The Human Gut Microbiome (GM) modulates a variety of structural, metabolic, and protective functions to benefit the host. A few recent studies also support the role of the gut microbiome in the regulation of bone health. The relationship between GM and bone health was analyzed based on the data collected from a group of twenty-three adolescent boys and girls who participated in a controlled feeding study, during which two different doses (0 g/d fiber and 12 g/d fiber) of Soluble Corn Fiber (SCF) were added to their diet. This analysis was performed by predicting measures of Bone Mineral Density (BMD) and Bone Mineral Content (BMC) which are indicators of bone strength, using the GM sequence of proportions of 178 microbes collected from 23 subjects, by building a machine learning regression model. The model developed was evaluated by calculating performance metrics such as Root Mean Squared Error, Pearson’s correlation coefficient, and Spearman’s rank correlation coefficient, using cross-validation. A noticeable correlation was observed between the GM and bone health, and it was observed that the overall prediction correlation was higher with SCF intervention (r ~ 0.51). The genera of microbes that played an important role in this relationship were identified. Eubacterium (g), Bacteroides (g), Megamonas (g), Acetivibrio (g), Faecalibacterium (g), and Paraprevotella (g) were some of the microbes that showed an increase in proportion with SCF intervention.

The following document describes the hardware implementation and analysis of Temporal Interference Mitigation using High-Level Synthesis. As the problem of spectral congestion becomes more chronic and widespread, Electromagnetic radio frequency (RF) based systems are posing as viable solution to this problem. Among the existing RF methods Cooperation based systems have been a solution to a host of congestion problems. One of the most important elements of RF receiver is the spatially adaptive part of the receiver. Temporal Mitigation is vital technique employed at the receiver for signal recovery and future propagation along the radar chain.

The computationally intensive parts of temporal mitigation are identified and hardware accelerated. The hardware implementation is based on sequential approach with optimizations applied on the individual components for better performance.

An extensive analysis using a range of fixed point data types is performed to find the optimal data type necessary.

Finally a hybrid combination of data types for different components of temporal mitigation is proposed based on results from the above analysis.

Alzheimer's disease is the 6th leading cause of death in the United States and vastly affects millions across the world each year. Currently, there are no medications or treatments available to slow or stop the progression of Alzheimer’s Disease. The GENUS therapy out of the Massachusetts Institute of Technology presently shows positive results in slowing the progression of the disease among animal trials. This thesis is a continuation of that study, to develop and build a testing apparatus for human clinical trials. Included is a complete outline into the design, development, testing measures, and instructional aid for the final apparatus.

The inverse problem in electroencephalography (EEG) is the determination of form and location of neural activity associated to EEG recordings. This determination is of interest in evoked potential experiments where the activity is elicited by an external stimulus. This work investigates three aspects of this problem: the use of forward methods in its solution, the elimination of artifacts that complicate the accurate determination of sources, and the construction of physical models that capture the electrical properties of the human head.

Results from this work aim to increase the accuracy and performance of the inverse solution process.

The inverse problem can be approached by constructing forward solutions where, for a know source, the scalp potentials are determined. This work demonstrates that the use of two variables, the dissipated power and the accumulated charge at interfaces, leads to a new solution method for the forward problem. The accumulated charge satisfies a boundary integral equation. Consideration of dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in this formulation. The new method uses the eigenvalue structure to regularize singular integral operators thus allowing unambiguous solutions to the forward problem.

A major problem in the estimation of properties of neural sources is the presence of artifacts that corrupt EEG recordings. A method is proposed for the determination of inverse solutions that integrates sequential Bayesian estimation with probabilistic data association in order to suppress artifacts before estimating neural activity. This method improves the tracking of neural activity in a dynamic setting in the presence of artifacts.

Solution of the inverse problem requires the use of models of the human head. The electrical properties of biological tissues are best described by frequency dependent complex conductivities. Head models in EEG analysis, however, usually consider head regions as having only constant real conductivities. This work presents a model for tissues as composed of confined electrolytes that predicts complex conductivities for macroscopic measurements. These results indicate ways in which EEG models can be improved.

