Detecting areas of change between two synthetic aperture radar (SAR) images of the same scene, taken at different times is generally performed using two approaches. Non-coherent change detection is performed using the sample variance ratio detector, and displays a good performance in detecting areas of significant changes. Coherent change detection can be implemented using the classical coherence estimator, which does better at detecting subtle changes, like vehicle tracks. A two-stage detector was proposed by Cha et al., where the sample variance ratio forms the first stage, and the second stage comprises of Berger's alternative coherence estimator.

A modification to the first stage of the two-stage detector is proposed in this study, which significantly simplifies the analysis of the this detector. Cha et al. have used a heuristic approach to determine the thresholds for this two-stage detector. In this study, the probability density function for the modified two-stage detector is derived, and using this probability density function, an approach for determining the thresholds for this two-dimensional detection problem has been proposed. The proposed method of threshold selection reveals an interesting behavior shown by the two-stage detector. With the help of theoretical receiver operating characteristic analysis, it is shown that the two-stage detector gives a better detection performance as compared to the other three detectors. However, the Berger's estimator proves to be a simpler alternative, since it gives only a slightly poorer performance as compared to the two-stage detector. All the four detectors have also been implemented on a SAR data set, and it is shown that the two-stage detector and the Berger's estimator generate images where the areas showing change are easily visible.

Signal compressed using classical compression methods can be acquired using brute force (i.e. searching for non-zero entries in component-wise). However, sparse solutions require combinatorial searches of high computations. In this thesis, instead, two Bayesian approaches are considered to recover a sparse vector from underdetermined noisy measurements. The first is constructed using a Bernoulli-Gaussian (BG) prior distribution and is assumed to be the true generative model. The second is constructed using a Gamma-Normal (GN) prior distribution and is, therefore, a different (i.e. misspecified) model. To estimate the posterior distribution for the correctly specified scenario, an algorithm based on generalized approximated message passing (GAMP) is constructed, while an algorithm based on sparse Bayesian learning (SBL) is used for the misspecified scenario. Recovering sparse signal using Bayesian framework is one class of algorithms to solve the sparse problem. All classes of algorithms aim to get around the high computations associated with the combinatorial searches. Compressive sensing (CS) is a widely-used terminology attributed to optimize the sparse problem and its applications. Applications such as magnetic resonance imaging (MRI), image acquisition in radar imaging, and facial recognition. In CS literature, the target vector can be recovered either by optimizing an objective function using point estimation, or recovering a distribution of the sparse vector using Bayesian estimation. Although Bayesian framework provides an extra degree of freedom to assume a distribution that is directly applicable to the problem of interest, it is hard to find a theoretical guarantee of convergence. This limitation has shifted some of researches to use a non-Bayesian framework. This thesis tries to close this gab by proposing a Bayesian framework with a suggested theoretical bound for the assumed, not necessarily correct, distribution. In the simulation study, a general lower Bayesian Cram\'er-Rao bound (BCRB) bound is extracted along with misspecified Bayesian Cram\'er-Rao bound (MBCRB) for GN model. Both bounds are validated using mean square error (MSE) performances of the aforementioned algorithms. Also, a quantification of the performance in terms of gains versus losses is introduced as one main finding of this report.

An analysis is presented of a network of distributed receivers encumbered by strong in-band interference. The structure of information present across such receivers and how they might collaborate to recover a signal of interest is studied. Unstructured (random coding) and structured (lattice coding) strategies are studied towards this purpose for a certain adaptable system model. Asymptotic performances of these strategies and algorithms to compute them are developed. A jointly-compressed lattice code with proper configuration performs best of all strategies investigated.

This thesis is a proposition for an addition to an engineering project that involves creating a heads up display for a scuba diving mask which displays important safety information. The premise of this thesis includes three different features: distress, distance, and direction. The distress feature is to alert a diver that their “buddy diver” is having an emergency and is requiring attention. Distance and direction are intended to be included on the heads up display, informing the diver of the relative location of their “buddy diver” in case they have lost sight of them. A set of requirements was created to find the most practical solutions. From these requirements and extensive research, three different methods of underwater communication were found, but only one, acoustics, was feasible for the scope of this project. Using modems and transducers, an acoustic signal is able to be sent from one diver to another in order to detect relative location as well as send a message of distress. Ultimately, two possible concepts were designed, with one deemed as most advantageous. This concept engages the use of four transponders that have the ability to transmit and receive high frequencies, minimizes blind spots, and is small enough to not cause discomfort or be obstructive to the divers experience.

In the past half century, low-power wireless signals from portable radar sensors, initially continuous-wave (CW) radars and more recently ultra-wideband (UWB) radar systems, have been successfully used to detect physiological movements of stationary human beings.

The thesis starts with a careful review of existing signal processing techniques and state of the art methods possible for vital signs monitoring using UWB impulse systems. Then an in-depth analysis of various approaches is presented.

Robust heart-rate monitoring methods are proposed based on a novel result: spectrally the fundamental heartbeat frequency is respiration-interference-limited while its higher-order harmonics are noise-limited. The higher-order statistics related to heartbeat can be a robust indication when the fundamental heartbeat is masked by the strong lower-order harmonics of respiration or when phase calibration is not accurate if phase-based method is used. Analytical spectral analysis is performed to validate that the higher-order harmonics of heartbeat is almost respiration-interference free. Extensive experiments have been conducted to justify an adaptive heart-rate monitoring algorithm. The scenarios of interest are, 1) single subject, 2) multiple subjects at different ranges, 3) multiple subjects at same range, and 4) through wall monitoring.

A remote sensing radar system implemented using the proposed adaptive heart-rate estimation algorithm is compared to the competing remote sensing technology, a remote imaging photoplethysmography system, showing promising results.

State of the art methods for vital signs monitoring are fundamentally related to process the phase variation due to vital signs motions. Their performance are determined by a phase calibration procedure. Existing methods fail to consider the time-varying nature of phase noise. There is no prior knowledge about which of the corrupted complex signals, in-phase component (I) and quadrature component (Q), need to be corrected. A precise phase calibration routine is proposed based on the respiration pattern. The I/Q samples from every breath are more likely to experience similar motion noise and therefore they should be corrected independently. High slow-time sampling rate is used to ensure phase calibration accuracy. Occasionally, a 180-degree phase shift error occurs after the initial calibration step and should be corrected as well. All phase trajectories in the I/Q plot are only allowed in certain angular spaces. This precise phase calibration routine is validated through computer simulations incorporating a time-varying phase noise model, controlled mechanic system, and human subject experiment.

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.