used for solving singular systems.Three new three-term search directions of Fletcher-Reeves type and two new hybrid search directions of Hu-Storey type are defined. PCG algorithm with five new CG type directions is proposed and its global convergence is established. Numerical performances of methods are tested on relevant examples from literature. These results point out that new projection based CG methods have good computational performances. They are efficient, robust and competitive with other methods.</p>

<p>Posmatra se problem optimizacije bez ograničenja. Za re&scaron;avanje<br />problema&nbsp; optimizacije bez ograničenja postoji mno&scaron;tvo raznovrsnih<br />metoda. Istraživanje ovde motivisano je potrebom za metodama koje<br />će brzo konvergirati.<br />Cilj je sistematizacija poznatih rezultata, kao i teorijska i numerička<br />analiza mogućnosti uvođenja parametra u gradijentne metode.<br />Najpre se razmatra problem minimizacije konveksne funkcije vi&scaron;e<br />promenljivih.<br />Problem minimizacije konveksne funkcije vi&scaron;e promenljivih ovde se<br />re&scaron;ava bez izračunavanja matrice hesijana, &scaron;to je naročito aktuelno za<br />sisteme velikih dimenzija, kao i za probleme optimizacije kod kojih<br />ne raspolažemo ni tačnom vredno&scaron;ću funkcije cilja, ni tačnom<br />vredno&scaron;ću gradijenta. Deo motivacije za istraživanjem ovde leži i u<br />postojanju problema kod kojih je funkcija cilja rezultat simulacija.<br />Numerički rezultati, predstavljeni u Glavi 6, pokazuju da uvođenje<br />izvesnog parametra može biti korisno, odnosno, dovodi do ubrzanja<br />određenog metoda optimizacije.<br />Takođe se predstavlja jedan novi hibridni metod konjugovanog<br />gradijenta, kod koga je parametar konjugovanog gradijenta<br />konveksna kombinacija dva poznata parametra konjugovanog<br />gradijenta.<br />U prvoj glavi opisuje se motivacija kao i osnovni pojmovi potrebni za<br />praćenje preostalih glava.<br />U drugoj glavi daje se pregled nekih gradijentnih metoda prvog i<br />drugog reda.<br />Četvrta glava sadrži pregled osnovnih pojmova i nekih rezultata<br />vezanih za metode konjugovanih gradijenata.<br />Pomenute glave su tu radi pregleda nekih poznatih rezultata, dok se<br />originalni doprinos predstavlja u trećoj, petoj i &scaron;estoj glavi.<br />U trećoj glavi se opisuje izvesna modifikacija određenog metoda u<br />kome se koristi multiplikativni parametar, izabran na slučajan način.<br />Dokazuje se linearna konvergencija tako formiranog novog metoda.<br />Peta glava sadrži originalne rezultate koji se odnose na metode<br />konjugovanih gradijenata. Naime, u ovoj glavi predstavlja se novi<br />hibridni metod konjugovanih gradijenata, koji je konveksna<br />kombinacija dva poznata metoda konjugovanih gradijenata.<br />U &scaron;estoj glavi se daju rezultati numeričkih eksperimenata, izvr&scaron;enih<br />na&nbsp; izvesnom skupu test funkcija, koji se odnose na metode iz treće i<br />pete glave. Implementacija svih razmatranih algoritama rađena je u<br />paketu MATHEMATICA. Kriterijum upoređivanja je vreme rada<br />centralne procesorske jedinice.6</p> / <p>The problem under consideration is an unconstrained optimization<br />problem. There are many different methods made in aim to solve the<br />optimization problems.&nbsp; The investigation made here is motivated by<br />the fact that the methods which converge fast are necessary.<br />The main goal is the systematization of some known results and also<br />theoretical and numerical analysis of the possibilities to int roduce<br />some parameters within gradient methods.<br />Firstly, the minimization problem is considered, where the objective<br />function is a convex, multivar iable function. This problem is solved<br />here without the calculation of Hessian, and such solution is very<br />important, for example, when the&nbsp; big dimension systems are solved,<br />and also for solving optimization problems with unknown values of<br />the objective function and its gradient. Partially, this investigation is<br />motivated by the existence of problems where the objective function<br />is the result of simulations.<br />Numerical results, presented in&nbsp; Chapter&nbsp; 6, show that the introduction<br />of a parameter is useful, i.e., such introduction results by the<br />acceleration of the known optimization method.<br />Further, one new hybrid conjugate gradient method is presented, in<br />which the conjugate gradient parameter is a convex combination of<br />two known conjugate gradient parameters.<br />In the first chapter, there is motivation and also the basic co ncepts<br />which are necessary for the other chapters.