Compressive Sensing (CS) is a novel signal-processing paradigm that allows sampling of sparse or compressible signals at lower than Nyquist rate. The past decade has seen substantial research on imaging applications using compressive sensing. In this thesis, CS is combined with the commercial electromagnetic (EM) simulation software newFASANT to improve its efficiency in solving EM scattering problems such as Radar Cross Section (RCS) of complex targets at GHz frequencies. This thesis proposes a CS-RCS approach that allows efficient and accurate recovery of under-sampled RCSs measured from a random set of incident angles using an accelerated iterative soft thresh-holding reconstruction algorithm. The RCS results of a generic missile and a Canadian KingAir aircraft model simulated using Physical Optics (PO) as the EM solver at various frequencies and angular resolutions demonstrate good efficiency and accuracy of the proposed method.

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In the past couple of decades, the amount of data available has dramatically in- creased. Thus, in modern large-scale inference problems, the dimension of the signal to be estimated is comparable or even larger than the number of available observa- tions. Yet the desired properties of the signal typically lie in some low-dimensional structure, such as sparsity, low-rankness, finite alphabet, etc. Recently, non-smooth regularized convex optimization has risen as a powerful tool for the recovery of such structured signals from noisy linear measurements in an assortment of applications in signal processing, wireless communications, machine learning, computer vision, etc. With the advent of Compressed Sensing (CS), there has been a huge number of theoretical results that consider the estimation performance of non-smooth convex optimization in such a high-dimensional setting. In this thesis, we focus on precisely analyzing the high dimensional error perfor- mance of such regularized convex optimization problems under the presence of im- pairments (such as uncertainties) in the measurement matrix, which has independent Gaussian entries. The precise nature of our analysis allows performance compari- son between different types of these estimators and enables us to optimally tune the involved hyper-parameters. In particular, we study the performance of some of the most popular cases in linear inverse problems, such as the LASSO, Elastic Net, Least Squares (LS), Regularized Least Squares (RLS) and their box-constrained variants. In each context, we define appropriate performance measures, and we sharply an- alyze them in the High-Dimensional Statistical Regime. We use our results for a concrete application of designing efficient decoders for modern massive multi-input multi-output (MIMO) wireless communication systems and optimally allocate their power. The framework used for the analysis is based on Gaussian process methods, in particular, on a recently developed strong and tight version of the classical Gor- don Comparison Inequality which is called the Convex Gaussian Min-max Theorem (CGMT). We use some results from Random Matrix Theory (RMT) in our analysis as well.

This thesis proposes a convex network utility maximization (NUM) problem that can be solved to optimize a cross-layer network based on user and system defined requirements for quality and link capacity of multimedia applications. The problem can also be converged to a distributed solution using dual decomposition. Current techniques do not address the changing system's requirements for the network in addition to the user's requirements for an application when optimizing a cross-layer network, but rather focus on optimizing a dynamic network to conform to a real-time application or for a specific performance. Optimizing the cross-layer network for the changing system and user requirements allows a more accurate optimization of the overall cross-layer network of any given multi-node, ad-hoc wireless application for data transmission quality and link capacity to meet overall mission demands.

