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Cognitive radio (CR) is a multi-disciplinary field that makes use of knowledge from a multitude of specialties such as antenna design, circuits, systems and digital signal processing among many others. CR has emerged as an area of interest over 20 years ago and in the years since has evolved to encompass both realizable theory and physical hardware. Key among the latter are reconfigurable, software defined radios and embedded sensors that incorporate flexible parameters, allowing a CR to operate in a wide variety of electromagnetic (EM) environments. The ideal cognitive radio would be capable of adapting to a changing EM environment without any specific knowledge or direction from the operator. This would require the radio itself to be aware of the EM environment and ideally, to sense the EM environment and act upon it in a semi-autonomous or autonomous way. While most research in this field has focused on the spectrum sensing aspects of the domain, development of the above-described "ideal CR" would require that the EM environment be characterized in domains such as angular, time and polarization among others. Signal dependent parameters can also be characterized such as bandwidth and modulation. The multi-dimensionality of the environment and the signals present within entail challenges with scalability and efficiency. This work focuses on the efficient sensing of signals in the angular domain also known as direction-of-arrival (DOA). There are a multitude of ways to find a signal's DOA. All require multiple antennas connected to a single or multiple radio nodes, antennas with patterns that gather energy in a particular direction, or multiple single antenna radios. The methods that utilize multiple antennas exploit the phase and/or amplitude relationships between the antennas themselves for a signal's DOA. The principal tradeoff between DOA methods typically converges to scan time vs. number of antenna elements. For many DOA architectures, this also means a scan time tradeoff with angular resolution as well. Since fast and accurate measurements are important for characterizing a quickly changing EM environment, sensing speed becomes a key requirement in designing a CR and associated sensing architecture. In this work, we present a DOA sensing architecture suitable for use in CR systems called the Direct Space to Information Converter (DSIC). Unlike current state-of-the art DOA methods, the DSIC breaks the tradeoff between scan time and the number of antenna elements needed for a given angular resolution when compared to other DOA and beamforming architectures. By randomly modulating the received signals in space, across multiple antenna elements and taking a few, compressed sensing (CS) measurements, the DSIC is able to angularly scan a wide field of view in an order of magnitude less time than other DOA methods. These CS measurements correspond to different random perturbations of the DSIC's antenna factor and can be quantized in as little as a single bit of resolution in the DSIC's phaseshifters/vector modulators. The DSIC is able to create multiple user-specified nulls in the antenna pattern to reduce the impact of strong known interferers while also simultaneously scanning the full field of view. Additionally, the designer has the option of performing simultaneous reception or nulling while sensing. If nulling, a few different methods are available each suitable for varying EM environments and potential use cases. We show in detail the multi-disciplinary process in designing a complete end-to-end hardware solution, selecting the parameters necessary to design the DSIC as well as test and characterize it. The benefits of the DSIC are discussed and compared to the current state-of the art with an emphasis on architectures suitable for use in interferer rich environments. We demonstrate that the energy usage of the DSIC is lower than comparable CR architectures by a large factor and scales much more favorably in terms of energy and physical complexity as the number of antenna elements increase. At the conclusion of this work we also discuss future areas of exploration in extending the DSIC's capability by incorporating an ability to sense the spectrum as well as the DOA of a signal.

<p> This thesis presents solutions to several inverse problems m electromagnetism and microwave engineering. In general, these inverse problems belong to two applications: breast cancer diagnosis using microwave imaging and defect characterization in metallic structures using magnetic flux leakage (MFL). </p> <p> Our contribution in microwave imaging for breast tumor detection can be divided into three parts. First, we propose a novel ultra-wide band (UWB) antenna that can operate in direct contact with the breast without the need for coupling liquids. This antenna is designed such that more than 90% of the radiated power is directed toward the tissue from its front aperture over the UWB. The performance of the antenna is investigated via simulation and measurement of the following parameters: return loss, near-field directivity, efficiency, fidelity, and group velocity. Overall, the results show that the antenna is a good candidate for frequency and time-domain imaging techniques. </p> <p> Second, we have proposed an aperture raster scanning setup that benefits from the features of our novel antenna. In this scanning setup, the breast tissue is compressed between two rectangular plates (apertures) while two antennas perform two-dimensional (2-D) scan by moving together on both sides of the compressed tissue. For each scanning step, the transmission S-parameter between the two antennas is recorded at several frequencies within UWB. Then, the modulus of the calibrated transmission S-parameter is plotted at each frequency to provide a 2-D image of the interior of the breast. The images are enhanced using a de-blurring technique based on blind de-convolution. This setup provides real time images of strong scatterers inside the normal tissue. </p> <p> Third, we propose 2-D and three-dimensional (3-D) holography algorithms to further improve the quality of the images obtained from the proposed planar scanning setup. These techniques are based on the Fourier transforms of the collected data to provide an image of a 2-D target (when collecting data at a single frequency) or a 3-D target (when collecting wide-band data). These techniques are fast and very robust to noise. The capability of the 2D and 3-D holographic imaging techniques is examined via simulation results. </p> <p> For defect characterization in metallic structures using MFL technique, we propose fast and reliable methodologies to invert the measured MFL response to the defect's shape parameters. First, we present a procedure to estimate the shape parameters of rectangular cracks which are the most common type of defects in the metallic structures. The procedure consists of estimating orientation, length, and depth of the cracks, consecutively. We validate this procedure via estimating the shape parameters of pre-known cracks from the simulated and measured MFL responses. Then, we present a methodology based on space mapping (SM) optimization for defect characterization. We examme the efficiency of this methodology for two types of defects: rectangular cracks and cylindrical pits. </p> / Thesis / Doctor of Philosophy (PhD)