<br />The second chapter contains the survey of some first order and<br />second order gradient methods.<br />The fourth chapter contains the survey of some basic concepts and<br />results corresponding to conjugate gradient methods.<br />The first, the second and the fourth&nbsp; chapters are here to help in<br />considering of some known results, and the original results are<br />presented in the chapters 3,5 and 6.<br />In the third chapter, a modification of one unco nstrained optimization<br />method is presented, in which the randomly chosen multiplicative<br />parameter is used. Also, the linear convergence of such modification<br />is proved.<br />The fifth chapter contains the original results, corresponding to<br />conjugate gradient methods. Namely, one new hybrid conjugate<br />gradient method is presented, and this&nbsp; method is the convex<br />combination of two known conjugate gradient methods.<br />The sixth chapter consists of the numerical results, performed on a set<br />of test functions, corresponding to methods in the chapters 3 and 5.<br />Implementation of all considered algorithms is made in Mathematica.<br />The comparison criterion is CPU time.</p> / <p>The problem under consideration is an unconstrained optimization<br />problem. There are many different methods made in aim to solve the<br />optimization problems.&nbsp; The investigation made here is motivated by<br />the fact that the methods which converge fast are necessary.<br />The main goal is the systematization of some known results and also<br />theoretical and numerical analysis of the possibilities to int roduce<br />some parameters within gradient methods.<br />Firstly, the minimization problem is considered, where the objective<br />function is a convex, multivar iable function. This problem is solved<br />here without the calculation of Hessian, and such solution is very<br />important, for example, when the&nbsp; big dimension systems are solved,<br />and also for solving optimization problems with unknown values of<br />the objective function and its gradient. Partially, this investigation is<br />motivated by the existence of problems where the objective function<br />is the result of simulations.<br />Numerical results, presented in&nbsp; Chapter&nbsp; 6, show that the introduction<br />of a parameter is useful, i.e., such introduction results by the<br />acceleration of the known optimization method.<br />Further, one new hybrid conjugate gradient method is presented, in<br />which the conjugate gradient parameter is a convex combination of<br />two known conjugate gradient parameters.<br />In the first chapter, there is motivation and also the basic co ncepts<br />which are necessary for the other chapters.<br />Key&nbsp; Words Documentation&nbsp; 97<br />The second chapter contains the survey of some first order and<br />second order gradient methods.<br />The fourth chapter contains the survey of some basic concepts and<br />results corresponding to conjugate gradient methods.<br />The first, the second and the fourth&nbsp; chapters are here to help in<br />considering of some known results, and the original results are<br />presented in the chapters 3,5 and 6.<br />In the third chapter, a modification of one unco nstrained optimization<br />method is presented, in which the randomly chosen multiplicative<br />parameter is used. Also, the linear convergence of such modification<br />is proved.<br />The fifth chapter contains the original results, corresponding to<br />conjugate gradient methods. Namely, one new hybrid conjugate<br />gradient method is presented, and this&nbsp; method is the convex<br />combination of two known conjugate gradient methods.<br />The sixth chapter consists of the numerical results, performed on a set<br />of test functions, corresponding to methods in the chapters 3 and 5.<br />Implementation of all considered algorithms is made in Mathematica.<br />The comparison criterion is CPU time</p>

