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A new technique is presented to study radio propagation and rough surface scattering problems based on a reformulation of the Magnetic Field Integration Equation (MFIE) called the Single-Scatter Subtraction (S^3) method. This technique amounts to a physical preconditioning by separating the single- and multiple-scatter currents and removing the single-scattering contribution from the integral term that is present in the MFIE. This requires the calculation of a new quantity that is the kernel of the MFIE integral call the kernel integral or Gbar. In this work, 1-dimensional deterministically rough surfaces are simulated by surfaces consisting of single and multiple cosines. In order to truncate the problem domain, a beam illumination is used as the source term and it is shown that this also causes the kernel integral to have a finite support. Using the Single Scatter Subtraction method on these surfaces, closed-form expressions are found for the kernel integral and thus the single-scatter current for a well defined region of validity of surface parameters which may then be efficiently radiated into the far field numerically. Both the closed-form expressions, and the computed radiated fields are studied for their physical significance. This provides a clear physical intuition for the technique as an augmentation to existing ones as a bent-plane approximation as shown analytically and also validated by numeric results. Further analysis resolves a controversy on the nature of Bragg scatter which is found to be a multiple-scatter phenomenon. Error terms present in the kernel integral also raise new questions on the effect of truncation for any MFIE-based solution. Additionally, a dramatic enhancement of backscatter predicted by this new approach versus the Kirchhoff method is observed as the angle of incidence increases due to the error terms. / Doctor of Philosophy / A new technique is presented to study the interaction of electromagnetic waves with rough surfaces. Building on the technique called the Magnetic Field Integral Equation (MFIE) which allows the solution for the electromagnetic fields scattered from the surface by considering only the induced electric and magnetic currents on the surface, the Single-Scatter Substraction (S 3 ) method separates the surface currents into those that interact with the surface only once or single-scatter, and those that interact multiple times called multiple-scatter. Since this is the introduction of this technique, only the former is investigated. In this study, a new quantity which is an integral of one of the components of the standard MFIE is studied and closed-form approximations are presented along with bounds of validity. This provides closed form solutions for the single-scattering currents, from which the radiated fields may be efficiently found numerically. Since they are closed form, the expressions provide insight into the nature of the physical scattering process. Numerical results of these expressions are compared to the standard approximate technique as well as the ”exact” solution found by numerically solving the MFIE. Compared to the standard approximate technique which approximates the surface by a tangent plane at each point on the surface, the single-scatter currents approximate the surface with a bent-plane at each point. This shifts the scattered fields from certain directions to others, and highlights where single- and multiple-scattering have an effect.

A poroelastic finite element formulation originally derived for modeling porous absorbing material in air is adapted to the problem of acoustic scattering from a poroelastic seafloor with a one-dimensional randomly rough interface. The developed formulation is verified through calculation of the plane wave reflection coefficient for the case of a flat surface and comparison with the well known analytical solution. The scattering strengths are then obtained for two different sets of material properties and roughness parameters using a Monte Carlo approach. These numerical results are compared with those given by three analytic scattering models---perturbation theory, the Kirchhoff approximation, and the small-slope approximation---and from those calculated using two finite element formulations where the sediment is modeled as an acoustic fluid. / text

The Method of Ordered Multiple Interactions provides a numerical solution to the integral<br />equations describing surface scattering which is both computationally efficient and reliably<br />convergent. The method has been applied in a variety of ways to solving the electromagnetic<br />scattering from perfectly-conducting rough surfaces. A desire to more accurately predict<br />the scattering from natural terrain has led to the representation of the surface material as<br />penetrable instead of conductive.<br /><br />For this purpose, the Method of Ordered Multiple Interactions is applied to numerically<br />solve the electromagnetic scattering from randomly-rough dielectric surfaces. A primary<br />consequence of the penetrable surface material is the introduction of a pair of coupled integral equations in place of the single integral equation used to solve the problem with a perfectly conducting surface. The method is tested and analyzed by developing independent scattering solutions for canonical cases in a transform domain and by comparing results with solutions from other techniques.<br /><br />The dielectric implementation of the Method of Ordered Multiple Interactions is used to solve<br />the electromagnetic scattering from a class of randomly-rough dielectric surfaces. This allows<br />for the characterization of the effect of a number of transmitter and surface parameters in the<br />scattering problem, observing bistatically and also specifically in the backscatter direction.<br /><br />MOMI is then applied as a method to examine subsurface penetration characteristics from<br />a similar family of rough surfaces. Characteristics of the environment parameters and the<br />scattered field itself are examined, and the numerical challenges associated with observing<br />beneath the surface are identified and addressed.<br /><br />The Method of Ordered Multiple Interactions is then incorporated as a major component of<br />a larger solution which computes the total scattering when a dielectric object is buried just<br />beneath the rough surface. This hyrid approach uses MOMI and the Method of Moments to<br />iteratively account for multiple interactions between the target and the dielectric interface,<br />enabling the study of scattering from the combined environment of a rough surface and the<br />embedded object, as well as the individual scattering events which combine to form the<br />steady-state solution. / Ph. D.

