Distributed inference has applications in fields as varied as source localization, evaluation of network quality, and remote monitoring of wildlife habitats. In this dissertation, distributed inference algorithms over multiple-access channels are considered. The performance of these algorithms and the effects of wireless communication channels on the performance are studied. In a first class of problems, distributed inference over fading Gaussian multiple-access channels with amplify-and-forward is considered. Sensors observe a phenomenon and transmit their observations using the amplify-and-forward scheme to a fusion center (FC). Distributed estimation is considered with a single antenna at the FC, where the performance is evaluated using the asymptotic variance of the estimator. The loss in performance due to varying assumptions on the limited amounts of channel information at the sensors is quantified. With multiple antennas at the FC, a distributed detection problem is also considered, where the error exponent is used to evaluate performance. It is shown that for zero-mean channels between the sensors and the FC when there is no channel information at the sensors, arbitrarily large gains in the error exponent can be obtained with sufficient increase in the number of antennas at the FC. In stark contrast, when there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the FC is shown to be no more than a factor of 8/π for Rayleigh fading channels between the sensors and the FC, independent of the number of antennas at the FC, or correlation among noise samples across sensors. In a second class of problems, sensor observations are transmitted to the FC using constant-modulus phase modulation over Gaussian multiple-access-channels. The phase modulation scheme allows for constant transmit power and estimation of moments other than the mean with a single transmission from the sensors. Estimators are developed for the mean, variance and signal-to-noise ratio (SNR) of the sensor observations. The performance of these estimators is studied for different distributions of the observations. It is proved that the estimator of the mean is asymptotically efficient if and only if the distribution of the sensor observations is Gaussian.

Analysis of social networks has the potential to provide insights into wide range of applications. As datasets continue to grow, a key challenge is the lack of a widely applicable algorithmic framework for detection of statistically anomalous networks and network properties. Unlike traditional signal processing, where models of truth or empirical verification and background data exist and are often well defined, these features are commonly lacking in social and other networks. Here, a novel algorithmic framework for statistical signal processing for graphs is presented. The framework is based on the analysis of spectral properties of the residuals matrix. The framework is applied to the detection of innovation patterns in publication networks, leveraging well-studied empirical knowledge from the history of science. Both the framework itself and the application constitute novel contributions, while advancing algorithmic and mathematical techniques for graph-based data and understanding of the patterns of emergence of novel scientific research. Results indicate the efficacy of the approach and highlight a number of fruitful future directions.

This dissertation introduces stochastic ordering of instantaneous channel powers of fading channels as a general method to compare the performance of a communication system over two different channels, even when a closed-form expression for the metric may not be available. Such a comparison is with respect to a variety of performance metrics such as error rates, outage probability and ergodic capacity, which share common mathematical properties such as monotonicity, convexity or complete monotonicity. Complete monotonicity of a metric, such as the symbol error rate, in conjunction with the stochastic Laplace transform order between two fading channels implies the ordering of the two channels with respect to the metric. While it has been established previously that certain modulation schemes have convex symbol error rates, there is no study of the complete monotonicity of the same, which helps in establishing stronger channel ordering results. Toward this goal, the current research proves for the first time, that all 1-dimensional and 2-dimensional modulations have completely monotone symbol error rates. Furthermore, it is shown that the frequently used parametric fading distributions for modeling line of sight exhibit a monotonicity in the line of sight parameter with respect to the Laplace transform order. While the Laplace transform order can also be used to order fading distributions based on the ergodic capacity, there exist several distributions which are not Laplace transform ordered, although they have ordered ergodic capacities. To address this gap, a new stochastic order called the ergodic capacity order has been proposed herein, which can be used to compare channels based on the ergodic capacity. Using stochastic orders, average performance of systems involving multiple random variables are compared over two different channels. These systems include diversity combining schemes, relay networks, and signal detection over fading channels with non-Gaussian additive noise. This research also addresses the problem of unifying fading distributions. This unification is based on infinite divisibility, which subsumes almost all known fading distributions, and provides simplified expressions for performance metrics, in addition to enabling stochastic ordering.