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Transmitarrays antennas (TAs) can be seen as the planar counterpart of optical lenses. They are composed of thin radiating elements (unit cells) which introduce different local phase shifts on an incident electromagnetic wave, emitted by a primary source, and re-radiate it. By properly designing the unit cells and their distribution in the TA, the properties of the incident wave, e.g. wavefront and polarization, as well as the pattern of the radiated field can be tailored. Moreover, TAs are suited to low-cost multilayer fabrication processes, e.g. printed circuit board (PCB) technology, and can achieve electronic reconfiguration embedding diodes. Therefore, TAs are natural and cost-effective candidates for applications requiring to steer and shape the antenna beam, such as satellite communications (Satcom) and future terrestrial wireless networks. For instance, satellite antennas radiate contoured beams to cover specific Earth regions, whereas Satcom ground terminals and mobile base stations require very directive beams compliant with prescribed radiation masks. In many cases, the amplitude of the field impinging on the TA is fixed and the TA phase profile, i.e. the spatial distribution of the phase-shifting elements, is the only parameter that can be designed to generate the desired radiation pattern. Thus, versatile, efficient and robust phase-only synthesis methods are essential. Closed-form expressions for the phase profile can be derived only in a few cases and for specific targeted far-field patterns. On the other hand, synthesis approaches based on global optimization techniques, such as genetic algorithms, are general purpose but their convergence and accuracy is often poor, despite the long computation time. In this thesis, a mathematical approach for the phase-only synthesis of TAs using convex optimization is developed to solve diverse pattern shaping problems. The use of convex optimization ensures a good compromise between the generality, robustness and computational cost of the method.First, a model for the analysis of the TA is presented. It accurately predicts the antenna radiation pattern using the equivalence theorem and includes the impact of the spillover, i.e. the direct radiation from the TA feed. Then, the TA synthesis is formulated in terms of the far-field intensity pattern computed by the model. The phase-only synthesis problem is inherently non-convex. However, a sequential convex optimization procedure relying on proper relaxations is proposed to approximately solve it. The accuracy of these sub-optimal solutions is discussed and methods to enhance it are compared. The procedure is successfully applied to synthesize relatively large TAs, with symmetrical and non-symmetrical phase profiles, radiating either focused-beam or shaped-beam patterns, with challenging mask constraints.Finally, three millimeter-wave TAs, comprising different sets of unit cells, are designed using the synthesis procedure. The good agreement between the predicted radiation patterns and those obtained from full-wave simulations of the antennas demonstrates the precision and versatility of the proposed tool, within its range of validity. / Transmitarray antennas (TAs) är en typ av antenna som konsiderades som optiska lenser motparten. Transmitterray antennas (TAs) are a type of antenna that is considered as optical lenses counterpart.De är sammansatta av tunna strålande element eller unit cell (UCs) som introducerar olika lokala fasförskjutningar på en inkommande elektromagnetisk våg och stråla ut den igen. They are composed of thin radiating elements or unit cells (UCs) that introduce different local phase shifts on an incoming electromagnetic wave and radiate it out again.Den här vågen kommer från en primär elektromagnetisk källa. This wave comes from a primary electromagnetic source.Syftet med detta examensarbete är att bestämma hur man ska UC placera för att skapa en önskad utgångsstråle.This master thesis aim is to determine how to place the UC in order to create a desired output beam.TAs är biliga att bygga och kan också vara elektroniska omkonfigurerbara med hjälp av dioder. TAs are cheap to produce and can also be electronically reconfigurable using diodes. TAs används i Satcom-domänen eller för att designa ny hög hastighet nätverk (6G).TAs are used in the Satcom domain or to design new high-speed network (6G). När man skapar en antenn, kan man stämma fas och amplitud av kompositerna för att skapa en önskad utgångsstråle. På TAs är det lite svårare.When someone create an antenna, one can tune phase and amplitude of the composants to create a desired output beam. For TAs it is a little bit more difficult.Faktiskt kan man stämma endast fas i TA- arkitektur. In fact, one can only tune the phase in the TA architecture. Så behöver vi speciell designprocedur som kallas: fassyntesSo, we need special design procedure called: phase-only synthesis.Konvex optimering är en bra kompromiss mellan metodens generalitet och uträkningstimeConvex optimization is a good compromise between generality and computation time.Här presenterar vi en fassyntes metod på skapa TAs som utstrålar en önskad stråle. Here we present a phase-only synthesis method in order to create TAs which radiate a precise beam. Metoden är baserade på konvex optimering.

A cooperative multi-agent system is a collection of interacting agents deployed in a mission space where each agent is allowed to control its local state so that the fleet of agents collectively optimizes a common global objective. While optimization problems associated with multi-agent systems intend to determine the fixed set of globally optimal agent states, control problems aim to obtain the set of globally optimal agent controls. Associated non-convexities in these problems result in multiple local optima. This dissertation explores systematic techniques that can be deployed to either escape or avoid poor local optima while in search of provably better (still local) optima. First, for multi-agent optimization problems with iterative gradient-based solutions, a distributed approach to escape local optima is proposed based on the concept of boosting functions. These functions temporarily transform gradient components at a local optimum into a set of boosted non-zero gradient components in a systematic manner so that it is more effective compared to the methods where gradient components are randomly perturbed. A novel variable step size adjustment scheme is also proposed to establish the convergence of this distributed boosting process. Developed boosting concepts are successfully applied to the class of coverage problems. Second, as a means of avoiding convergence to poor local optima in multi-agent optimization, the use of greedy algorithms in generating effective initial conditions is explored. Such greedy methods are computationally cheap and can often exploit submodularity properties of the problem to provide performance bound guarantees to the obtained solutions. For the class of submodular maximization problems, two new performance bounds are proposed and their effectiveness is illustrated using the class of coverage problems. Third, a class of multi-agent control problems termed Persistent Monitoring on Networks (PMN) is considered where a team of agents is traversing a set of nodes (targets) interconnected according to a network topology aiming to minimize a measure of overall node state. For this class of problems, a gradient-based parametric control solution developed in a prior work relies heavily on the initial selection of its `parameters' which often leads to poor local optima. To overcome this initialization challenge, the PMN system's asymptotic behavior is analyzed, and an off-line greedy algorithm is proposed to systematically generate an effective set of initial parameters. Finally, for the same class of PMN problems, a computationally efficient distributed on-line Event-Driven Receding Horizon Control (RHC) solution is proposed as an alternative. This RHC solution is parameter-free as it automatically optimizes its planning horizon length and gradient-free as it uses explicitly derived solutions for each RHC problem invoked at each agent upon each event of interest. Hence, unlike the gradient-based parametric control solutions, the proposed RHC solution does not force the agents to converge to one particular behavior that is likely to be a poor local optimum. Instead, it keeps the agents actively searching for the optimum behavior. In each of these four parts of the thesis, an interactive simulation platform is developed (and made available online) to generate extensive numerical examples that highlight the respective contributions made compared to the state of the art.