Este trabalho apresenta uma nova abordagem para a modelagem e resolução de problemas de fluxo de carga em sistemas elétricos de potência. O modelo proposto é formado simultaneamente pelo conjunto de equações não lineares que representam as restrições de carga do problema e por restrições de complementaridade associadas com as restrições de operação da rede, as quais propiciam o controle implícito das tensões nas barras com controle de geração. Também é proposta uma técnica para a obtenção dos valores discretos dos taps de tranformadores, de maneira que o ajuste dessas variáveis possa ser realizado em passos discretos. A metodologia desenvolvida consiste em tratar o sistema misto de equações e inequações não lineares como um problema de factibilidade não linear e transformá-lo em um problema de mínimos quadrados não lineares, o qual é resolvido por uma sequência de subproblemas linearizados dentro de uma região de confiança. Para a obtenção de soluções aproximadas desse subproblema foi adotado o método do gradiente conjugado de Steihaug, combinando estratégias de região de confiança e filtros multidimensionais para analisar a qualidade das soluções fornecidas. Foram realizados testes numéricos com os sistemas de 14, 30, 57, 118 e 300 barras do IEEE, e com um sistema brasileiro equivalente CESP 53 barras, os quais indicaram boa flexibilidade e robustez do método proposto. / This work presents a new approach to the load flow problem in electrical power systems and develops a methodology for its resolution. The proposed model is simultaneously composed by nonlinear equations and inequations which represent the load and operational restrictions of the system, where a set of complementarity constraints model the relationship between voltage and reactive power generation in controled buses. It is also proposed a new technique to obtaining a discrete solution for the transformer taps, allowing their discrete adjustment. The method developed treats the mixed system of equations and inequations of the load flow problem as a nonlinear feasibility problem and converts it in a nonlinear least squares problem, which is solved by minimizing a sequence of linearized subproblems, whitin a trust region. To obtain approximate solutions at every iteration, we use the Steihaug conjugate gradient method, combining trust region and multidimensional filters techniques to analyse the quality of the provided solution. Numerical results using 14, 30, 57, 118 and 300-bus IEEE power systems, and a real brazilian equivalent system CESP 53-bus, indicate the flexibility and robustness of the proposed method.

Este trabalho apresenta uma nova abordagem para a modelagem e resolução de problemas de fluxo de carga em sistemas elétricos de potência. O modelo proposto é formado simultaneamente pelo conjunto de equações não lineares que representam as restrições de carga do problema e por restrições de complementaridade associadas com as restrições de operação da rede, as quais propiciam o controle implícito das tensões nas barras com controle de geração. Também é proposta uma técnica para a obtenção dos valores discretos dos taps de tranformadores, de maneira que o ajuste dessas variáveis possa ser realizado em passos discretos. A metodologia desenvolvida consiste em tratar o sistema misto de equações e inequações não lineares como um problema de factibilidade não linear e transformá-lo em um problema de mínimos quadrados não lineares, o qual é resolvido por uma sequência de subproblemas linearizados dentro de uma região de confiança. Para a obtenção de soluções aproximadas desse subproblema foi adotado o método do gradiente conjugado de Steihaug, combinando estratégias de região de confiança e filtros multidimensionais para analisar a qualidade das soluções fornecidas. Foram realizados testes numéricos com os sistemas de 14, 30, 57, 118 e 300 barras do IEEE, e com um sistema brasileiro equivalente CESP 53 barras, os quais indicaram boa flexibilidade e robustez do método proposto. / This work presents a new approach to the load flow problem in electrical power systems and develops a methodology for its resolution. The proposed model is simultaneously composed by nonlinear equations and inequations which represent the load and operational restrictions of the system, where a set of complementarity constraints model the relationship between voltage and reactive power generation in controled buses. It is also proposed a new technique to obtaining a discrete solution for the transformer taps, allowing their discrete adjustment. The method developed treats the mixed system of equations and inequations of the load flow problem as a nonlinear feasibility problem and converts it in a nonlinear least squares problem, which is solved by minimizing a sequence of linearized subproblems, whitin a trust region. To obtain approximate solutions at every iteration, we use the Steihaug conjugate gradient method, combining trust region and multidimensional filters techniques to analyse the quality of the provided solution. Numerical results using 14, 30, 57, 118 and 300-bus IEEE power systems, and a real brazilian equivalent system CESP 53-bus, indicate the flexibility and robustness of the proposed method.