Radio propagation models provide an estimate of the power loss in a communication link caused by the surface of the ground, atmospheric refraction, foliage, and other environmental factors.  Many of the models rely on digital topographic databases to provide information about the terrain, and generally the databases are sparsely sampled relative to the electromagnetic wavelengths used for communication systems.  This work primarily develops a technique to evaluate the effects of that sparsity on the uncertainty of propagation models. That is accomplished by accurately solving the electromagnetic fields over many randomly  rough surfaces which pass through the sparse topographic data points, many possible communication links, all of which fit the underlying data, are represented.  The power variation caused by the different surface realizations is that due to the sparse sampling. Additionally, to verify that this solution technique is a good model, experimental propagation measurements were taken, and compared to the computations. / Master of Science

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This research solves current RF propagation modeling gaps by modifying a single-frequency electromagnetic propagation analysis technique for use on communication signals and propagation channels. This research extended the Methods of Ordered Multiple Interactions (MOMI) algorithm to communication signal propagation studies through the use of Fourier decomposition thereby allowing the analysis and prediction of communication signals propagating over rough surfaces. Current methods of predicting and analyzing communication signal propagation rely on either using only a single frequency instead of a band of frequencies, stochastic techniques that model the environmental effect on the propagated signal, or on empirical models based of large amounts of measured situational data. None of these methods fully capture the actual effect that an environment imparts on a communication signal as it propagates. This research also modifies the Physical Optics (PO) algorithm utilizing Fourier decomposition to compare the Extended MOMI algorithm to. Both algorithms are applied to propagation scenarios utilizing frequencies in the 1-GHz and 5-GHz bands against a series of signal bandwidths and surface roughnesses. The results are analyzed singularly for Extended-MOMI and against Extended-Physical Optics to better understand the benefits associated with using the Extended-MOMI, the limits of the narrowband approximation, the errors incurred when utilizing a simpler or faster propagation algorithm, and to generally characterize these rough surface propagation channels. This research also defines and explores which metrics provide the best characterization and utility for communication signal propagation with the additional insights of amplitude-frequency-phase relationships the new algorithm provides. / Doctor of Philosophy / Communication signal propagation, defined as the propagation of signals that have non-zero bandwidths from one point to another, has significant importance in communication signal design, system design, and deployment as well as in spectrum planning applications. Current methods of predicting and analyzing communication signal propagation rely on either using only a single frequency instead of a band of frequencies, stochastic techniques that model the environmental effect on the propagated signal, or on empirical models based of large amounts of measured situational data. None of these methods fully capture the actual effect that an environment imparts on a communication signal as it propagates. A technique that accurately models the environmental effect on propagating communication signals would result in knowledge about a communication signal strength and shape as it passes through the propagation space. Analyzing communication signals with single frequency propagation algorithms requires assuming all the frequencies that make up the communication signal propagate exactly the same way, an assumption known as the narrowband approximation. It is not known when the narrowband approximation breaks down in various circumstances. Consequently a more rigorous approach needed to be identified to enable a more accurate and complete analysis of communication signals, which is the objective of the research. This research solves these modeling gaps by modifying a single-frequency electromagnetic propagation analysis technique, the Method of Ordered Multiple Interactions, for use on communication signals and propagation channels. The new algorithm, Extended-MOMI, allows for an examination of communication signal propagation over rough surfaces. This new algorithm incorporates all of the information needed for communication signal propagation analysis; something that is missing from current methods. This technique enables tailored communication signal propagation studies as well as an investigations into when the narrowband assumption is valid and when simpler and faster algorithms could be utilized for a now known increase in error. This research also explores which metrics are best utilized with the additional signal information the new algorithm enables.

abstract: A domain decomposition method for analyzing very large FDTD domains, hundreds of thousands of wavelengths long, is demonstrated by application to the problem of radar scattering in the maritime environment. Success depends on the elimination of artificial scattering from the “sky” boundary and is ensured by an ultra-high-performance absorbing termination which eliminates this reflection at angles of incidence as shallow as 0.03 degrees off grazing. The two-dimensional (2D) problem is used to detail the features of the method. The results are cross-validated by comparison to a parabolic equation (PE) method and surface integral equation method on a 1.7km sea surface problem, and to a PE method on propagation through an inhomogeneous atmosphere in a 4km-long space, both at X-band. Additional comparisons are made against boundary integral equation and PE methods from the literature in a 3.6km space containing an inhomogeneous atmosphere above a flat sea at S-band. The applicability of the method to the three-dimensional (3D) problem is shown via comparison of a 2D solution to the 3D solution of a corridor of sea. As a technical proof of the scalability of the problem with computational power, a 5m-wide, 2m-tall, 1050m-long 3D corridor containing 321.8 billion FDTD cells has been simulated at X-band. A plane wave spectrum analysis of the (X-band) scattered fields produced by a 5m-wide, 225m-long realistic 3D sea surface, and the 2D analog surface obtained by extruding a 2D sea along the width of the corridor, reveals the existence of out-of-plane 3D phenomena missed by the traditional 2D analysis. The realistic sea introduces random strong flashes and nulls in addition to a significant amount of cross-polarized field. Spatial integration using a dispersion-corrected Green function is used to reconstruct the scattered fields outside of the computational FDTD space which would impinge on a 3D target at the end of the corridor. The proposed final approach is a hybrid method where 2D FDTD carries the signal for the first tens of kilometers and the last kilometer is analyzed in 3D. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2018

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