In this thesis, the theory and application of black-box optimization methods are explored. More specifically, we looked at two families of algorithms, descent methods andresponse surface methods (closely related to trust region methods). We also looked at possibilities in using a dimension reduction technique called active subspace which utilizes sampled gradients. This dimension reduction technique can make the descent methods more suitable to high-dimensional problems, which turned out to be most effective when the data have a ridge-like structure. Finally, the optimization methods were used on a real-world problem in the context of pre-hospital care where the objective is to minimize the ambulance response times in the municipality of Umea by changing the positions of the ambulances. Before applying the methods on the real-world ambulance problem, a simulation study was performed on synthetic data, aiming at finding the strengths and weaknesses of the different models when applied to different test functions, at different levels of noise. The results showed that we could improve the ambulance response times across several different performance metrics compared to the response times of the current ambulancepositions. This indicates that there exist adjustments that can benefit the pre-hospitalcare in the municipality of Umea. However, since the models in this thesis work find local and not global optimums, there might still exist even better ambulance positions that can improve the response time further. / I denna rapport undersöks teorin och tillämpningarna av diverse blackbox optimeringsmetoder. Mer specifikt så har vi tittat på två familjer av algoritmer, descentmetoder och responsytmetoder (nära besläktade med tillitsregionmetoder). Vi tittar också på möjligheterna att använda en dimensionreduktionsteknik som kallas active subspace som använder samplade gradienter för att göra descentmetoderna mer lämpade för högdimensionella problem, vilket visade sig vara mest effektivt när datat har en struktur där ändringar i endast en riktning har effekt på responsvärdet. Slutligen användes optimeringsmetoderna på ett verkligt problem från sjukhusvården, där målet var att minimera svarstiderna för ambulansutryckningar i Umeå kommun genom att ändra ambulanspositionerna. Innan metoderna tillämpades på det verkliga ambulansproblemet genomfördes också en simuleringsstudie på syntetiskt data. Detta för att hitta styrkorna och svagheterna hos de olika modellerna genom att undersöka hur dem hanterar ett flertal testfunktioner under olika nivåer av brus. Resultaten visade att vi kunde förbättra ambulansernas responstider över flera olika prestandamått jämfört med responstiderna för de nuvarande ambulanspositionerna. Detta indikerar att det finns förändringar av positioneringen av ambulanser som kan gynna den pre-hospitala vården inom Umeå kommun. Dock, eftersom modellerna i denna rapport hittar lokala och inte globala optimala punkter kan det fortfarande finnas ännu bättre ambulanspositioner som kan förbättra responstiden ytterligare.

The demand for outdoor precise location is increasing with the development of new applications such as autonomous vehicles, exploration robots and wireless sensor networks. Global Navigation Satellite System (GNSS) is the go-to system for outdoor localization. This thesis focuses on developing new methods for GNSS single-point positioning (SPP) model, where no access to a reference station or precise GNSS parameters is needed. We investigated the limitations of the standard method, least- squares adjustment (LSA), and we derived the Cramer-Rao bounds for the SPP estimation problem. We also investigated different techniques to formulate the positioning problem with the goal to increase the accuracy. A new method is developed by reformulating the problem as difference-of-convex program (DC program) and utilizing convex-concave procedure (CCCP) to solve the positioning problem without linearizing the observation equations. In addition, we examined the potential of multiple-receiver systems in increasing the accuracy. We formulated the multiple- receiver SPP estimation problem, and we proposed to configure the multiple receivers in a fixed equilateral triangle to exploit the symmetry and the geometrical constraints of the configuration. We extended the use of LSA in multiple-receiver system. We also developed a modification of LSA algorithm, named least-squares adjustment extension (LSAE), that utilizes attitude information and the constraints of the multiple-receiver system. In addition, we developed a new algorithm to optimizes the SPP estimates over the equilateral triangles Riemannian manifold, which enforces the geometrical constraints of the multiple-receiver system. Furthermore, we derived the constrained and the unconstrained Cramer-Rao bounds (CRB and CCRB) for the multiple-receiver SPP problem. Moreover, we investigated the influence of both attitude information and the equilateral triangle baseline length on the algorithms’ performances and the derived CCRB. Finally, we carried out a numerical analysis by implementing the algorithms and the bounds in MATLAB, where we tested the algorithms on simulated GNSS scenarios. The proposed multiple-receiver methods provide more precise estimates for the SPP problem in comparison to the single receiver methods.

Minimax D-optimal designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, the minimax D-optimal design problem has an objective function as a difference of two convex functions. An effective algorithm is developed to compute minimax D-optimal designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax D-optimal designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax D-optimal designs. / Graduate