Radar systems seek to detect targets in some search space (e.g. volume of airspace, or area on the ground surface) by actively illuminating the environment with radio waves. This illumination yields a return from targets of interest as well as highly reflective terrain features that perhaps are not of interest (called clutter). Data adaptive algorithms are therefore employed to provide robust detection of targets against a background of clutter and other forms of interference. The adaptive matched filter (AMF) is an effective, well-established detection statistic whose exact probability density function (PDF) is known under prevalent radar system model assumptions. Variations of this approach, however, lead to tests whose PDFs remain unknown or incalculable. This project will study the effectiveness of saddlepoint methods applied to approximate the known pdf of the clairvoyant matched filter, using MATLAB to complete the numerical calculations. Specifically, the approximation was used to compute tail probabilities for a range of thresholds, as well as compute the threshold and probability of detection for a specific desired probability of false alarm. This was compared to the same values computed using the known exact PDF of the filter, with the comparison demonstrating high levels of accuracy for the saddlepoint approximation. The results are encouraging, and justify further study of the approximation as applied to more strained or complicated scenarios.

Limited spectral access motivates technologies that adapt to diminishing resources and increasingly cluttered environments. A joint positioning-communications system is designed and implemented on \acf{COTS} hardware. This system enables simultaneous positioning of, and communications between, nodes in a distributed network of base-stations and unmanned aerial systems (UASs). This technology offers extreme ranging precision ($<$ 5 cm) with minimal bandwidth (10 MHz), a secure communications link to protect against cyberattacks, a small form factor that enables integration into numerous platforms, and minimal resource consumption which supports high-density networks. The positioning and communications tasks are performed simultaneously with a single, co-use waveform, which efficiently utilizes limited resources and supports higher user densities. The positioning task uses a cooperative, point-to-point synchronization protocol to estimate the relative position and orientation of all users within the network. The communications task distributes positioning information between users and secures the positioning task against cyberattacks. This high-performance system is enabled by advanced time-of-arrival estimation techniques and a modern phase-accurate distributed coherence synchronization algorithm. This technology may be installed in ground-stations, ground vehicles, unmanned aerial systems, and airborne vehicles, enabling a highly-mobile, re-configurable network with numerous applications.

Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.

The use of conventional weather radar in vulcanology leads to two problems: the radars often use wavelengths which are too long to detect the fine ash particles, and they cannot be field–adjusted to fit the wide variety of eruptions. Thus, to better study these geologic processes, a new radar must be developed that is easily reconfigurable to allow for flexibility and can operate at sufficiently short wavelengths.

This thesis investigates how to design a radar using a field–programmable gate array board to generate the radar signal, and process the returned signal to determine the distance and concentration of objects (in this case, ash). The purpose of using such a board lies in its reconfigurability—a design can (relatively easily) be adjusted, recompiled, and reuploaded to the hardware with none of the cost or time overhead required of a standard weather radar.

The design operates on the principle of frequency–modulated continuous–waves, in which the output signal frequency changes as a function of time. The difference in transmit and echo frequencies determines the distance of an object, while the magnitude of a particular difference frequency corresponds to concentration. Thus, by viewing a spectrum of frequency differences, one is able to see both the concentration and distances of ash from the radar.

The transmit signal data was created in MATLAB®, while the radar was designed with MATLAB® Simulink® using hardware IP blocks and implemented on the ROACH2 signal processing hardware, which utilizes a Xilinx® Virtex®–6 chip. The output is read from a computer linked to the hardware through Ethernet, using a Python™ script. Testing revealed minor flaws due to the usage of lower–grade components in the prototype. However, the functionality of the proposed radar design was proven, making this approach to radar a promising path for modern vulcanology.

The use of conventional weather radar in vulcanology leads to two problems: the radars often use wavelengths which are too long to detect the fine ash particles, and they cannot be field–adjusted to fit the wide variety of eruptions. Thus, to better study these geologic processes, a new radar must be developed that is easily reconfigurable to allow for flexibility and can operate at sufficiently short wavelengths.

This thesis investigates how to design a radar using a field–programmable gate array board to generate the radar signal, and process the returned signal to determine the distance and concentration of objects (in this case, ash). The purpose of using such a board lies in its reconfigurability—a design can (relatively easily) be adjusted, recompiled, and reuploaded to the hardware with none of the cost or time overhead required of a standard weather radar.

The design operates on the principle of frequency–modulated continuous–waves, in which the output signal frequency changes as a function of time. The difference in transmit and echo frequencies determines the distance of an object, while the magnitude of a particular difference frequency corresponds to concentration. Thus, by viewing a spectrum of frequency differences, one is able to see both the concentration and distances of ash from the radar.

The transmit signal data was created in MATLAB®, while the radar was designed with MATLAB® Simulink® using hardware IP blocks and implemented on the ROACH2 signal processing hardware, which utilizes a Xilinx® Virtex®–6 chip. The output is read from a computer linked to the hardware through Ethernet, using a Python™ script. Testing revealed minor flaws due to the usage of lower–grade components in the prototype. However, the functionality of the proposed radar design was proven, making this approach to radar a promising path for modern vulcanology.

Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain.

This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges.

Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.