Within the near future, a vast demand for autonomous vehicular techniques can be forecast on both aviation and ground platforms, including autonomous driving, automatic landing, air traffic management. These techniques usually rely on the positioning system and the communication system independently, where it potentially causes spectrum congestion. Inspired by the spectrum sharing technique, Communications and High-Precision Positioning (CHP2) system is invented to provide a high precision position service (precision ~1cm) while performing the communication task simultaneously under the same spectrum. CHP2 system is implemented on the consumer-off-the-shelf (COTS) software-defined radio (SDR) platform with customized hardware. Taking the advantages of the SDR platform, the completed baseband processing chain, time-of-arrival estimation (ToA), time-of-flight estimation (ToF) are mathematically modeled and then implemented onto the system-on-chip (SoC) system. Due to the compact size and cost economy, the CHP2 system can be installed on different aerial or ground platforms enabling a high-mobile and reconfigurable network.

In this dissertation report, the implementation procedure of the CHP2 system is discussed in detail. It mainly focuses on the system construction on the Xilinx Ultrascale+ SoC platform. The CHP2 waveform design, ToA solution, and timing exchanging algorithms are also introduced. Finally, several in-lab tests and over-the-air demonstrations are conducted. The demonstration shows the best ranging performance achieves the ~1 cm standard deviation and 10Hz refreshing rate of estimation by using a 10MHz narrow-band signal over 915MHz (US ISM) or 783MHz (EU Licensed) carrier frequency.

Object localization is used to determine the location of a device, an important aspect of applications ranging from autonomous driving to augmented reality. Commonly-used localization techniques include global positioning systems (GPS), simultaneous localization and mapping (SLAM), and positional tracking, but all of these methodologies have drawbacks, especially in high traffic indoor or urban environments. Using recent improvements in the field of machine learning, this project proposes a new method of localization using networks with several wireless transceivers and implemented without heavy computational loads or high costs. This project aims to build a proof-of-concept prototype and demonstrate that the proposed technique is feasible and accurate.

Modern communication networks heavily depend upon an estimate of the communication channel, which represents the distortions that a transmitted signal takes as it moves towards a receiver. A channel can become quite complicated due to signal reflections, delays, and other undesirable effects and, as a result, varies significantly with each different location. This localization system seeks to take advantage of this distinctness by feeding channel information into a machine learning algorithm, which will be trained to associate channels with their respective locations. A device in need of localization would then only need to calculate a channel estimate and pose it to this algorithm to obtain its location.

As an additional step, the effect of location noise is investigated in this report. Once the localization system described above demonstrates promising results, the team demonstrates that the system is robust to noise on its location labels. In doing so, the team demonstrates that this system could be implemented in a continued learning environment, in which some user agents report their estimated (noisy) location over a wireless communication network, such that the model can be implemented in an environment without extensive data collection prior to release.

The open nature of the wireless communication medium makes it inherently vulnerable to an active attack, wherein a malicious adversary (or jammer) transmits into the medium to disrupt the operation of the legitimate users. Therefore, developing techniques to manage the presence of a jammer and to characterize the effect of an attacker on the fundamental limits of wireless communication networks is important. This dissertation studies various Gaussian communication networks in the presence of such an adversarial jammer.

First of all, a standard Gaussian channel is considered in the presence of a jammer, known as a Gaussian arbitrarily-varying channel, but with list-decoding at the receiver. The receiver decodes a list of messages, instead of only one message, with the goal of the correct message being an element of the list. The capacity is characterized, and it is shown that under some transmitter's power constraints the adversary is able to suspend the communication between the legitimate users and make the capacity zero.

Next, generalized packing lemmas are introduced for Gaussian adversarial channels to achieve the capacity bounds for three Gaussian multi-user channels in the presence of adversarial jammers. Inner and outer bounds on the capacity regions of Gaussian multiple-access channels, Gaussian broadcast channels, and Gaussian interference channels are derived in the presence of malicious jammers. For the Gaussian multiple-access channels with jammer, the capacity bounds coincide. In this dissertation, the adversaries can send any arbitrary signals to the channel while none of the transmitter and the receiver knows the adversarial signals' distribution.