Wireless communication systems require advanced techniques at the transmitter and at the receiver that improve the performance in hostile radio environments. The received signal is significantly distorted due to the dynamic nature of the wireless channel caused by multipath fading and Doppler spread. In order to mitigate the negative impact of the channel to the received signal quality, techniques as equalization and diversity are usually employed in the system design. During the transmission, the phenomenon of inter-symbol interference (ISI) occurs at the receiver due to the time dispersion of the involved channels. Hence, several delayed replicas of previous symbols interfere with the current symbol. Equalization is usually employed in order to combat the effect of the ISI. Several implementations for equalization filters have been proposed, including linear and non-linear processing, providing complexity-performance trade-offs. It is known that the length of the equalization filter determines the complexity of the technique. Since the wireless channels are characterized by long and sparse impulse responses, the conventional equalizers require high computational complexity due to the large size of their filters. In this dissertation, we have further investigated the long standing problem of equalization in light of the recently derived theory of compressed sampling (CS) for sparse and redundant representations. The developed heuristic algorithms for equalization, can exploit either the sparsity of the channel impulse response (CIR), or the sparsity of the equalizer filters, in order to derive efficient implementation designs. To this end, building on basis pursuit and matching pursuit techniques new equalization schemes have been proposed that exhibit considerable computational savings, increased performance properties and short training sequence requirements. Our main contribution for this part is the Stochastic Gradient Pursuit algorithm for sparse adaptive equalization. An alternative approach to combat ISI is based on the orthogonal frequency division multiplexing (OFDM) system. In this system, the entire channel is divided into many narrow subchannels, so as the transmitted signals to be orthogonal to each other, despite their spectral overlap. However, in the case of doubly selective channels, the Doppler effect destroys the orthogonality between subcarriers. Thus, similarly to ISI, the effect of intercarrier interference (ICI) is introduced at the receiver, where symbols which belong to other subcarriers interfere with the current one. Considering this problem, we have developed iterative algorithms which recursively cancels the ICI at the receiver, providing performance-complexity trade-offs. For low or medium Doppler spreads, the typical approach is to approximate the frequency-domain channel matrix with a banded one. On this premise, we derived reduced-rank preconditioned conjugate gradient (PCG) algorithms in order to estimate the equalization matrix with a reduced number of iterations. Also developed an improved PCG algorithm with the same complexity order, using the Galerkin projections theory. However, in rapidly changing environments, a severe ICI is introduced and the banded approximation results in significant performance degradation. In order to recover this performance loss, we developed regularized estimation framework for ICI equalization, with linear complexity with respect the the number of the subcarriers. Moreover, we proposed a new equalization technique which has the potential to completely cancel the ICI. This approach works in a successive manner through a number of stages, conveying from the fully-connected ordered successive interference cancellation architecture (OSIC) in order to fully suppress the residual interference at each stage of the equalizer. On the other hand, diversity can improve the performance of the communication system by