Spectral congestion is quickly becoming a problem for the telecommunications sector. In order to alleviate spectral congestion and achieve electromagnetic radio frequency (RF) convergence, communications and radar systems are increasingly encouraged to share bandwidth. In direct opposition to the traditional spectrum sharing approach between radar and communications systems of complete isolation (temporal, spectral or spatial), both systems can be jointly co-designed from the ground up to maximize their joint performance for mutual benefit. In order to properly characterize and understand cooperative spectrum sharing between radar and communications systems, the fundamental limits on performance of a cooperative radar-communications system are investigated. To facilitate this investigation, performance metrics are chosen in this dissertation that allow radar and communications to be compared on the same scale. To that effect, information is chosen as the performance metric and an information theoretic radar performance metric compatible with the communications data rate, the radar estimation rate, is developed. The estimation rate measures the amount of information learned by illuminating a target. With the development of the estimation rate, standard multi-user communications performance bounds are extended with joint radar-communications users to produce bounds on the performance of a joint radar-communications system. System performance for variations of the standard spectrum sharing problem defined in this dissertation are investigated, and inner bounds on performance are extended to account for the effect of continuous radar waveform optimization, multiple radar targets, clutter, phase noise, and radar detection. A detailed interpretation of the estimation rate and a brief discussion on how to use these performance bounds to select an optimal operating point and achieve RF convergence are provided.

China's rapid growth was fueled by an unsustainable method: trade environment for GDP. Air pollution has reached dangerous levels and has taken a serious toll on China's economic progress. The World Bank estimates that in 2013, China lost about 10% of its GDP to pollution. As the cost of burning fossil fuels and public dismay continue to mount, the government is taking steps to reduce carbon emissions and appease the people. The rapidly growing nuclear energy program is one of the energy solutions that China is using to addressing carbon emissions. While China has built a respectable amount of renewable energy capacity (such as wind and solar), much of that capacity is not connected to the power grid. Nuclear energy on the other hand, provides a low-emission alternative that operates independently of weather and sunlight. However, the accelerated pace of reactor construction in recent years presents challenges for the safe operation of nuclear energy in China. It is in China's (and the world's) best interest that a repeat of the Fukushima accident does not occur. In the wake of the Fukushima nuclear accident, public support for nuclear energy in China took a serious hit. A major domestic nuclear accident would be detrimental to the development of nuclear energy in China and diminish the government's reliability in the eyes of the people. This paper will outline those risk factors such as regulatory efforts, legal framework, technological issues, spent fuel disposal, and public perception and provide suggestions to decrease the risk of a major nuclear accident.

Scattering from random rough surface has been of interest for decades. Several

methods were proposed to solve this problem, and Kirchho approximation (KA)

and small perturbation method (SMP) are among the most popular. Both methods

provide accurate results on rst order scattering, and the range of validity is limited

and cross-polarization scattering coecient is zero for these two methods unless these

two methods are carried out for higher orders. Furthermore, it is complicated for

higher order formulation and multiple scattering and shadowing are neglected in these

classic methods.

Extension of these two methods has been made in order to x these problems.

However, it is usually complicated and problem specic. While small slope approximation

is one of the most widely used methods to bridge KA and SMP, it is not easy

to implement in a general form. Two scale model can be employed to solve scattering

problems for a tilted perturbation plane, the range of validity is limited.

A new model is proposed in this thesis to deal with cross-polarization scattering

phenomenon on perfect electric conducting random surfaces. Integral equation

is adopted in this model. While integral equation method is often combined with

numerical method to solve the scattering coecient, the proposed model solves the

integral equation iteratively by analytic approximation. We utilize some approximations

on the randomness of the surface, and obtain an explicit expression. It is shown

that this expression achieves agreement with SMP method in second order.

There is an ever-growing need for broadband conformal antennas to not only reduce the number of antennas utilized to cover a broad range of frequencies (VHF-UHF) but also to reduce visual and RF signatures associated with communication systems. In many applications antennas needs to be very close to low-impedance mediums or embedded inside low-impedance mediums. However, for conventional metal and dielectric antennas to operate efficiently in such environments either a very narrow bandwidth must be tolerated, or enough loss added to expand the bandwidth, or they must be placed one quarter of a wavelength above the conducting surface. The latter is not always possible since in the HF through low UHF bands, critical to Military and Security functions, this quarter-wavelength requirement would result in impractically large antennas.

Despite an error based on a false assumption in the 1950’s, which had severely underestimated the efficiency of magneto-dielectric antennas, recently demonstrated magnetic-antennas have been shown to exhibit extraordinary efficiency in conformal applications. Whereas conventional metal-and-dielectric antennas carrying radiating electric currents suffer a significant disadvantage when placed conformal to the conducting surface of a platform, because they induce opposing image currents in the surface, magnetic-antennas carrying magnetic radiating currents have no such limitation. Their magnetic currents produce co-linear image currents in electrically conducting surfaces.

However, the permeable antennas built to date have not yet attained the wide bandwidth expected because the magnetic-flux-channels carrying the wave have not been designed to guide the wave near the speed of light at all frequencies. Instead, they tend to lose the wave by a leaky fast-wave mechanism at low frequencies or they over-bind a slow-wave at high frequencies. In this dissertation, we have studied magnetic antennas in detail and presented the design approach and apparatus required to implement a flux-channel carrying the magnetic current wave near the speed of light over a very broad frequency range which also makes the design of a frequency independent antenna (spiral) possible. We will learn how to construct extremely thin conformal antennas, frequency-independent permeable antennas, and even micron-sized antennas that can be embedded inside the brain without damaging the tissue.