Recently, the location of the nodes in wireless networks has been modeled as point processes. In this dissertation, various scenarios of wireless communications in large-scale networks modeled as point processes are considered. The first part of the dissertation considers signal reception and detection problems with symmetric alpha stable noise which is from an interfering network modeled as a Poisson point process. For the signal reception problem, the performance of space-time coding (STC) over fading channels with alpha stable noise is studied. We derive pairwise error probability (PEP) of orthogonal STCs. For general STCs, we propose a maximum-likelihood (ML) receiver, and its approximation. The resulting asymptotically optimal receiver (AOR) does not depend on noise parameters and is computationally simple, and close to the ML performance. Then, signal detection in coexisting wireless sensor networks (WSNs) is considered. We define a binary hypothesis testing problem for the signal detection in coexisting WSNs. For the problem, we introduce the ML detector and simpler alternatives. The proposed mixed-fractional lower order moment (FLOM) detector is computationally simple and close to the ML performance. Stochastic orders are binary relations defined on probability. The second part of the dissertation introduces stochastic ordering of interferences in large-scale networks modeled as point processes. Since closed-form results for the interference distributions for such networks are only available in limited cases, it is of interest to compare network interferences using stochastic. In this dissertation, conditions on the fading distribution and path-loss model are given to establish stochastic ordering between interferences. Moreover, Laplace functional (LF) ordering is defined between point processes and applied for comparing interference. Then, the LF orderings of general classes of point processes are introduced. It is also shown that the LF ordering is preserved when independent operations such as marking, thinning, random translation, and superposition are applied. The LF ordering of point processes is a useful tool for comparing spatial deployments of wireless networks and can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions for such metrics are unavailable.

Structural health management (SHM) is emerging as a vital methodology to help engineers improve the safety and maintainability of critical structures. SHM systems are designed to reliably monitor and test the health and performance of structures in aerospace, civil, and mechanical engineering applications. SHM combines multidisciplinary technologies including sensing, signal processing, pattern recognition, data mining, high fidelity probabilistic progressive damage models, physics based damage models, and regression analysis. Due to the wide application of carbon fiber reinforced composites and their multiscale failure mechanisms, it is necessary to emphasize the research of SHM on composite structures. This research develops a comprehensive framework for the damage detection, localization, quantification, and prediction of the remaining useful life of complex composite structures. To interrogate a composite structure, guided wave propagation is applied to thin structures such as beams and plates. Piezoelectric transducers are selected because of their versatility, which allows them to be used as sensors and actuators. Feature extraction from guided wave signals is critical to demonstrate the presence of damage and estimate the damage locations. Advanced signal processing techniques are employed to extract robust features and information. To provide a better estimate of the damage for accurate life estimation, probabilistic regression analysis is used to obtain a prediction model for the prognosis of complex structures subject to fatigue loading. Special efforts have been applied to the extension of SHM techniques on aerospace and spacecraft structures, such as UAV composite wings and deployable composite boom structures. Necessary modifications of the developed SHM techniques were conducted to meet the unique requirements of the aerospace structures. The developed SHM algorithms are able to accurately detect and quantify impact damages as well as matrix cracking introduced.

Global Positioning System (GPS) is a navigation system widely used in civilian and military application, but its accuracy is highly impacted with consequential fading, and possible loss of communication due to multipath propagation and high power interferences. This dissertation proposes alternatives to improve the performance of the GPS receivers to obtain a system that can be reliable in critical situations. The basic performance of the GPS receiver consists of receiving the signal with an antenna array, delaying the signal at each antenna element, weighting the delayed replicas, and finally, combining the weighted replicas to estimate the desired signal. Based on these, three modifications are proposed to improve the performance of the system. The first proposed modification is the use of the Least Mean Squares (LMS) algorithm with two variations to decrease the convergence time of the classic LMS while achieving good system stability. The results obtained by the proposed LMS demonstrate that the algorithm can achieve the same stability as the classic LMS using a small step size, and its convergence rate is better than the classic LMS using a large step size. The second proposed modification is to replace the uniform distribution of the time delays (or taps) by an exponential distribution that decreases the bit-error rate (BER) of the system without impacting the computational efficiency of the uniform taps. The results show that, for a BER of 0.001, the system can operate with a 1 to 2 dB lower signal-to-noise ratio (SNR) when an exponential distribution is used rather than a uniform distribution. Finally, the third modification is implemented in the design of the antenna array. In this case, the gain of each microstrip element is enhanced by embedding ferrite rings in the substrate, creating a hybrid substrate. The ferrite rings generates constructive interference between the incident and reflected fields; consequently, the gain of a single microstrip element is enhanced by up to 4 dB. When hybrid substrates are used in microstrip element arrays, a significant enhancement in angle range is achieved for a given reflection coefficient compared to using a conventional substrate.

