Matching Items (2)
Filtering by

Clear all filters

137020-Thumbnail Image.png

Phase Recovery and Unimodular Waveform Design

Description
In many systems, it is difficult or impossible to measure the phase of a signal. Direct recovery from magnitude is an ill-posed problem. Nevertheless, with a sufficiently large set of magnitude measurements, it is often possible to reconstruct the original signal using algorithms that implicitly impose regularization conditions on this…

In many systems, it is difficult or impossible to measure the phase of a signal. Direct recovery from magnitude is an ill-posed problem. Nevertheless, with a sufficiently large set of magnitude measurements, it is often possible to reconstruct the original signal using algorithms that implicitly impose regularization conditions on this ill-posed problem. Two such algorithms were examined: alternating projections, utilizing iterative Fourier transforms with manipulations performed in each domain on every iteration, and phase lifting, converting the problem to that of trace minimization, allowing for the use of convex optimization algorithms to perform the signal recovery. These recovery algorithms were compared on a basis of robustness as a function of signal-to-noise ratio. A second problem examined was that of unimodular polyphase radar waveform design. Under a finite signal energy constraint, the maximal energy return of a scene operator is obtained by transmitting the eigenvector of the scene Gramian associated with the largest eigenvalue. It is shown that if instead the problem is considered under a power constraint, a unimodular signal can be constructed starting from such an eigenvector that will have a greater return.
ContributorsJones, Scott Robert (Author) / Cochran, Douglas (Thesis director) / Diaz, Rodolfo (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
137100-Thumbnail Image.png

Maximum Entropy Surrogation in Multiple Channel Signal Detection

Description
Multiple-channel detection is considered in the context of a sensor network where data can be exchanged directly between sensor nodes that share a common edge in the network graph. Optimal statistical tests used for signal source detection with multiple noisy sensors, such as the Generalized Coherence (GC) estimate, use pairwise…

Multiple-channel detection is considered in the context of a sensor network where data can be exchanged directly between sensor nodes that share a common edge in the network graph. Optimal statistical tests used for signal source detection with multiple noisy sensors, such as the Generalized Coherence (GC) estimate, use pairwise measurements from every pair of sensors in the network and are thus only applicable when the network graph is completely connected, or when data are accumulated at a common fusion center. This thesis presents and exploits a new method that uses maximum-entropy techniques to estimate measurements between pairs of sensors that are not in direct communication, thereby enabling the use of the GC estimate in incompletely connected sensor networks. The research in this thesis culminates in a main conjecture supported by statistical tests regarding the topology of the incomplete network graphs.
ContributorsCrider, Lauren Nicole (Author) / Cochran, Douglas (Thesis director) / Renaut, Rosemary (Committee member) / Kosut, Oliver (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05