sending the information symbols through multiple signal paths, each of which fades independently. One approach to obtain diversity is through cooperative transmission, considering a group of nearby terminals (relays) as forming one virtual antenna array and applying a spatial beamforming technique so as to optimize the communication via them. Such beamforming techniques differ from their classical counterparts where the array elements are located in a common processing unit, due to the distribution of the relays in the space. In this setting, we developed new distributed algorithms which enable the relay cooperation for the computation of the beamforming weights leveraging the computational abilities of the relays. Each relay can estimate only the corresponding entry of the principal eigenvector, combining data from its network neighbours. The proposed algorithms are applied to two distributed beamforming schemes for relay networks. In the first scheme, the beamforming vector is computed through minimization of a total transmit power subject to the receiver quality-of-service (QoS) constraint. In the second scheme, the beamforming weights are obtained through maximization of the receiver SNR subject to a total transmit power constraint. Moreover, the proposed algorithms operate blindly, implying that no training data are required to be transmitted to the relays, and adaptively, exhibiting a quite short convergence period. / Τα συστήματα ασύρματων επικοινωνιών απαιτούν εξειδικευμένες τεχνικές στον πομπό και στον δέκτη, οι οποίες να βελτιώνουν την απόδοση του συστήματος σε εχθρικά περιβάλλοντα ασύρματης μετάδοσης. Λόγω της δυναμικής φύσης του ασύρματου καναλιού, που περιγράφεται από τα φαινόμενα της απόσβεσης, της πολυδιόδευσης και του Doppler, το λαμβανόμενο σήμα είναι παραμορφωμένο σε σημαντικό βαθμό. Για να αναιρέσουμε αυτήν την αρνητική επίδραση του καναλιού στην ποιότητα του λαμβανόμενου σήματος, κατά τον σχεδιασμό του συστήματος συνήθως υιοθετούνται τεχνικές όπως η ισοστάθμιση και η ποικιλομορφία. Ένα φαινόμενο που προκύπτει στο δέκτη ενός ασύρματου συστήματος επικοινωνίας, λόγω της χρονικής διασποράς που παρουσιάζουν τα κανάλια, είναι η διασυμβολική παρεμβολή, όπου χρονικά καθυστερημένα αντίγραφα προηγούμενων συμβόλων παρεμβάλουν με το τρέχων σύμβολο. Ένας τρόπος για την αντιμετώπιση του φαινομένου αυτού, είναι μέσω της ισοστάθμισης στο δέκτη, όπου χρησιμοποιώντας γραμμικές και μη-γραμμικές τεχνικές επεξεργασίας, τα μεταδιδόμενα σύμβολα ανιχνεύονται από το ληφθέν σήμα. Ωστόσο, συνήθως τα ασύρματα κανάλια χαρακτηρίζονται από κρουστικές αποκρούσεις μεγάλου μήκους αλλά λίγων μη μηδενικών συντελεστών, και σε αυτήν την περίπτωση η υπολογιστική πολυπλοκότητα των συνήθων τεχνικών είναι πολύ υψηλή. Στα πλαίσια αυτής της διατριβής, αναπτύχθηκαν νέοι ευριστικοί αλγόριθμοι για το πρόβλημα της ισοστάθμισης, οι οποίοι εκμεταλλεύονται είτε την αραιότητα της κρουστικής απόκρισης είναι την αραιότητα του αντιστρόφου φίλτρου, προκειμένου να παραχθούν αποδοτικές υλοποιήσεις. Θεωρώντας τον μη γραμμικό ισοσταθμιστή ανατροφοδότησης-απόφασης, έχει δειχθεί ότι κάτω από συνήθεις υποθέσεις για τους συντελεστές της κρουστικής απόκρισης του καναλιού, το εμπρόσθιο φίλτρο και το φίλτρο ανατροφοδότησης μπορούν να αναπαρασταθούν από αραιά διανύσματα. Για τον σκοπό αυτό, τεχνικές Συμπιεσμένης Καταγραφής, οι οποίες έχουν χρησιμοποιηθεί κατα κόρον σε προβλήματα ταυτοποίησης συστήματος, μπορούν να βελτιώσουν σε μεγάλο βαθμό την απόδοση κλασσικών ισοσταθμιστών που δεν λαμβάνουν υπόψιν τους την αραιότητα των διανυσμάτων. Έχοντας ως βάση τις τεχνικές basis pursuit και matching pursuit, αναπτύχθηκαν νέα σχήματα ισοσταθμιστών τα οποία παρουσιάζουν αξιοσημείωτη μείωση στο υπολογιστικό κόστος. Επίσης, αντίθετα με τη συνήθη πρακτική ταυτοποίησης συστήματος, αναπτύχθηκε νέος ευριστικό αλγόριθμος για το πρόβλημα αραιής προσαρμοστικής ισοστάθμισης, με την ονομασία Stochastic Gradient Pursuit. Επιπλέον, ο αλγόριθμος