Structural integrity is an important characteristic of performance for critical components used in applications such as aeronautics, materials, construction and transportation. When appraising the structural integrity of these components, evaluation methods must be accurate. In addition to possessing capability to perform damage detection, the ability to monitor the level of damage over time can provide extremely useful information in assessing the operational worthiness of a structure and in determining whether the structure should be repaired or removed from service. In this work, a sequential Bayesian approach with active sensing is employed for monitoring crack growth within fatigue-loaded materials. The monitoring approach is based on predicting crack damage state dynamics and modeling crack length observations. Since fatigue loading of a structural component can change while in service, an interacting multiple model technique is employed to estimate probabilities of different loading modes and incorporate this information in the crack length estimation problem. For the observation model, features are obtained from regions of high signal energy in the time-frequency plane and modeled for each crack length damage condition. Although this observation model approach exhibits high classification accuracy, the resolution characteristics can change depending upon the extent of the damage. Therefore, several different transmission waveforms and receiver sensors are considered to create multiple modes for making observations of crack damage. Resolution characteristics of the different observation modes are assessed using a predicted mean squared error criterion and observations are obtained using the predicted, optimal observation modes based on these characteristics. Calculation of the predicted mean square error metric can be computationally intensive, especially if performed in real time, and an approximation method is proposed. With this approach, the real time computational burden is decreased significantly and the number of possible observation modes can be increased. Using sensor measurements from real experiments, the overall sequential Bayesian estimation approach, with the adaptive capability of varying the state dynamics and observation modes, is demonstrated for tracking crack damage.

Super-Resolution (SR) techniques are widely developed to increase image resolution by fusing several Low-Resolution (LR) images of the same scene to overcome sensor hardware limitations and reduce media impairments in a cost-effective manner. When choosing a solution for the SR problem, there is always a trade-off between computational efficiency and High-Resolution (HR) image quality. Existing SR approaches suffer from extremely high computational requirements due to the high number of unknowns to be estimated in the solution of the SR inverse problem. This thesis proposes efficient iterative SR techniques based on Visual Attention (VA) and perceptual modeling of the human visual system. In the first part of this thesis, an efficient ATtentive-SELective Perceptual-based (AT-SELP) SR framework is presented, where only a subset of perceptually significant active pixels is selected for processing by the SR algorithm based on a local contrast sensitivity threshold model and a proposed low complexity saliency detector. The proposed saliency detector utilizes a probability of detection rule inspired by concepts of luminance masking and visual attention. The second part of this thesis further enhances on the efficiency of selective SR approaches by presenting an ATtentive (AT) SR framework that is completely driven by VA region detectors. Additionally, different VA techniques that combine several low-level features, such as center-surround differences in intensity and orientation, patch luminance and contrast, bandpass outputs of patch luminance and contrast, and difference of Gaussians of luminance intensity are integrated and analyzed to illustrate the effectiveness of the proposed selective SR frameworks. The proposed AT-SELP SR and AT-SR frameworks proved to be flexible by integrating a Maximum A Posteriori (MAP)-based SR algorithm as well as a fast two-stage Fusion-Restoration (FR) SR estimator. By adopting the proposed selective SR frameworks, simulation results show significant reduction on average in computational complexity with comparable visual quality in terms of quantitative metrics such as PSNR, SNR or MAE gains, and subjective assessment. The third part of this thesis proposes a Perceptually Weighted (WP) SR technique that incorporates unequal weighting parameters in the cost function of iterative SR problems. The proposed approach is inspired by the unequal processing of the Human Visual System (HVS) to different local image features in an image. Simulation results show an enhanced reconstruction quality and faster convergence rates when applied to the MAP-based and FR-based SR schemes.