Electromagnetism and optimal control stand out as a topics that feature impactful applications in modern engineering, as well as challenging theoretical aspects of mathematical analysis. Within this context, a major role is played by the search of necessary and sufficient conditions characterizing optimal solutions, as they are functional to numerical algorithms aiming to approximate such solutions. In this thesis, three standalone topics in optimization sharing the underlying framework of Maxwell-related PDEs are discussed. First, I present an optimal control problem driven by a quasi-linear magneto-static obstacle problem featuring first-order differential state constraints. The non-linearity allows to suitably model electromagnetic waves in the presence of ferromagnetic materials, while the first-order obstacle is relevant for applications in the field of magnetic shielding. Existence theory and the derivation of an optimality system are addressed with an approximation technique based on a relaxation-penalization of the variational inequality. Second, I analyze an eddy current problem controlled through a dipole type source, i.e. a Dirac mass with fixed position and variable intensity: well-posedness of the state equation through a fundamental solution (of a curl curl - Id operator) approach and first order conditions are dealt with. To conclude, I discuss the computation of the topological derivative for shape functionals constrained to low-frequency electromagnetic problems (closely related to the eddy current model), with respect to the inclusion/removal of conducting material; the results are obtained using a Lagrangian approach and in particular the so-called averaged adjoint method. This approach requires the study of the asymptotic behavior of the solutions of some problems defined in the whole space, and the introduction and consequent analysis of appropriate function spaces.

Having an in-depth knowledge on the performance characteristics of space mechanisms in flight operation, with special attention to nominal vs. anomalous performance, is vital for mission success. On many unmanned spacecraft for Earth observation missions, reaction wheel assemblies are used in combination with magnetic torquers for their attitude control. Understanding the magnitude of potential electromagnetic interactions between both types of attitude control actuators is of particular interest for large spacecraft as they are usually equipped with strong magnetic torquers. In this frame, experimental investigations have been performed on simplified test set-ups with flight representative reaction wheel assemblies operated in external homogeneous magnetic fields as well as in close vicinity of magnetic torquers which create inhomogeneous magnetic fields. The test results have been successfully correlated with computer-based simulation output obtained from models with different levels of complexity. The impact of critical parameters like the location of magnetic torquers relative to reaction wheels and their material properties such as electrical conductivity and magnetic permeability have been particularly studied. It has been found that magnetic torquers pointing orthogonal to the reaction wheel spin axis cause the highest influence on the reaction wheel's performance characteristics. The material choice for the flywheel rotor, being either ferromagnetic or paramagnetic, has a strong influence when exposing the reaction wheel assembly to external magnetic fields. In general, the increase of loss torque noticed with all reaction wheels tested has been caused by eddy current effects. In this frame, the impact of using ferromagnetic materials has been surprisingly strong. Specifically, the local distortions and guidance of the magnetic field due to ferromagnetism has a highly amplifying effect on eddy currents. However, interestingly it has also been found that the impact of material choice is much more severe when considering homogeneous magnetic fields and strong magnetic torquers while being less important with relatively small magnetic torquers. The main reasons for this finding have been compensating effects of ferromagnetic vs. highly conductive materials. / Une connaissance approfondie des caractéristiques de performance des mécanismes spatiaux en vol, et plus particulièrement des performances nominales comparées aux performances anormales, est d’importance vitale pour la réussite d’une mission. Pour les missions d’observation de la Terre, la plupart des engins spatiaux non habités sont équipés d’ensembles de roues de réaction ainsi que de magnéto-coupleurs pour le contrôle d’attitude et la stabilisation. Comprendre l'ampleur des interactions électromagnétiques potentielles entre les deux types de capteurs de contrôle d'attitude est particulièrement pertinent pour les engins spatiaux de grande taille car ceux-ci sont généralement équipés de puissants magnéto-coupleurs. Dans ce cadre, des études expérimentales ont été réalisées sur des bancs d'essais simplifiés avec des ensembles de roues à réaction représentatifs du vol fonctionnant dans des champs magnétiques externes homogènes ainsi qu'à proximité immédiate de coupleurs magnétiques (champs magnétiques hétérogènes). Les résultats des tests ont été corrélés avec succès grâce à des simulations informatiques sur des modèles présentant différents niveaux de complexité. L'influence de paramètres critiques comme l'emplacement des magnéto-coupleurs par rapport aux roues de réaction et leurs propriétés matérielles telles que la conductivité électrique et la perméabilité relative ont été particulièrement étudiés. Il a été établi que les couples magnétiques pointant orthogonalement à l'axe de rotation de la roue de réaction ont le plus d'influence sur les caractéristiques de performance des roues de réaction. Le choix du matériau pour le rotor de volant, c’est à dire ferromagnétique ou paramagnétique, a une forte influence si l'ensemble de roue de réaction est exposé à des champs magnétiques externes. En général, l'augmentation de la perte de transfert de couple constatée avec toutes les roues de réaction testées a été causée par les effets de courants de Foucault.Dans ce cadre, l'influence des matériaux ferromagnétiques a été étonnamment forte. En effet, les distorsions qui en résultent et le guidage du champ magnétique amplifient fortement les courants de Foucault. Cependant, il a été constaté que l'effet du choix du matériau est beaucoup plus important si l'on considère des champs magnétiques homogènes et des grands coupleurs magnétiques. Toutefois, cet effet est moins important avec des petits coupleurs magnétiques.

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