αυτός επεκτάθηκε και για την περίπτωση όπου ο αριθμός των μη μηδενικών στοιχείων του ισοσταθμιστή είναι άγνωστος. Μία διαφορετική προσέγγιση για την αντιμετώπιση του φαινομένου της διασυμβολικής παρεμβολής είναι μέσω του συστήματος orthogonal frequency-division multiplexing (OFDM), όπου το συνολικό κανάλι χωρίζεται σε πολλά στενά υπο-κανάλια, με τέτοιον τρόπο ώστε τα μεταδιδόμενα σήματα να είναι ορθογώνια μεταξύ τους, παρότι παρουσιάζουν φασματική επικάλυψη. Ωστόσο, σε χρονικά και συχνοτικά επιλεκτικά κανάλια, το φαινόμενο Doppler καταστρέφει την ορθογωνιότητα των υπο-καναλιών. Σε αυτήν την περίπτωση, παρόμοια με το φαινόμενο της διασυμβολικής παρεμβολής, εμφανίζεται το φαινόμενο της διακαναλικής παρεμβολής, όπου τα σύμβολα που ανήκουν σε διαφορετικά υπο-κανάλια παρεμβάλουν στο τρέχον. Θεωρώντας αυτό το πρόβλημα, αναπτύχθηκαν νέα σχήματα ισοστάθμισης που ακυρώνουν διαδοχικά την παρεμβολή αυτή, παρέχοντας έναν συμβιβασμό μεταξύ της απόδοσης και της πολυπλοκότητας. Στις περιπτώσεις όπου το φαινόμενο Doppler δεν είναι τόσο ισχυρό, η συνήθης τακτική είναι η προσέγγιση του πίνακα του καναλιού με έναν πίνακα ζώνης. Με αυτό το σκεπτικό, αναπτύχθηκαν αλγόριθμοι μειωμένης τάξης που βασίζονται στην επαναληπτική μέθοδο preconditioned conjugate gradient (PCG), προκειμένου να εκτιμήσουμε τον πίνακα ισοστάθμισης με έναν μειωμένο αριθμό επαναλήψεων. Επίσης, αναπτύχθηκαν τεχνικές που βασίζονται σε προβολές Galerkin για την βελτίωση της απόδοσης των συστημάτων χωρίς να αυξάνουν σημαντικά την πολυπλοκότητα. Ωστόσο, για τις περιπτώσεις όπου το φαινόμενο Doppler έχει ισχυρή επίδραση στο δέκτη του τηλεπικοινωνιακού συστήματος, όπως στις περιπτώσεις πολύ δυναμικών καναλιών, τότε η προσέγγιση με τον πίνακα ζώνης μειώνει σημαντικά την απόδοση του συστήματος. Με στόχο να ανακτήσουμε την απώλεια αυτή, αναπτύχθηκαν τεχνικές κανονικοποιημένης εκτίμησης, με γραμμική πολυπλοκότητα σε σχέση με τον αριθμό των υπο-καναλιών. Επιπρόσθετα, αναπτύχθηκε ένα νέο σχήμα ισοστάθμισης που έχει την δυνατότητα να ακυρώσει πλήρως την διακαναλική παρεμβολή. Το συγκεκριμένο σχήμα λειτουργεί βασιζόμενο σε έναν αριθμό διαδοχικών σταδίων, ακολουθώντας την φιλοσοφία της αρχιτεκτονικής fully-connected ordered successive interference cancellation (OSIC), με στόχο να μειώσει την εναπομείναντα παρεμβολή σε κάθε στάδιο του ισοσταθμιστή Η απόδοση ενός τηλεπικοινωνιακού συστήματος μπορεί επίσης να βελτιωθεί με την χρήση τεχνικών ποικιλομορφίας, δηλαδή με την μετάδοση των συμβόλων μέσω πολλών ανεξάρτητων μονοπατιών. Μία τεχνική ποικιλομορφίας είναι η συνεργατική μετάδοση, όπου μία ομάδα κοντινών τερματικών (relays) σχηματίζουν μία εικονική συστοιχία κεραιών και τεχνικές διαμόρφωσης λοβού μετάδοσης χρησιμοποιούνται προκειμένου να βελτιστοποιηθεί η επικοινωνία μέσω των τερματικών. Οι συγκεκριμένες τεχνικές διαμόρφωσης λοβού μετάδοσης, διαφέρουν από τις κλασσικές όπου η συστοιχία κεραιών βρίσκεται τοποθετημένη σε έναν κόμβο, καθώς τα τερματικά κατανέμονται στον χώρο. Υπό αυτές τις συνθήκες, αναπτύχθηκαν κατανεμημένοι αλγόριθμοι οι οποίοι εκμεταλλεύονται την επικοινωνία και τις υπολογιστικές δυνατότητες των τερματικών για τον υπολογισμό των συνιστωσών του διανύσματος διαμόρφωσης λοβού μετάδοσης. Κάθε τερματικό εκτιμά μόνο την αντίστοιχη συνιστώσα από το κύριο ιδιοδιάνυσμα, συνδιάζοντας δεδομένα από τα γειτονικά τερματικά. Οι προτεινόμενοι αλγόριθμοι εφαρμόστηκαν σε δύο σχήματα κατανεμημένης μετάδοσης μέσω ενδιάμεσων κόμβων. Στο πρώτο σχήμα, τα βάρη του διανύσματος διαμόρφωσης λοβού μετάδοσης υπολογίστηκαν με βάση την ελαχιστοποίηση της συνολικής ισχύος μετάδοσης υπό τον περιορισμό συγκεκριμένου κατωφλίου για την ποιότητα του λαμβανόμενου σήματος. Στο δεύτερο σχήμα, υπολογίστηκαν μεγιστοποιώντας την ποιότητα του λαμβανόμενου σήματος υπό τον περιορισμό ενός κατωφλίου για την συνολική ισχύ μετάδοσης. Επιπλέον, οι αλγόριθμοι που αναπτύχθηκαν λειτουργούν τυφλά, δηλαδή χωρίς φάση εκπαίδευσης, και προσαρμοστικά με μικρό διάστημα σύγκλισης.