Multidimensional (MD) discrete Fourier transform (DFT) is a key kernel algorithm in many signal processing applications, such as radar imaging and medical imaging. Traditionally, a two-dimensional (2-D) DFT is computed using Row-Column (RC) decomposition, where one-dimensional (1-D) DFTs are computed along the rows followed by 1-D DFTs along the columns. However, architectures based on RC decomposition are not efficient for large input size data which have to be stored in external memories based Synchronous Dynamic RAM (SDRAM). In this dissertation, first an efficient architecture to implement 2-D DFT for large-sized input data is proposed. This architecture achieves very high throughput by exploiting the inherent parallelism due to a novel 2-D decomposition and by utilizing the row-wise burst access pattern of the SDRAM external memory. In addition, an automatic IP generator is provided for mapping this architecture onto a reconfigurable platform of Xilinx Virtex-5 devices. For a 2048x2048 input size, the proposed architecture is 1.96 times faster than RC decomposition based implementation under the same memory constraints, and also outperforms other existing implementations. While the proposed 2-D DFT IP can achieve high performance, its output is bit-reversed. For systems where the output is required to be in natural order, use of this DFT IP would result in timing overhead. To solve this problem, a new bandwidth-efficient MD DFT IP that is transpose-free and produces outputs in natural order is proposed. It is based on a novel decomposition algorithm that takes into account the output order, FPGA resources, and the characteristics of off-chip memory access. An IP generator is designed and integrated into an in-house FPGA development platform, AlgoFLEX, for easy verification and fast integration. The corresponding 2-D and 3-D DFT architectures are ported onto the BEE3 board and their performance measured and analyzed. The results shows that the architecture can maintain the maximum memory bandwidth throughout the whole procedure while avoiding matrix transpose operations used in most other MD DFT implementations. The proposed architecture has also been ported onto the Xilinx ML605 board. When clocked at 100 MHz, 2048x2048 images with complex single-precision can be processed in less than 27 ms. Finally, transpose-free imaging flows for range-Doppler algorithm (RDA) and chirp-scaling algorithm (CSA) in SAR imaging are proposed. The corresponding implementations take advantage of the memory access patterns designed for the MD DFT IP and have superior timing performance. The RDA and CSA flows are mapped onto a unified architecture which is implemented on an FPGA platform. When clocked at 100MHz, the RDA and CSA computations with data size 4096x4096 can be completed in 323ms and 162ms, respectively. This implementation outperforms existing SAR image accelerators based on FPGA and GPU.

Damage detection in heterogeneous material systems is a complex problem and requires an in-depth understanding of the material characteristics and response under varying load and environmental conditions. A significant amount of research has been conducted in this field to enhance the fidelity of damage assessment methodologies, using a wide range of sensors and detection techniques, for both metallic materials and composites. However, detecting damage at the microscale is not possible with commercially available sensors. A probable way to approach this problem is through accurate and efficient multiscale modeling techniques, which are capable of tracking damage initiation at the microscale and propagation across the length scales. The output from these models will provide an improved understanding of damage initiation; the knowledge can be used in conjunction with information from physical sensors to improve the size of detectable damage. In this research, effort has been dedicated to develop multiscale modeling approaches and associated damage criteria for the estimation of damage evolution across the relevant length scales. Important issues such as length and time scales, anisotropy and variability in material properties at the microscale, and response under mechanical and thermal loading are addressed. Two different material systems have been studied: metallic material and a novel stress-sensitive epoxy polymer.

For metallic material (Al 2024-T351), the methodology initiates at the microscale where extensive material characterization is conducted to capture the microstructural variability. A statistical volume element (SVE) model is constructed to represent the material properties. Geometric and crystallographic features including grain orientation, misorientation, size, shape, principal axis direction and aspect ratio are captured. This SVE model provides a computationally efficient alternative to traditional techniques using representative volume element (RVE) models while maintaining statistical accuracy. A physics based multiscale damage criterion is developed to simulate the fatigue crack initiation. The crack growth rate and probable directions are estimated simultaneously.

Mechanically sensitive materials that exhibit specific chemical reactions upon external loading are currently being investigated for self-sensing applications. The "smart" polymer modeled in this research consists of epoxy resin, hardener, and a stress-sensitive material called mechanophore The mechanophore activation is based on covalent bond-breaking induced by external stimuli; this feature can be used for material-level damage detections. In this work Tris-(Cinnamoyl oxymethyl)-Ethane (TCE) is used as the cyclobutane-based mechanophore (stress-sensitive) material in the polymer matrix. The TCE embedded polymers have shown promising results in early damage detection through mechanically induced fluorescence. A spring-bead based network model, which bridges nanoscale information to higher length scales, has been developed to model this material system. The material is partitioned into discrete mass beads which are linked using linear springs at the microscale. A series of MD simulations were performed to define the spring stiffness in the statistical network model. By integrating multiple spring-bead models a network model has been developed to represent the material properties at the mesoscale. The model captures the statistical distribution of crosslinking degree of the polymer to represent the heterogeneous material properties at the microscale. The developed multiscale methodology is computationally efficient and provides a possible means to bridge multiple length scales (from 10 nm in MD simulation to 10 mm in FE model) without significant loss of accuracy. Parametric studies have been conducted to investigate the influence of the crosslinking degree on the material behavior. The developed methodology has been used to evaluate damage evolution in the self-sensing polymer.