Finally, the capacity of the standard point-to-point Gaussian fading channel in the presence of one jammer is investigated under multiple scenarios of channel state information availability, which is the knowledge of exact fading coefficients. The channel state information is always partially or fully known at the receiver to decode the message while the transmitter or the adversary may or may not have access to this information. Here, the adversary model is the same as the previous cases with no knowledge about the user's transmitted signal except possibly the knowledge of the fading path.

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.

Power spectral analysis is a fundamental aspect of signal processing used in the detection and \\estimation of various signal features. Signals spaced closely in frequency are problematic and lead analysts to miss crucial details surrounding the data. The Capon and Bartlett methods are non-parametric filterbank approaches to power spectrum estimation. The Capon algorithm is known as the "adaptive" approach to power spectrum estimation because its filter impulse responses are adapted to fit the characteristics of the data. The Bartlett method is known as the "conventional" approach to power spectrum estimation (PSE) and has a fixed deterministic filter. Both techniques rely on the Sample Covariance Matrix (SCM). The first objective of this project is to analyze the origins and characteristics of the Capon and Bartlett methods to understand their abilities to resolve signals closely spaced in frequency. Taking into consideration the Capon and Bartlett's reliance on the SCM, there is a novelty in combining these two algorithms using their cross-coherence. The second objective of this project is to analyze the performance of the Capon-Bartlett Cross Spectra. This study will involve Matlab simulations of known test cases and comparisons with approximate theoretical predictions.

Multiple-input multiple-output systems have gained focus in the last decade due to the benefits they provide in enhancing the quality of communications. On the other hand, full-duplex communication has attracted remarkable attention due to its ability to improve the spectral efficiency compared to the existing half-duplex systems. Using full-duplex communications on MIMO co-operative networks can provide us solutions that can completely outperform existing systems with simultaneous transmission and reception at high data rates.

This thesis considers a full-duplex MIMO relay which amplifies and forwards the received signals, between a source and a destination that do not a have line of sight. Full-duplex mode raises the problem of self-interference. Though all the links in the system undergo frequency flat fading, the end-to-end effective channel is frequency selective. This is due to the imperfect cancellation of the self-interference at the relay and this residual self-interference acts as intersymbol interference at the destination which is treated by equalization. This also leads to complications in form of recursive equations to determine the input-output relationship of the system. This also leads to complications in the form of recursive equations to determine the input-output relationship of the system.

To overcome this, a signal flow graph approach using Mason's gain formula is proposed, where the effective channel is analyzed with keen notice to every loop and path the signal traverses. This gives a clear understanding and awareness about the orders of the polynomials involved in the transfer function, from which desired conclusions can be drawn. But the complexity of Mason's gain formula increases with the number of antennas at relay which can be overcome by the proposed linear algebraic method. Input-output relationship derived using simple concepts of linear algebra can be generalized to any number of antennas and the computation complexity is comparatively very low.

For a full-duplex amplify-and-forward MIMO relay system, assuming equalization at the destination, new mechanisms have been implemented at the relay that can compensate the effect of residual self-interference namely equal-gain transmission and antenna selection. Though equal-gain transmission does not perform better than the maximal ratio transmission, a trade-off can be made between performance and implementation complexity. Using the proposed antenna selection strategy, one pair of transmit-receive antennas at the relay is selected based on four selection criteria discussed. Outage probability analysis is performed for all the strategies presented and detailed comparison has been established. Considering minimum mean-squared error decision feedback equalizer at the destination, a bound on the outage probability has been obtained for the antenna selection case and is used for comparisons. A cross-over point is observed while comparing the outage probabilities of equal-gain transmission and antenna selection techniques, as the signal-to-noise ratio increases and from that point antenna selection outperforms equal-gain transmission and this is explained by the fact of reduced residual self-interference in antenna selection method.