Matching Items (45)

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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

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.

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  • 2014-05

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Passive Radar Signal Generation and Scenario Simulation

Description

Passive radar can be used to reduce the demand for radio frequency spectrum bandwidth. This paper will explain how a MATLAB simulation tool was developed to analyze the feasibility of

Passive radar can be used to reduce the demand for radio frequency spectrum bandwidth. This paper will explain how a MATLAB simulation tool was developed to analyze the feasibility of using passive radar with digitally modulated communication signals. The first stage of the simulation creates a binary phase-shift keying (BPSK) signal, quadrature phase-shift keying (QPSK) signal, or digital terrestrial television (DTTV) signal. A scenario is then created using user defined parameters that simulates reception of the original signal on two different channels, a reference channel and a surveillance channel. The signal on the surveillance channel is delayed and Doppler shifted according to a point target scattering profile. An ambiguity function detector is implemented to identify the time delays and Doppler shifts associated with reflections off of the targets created. The results of an example are included in this report to demonstrate the simulation capabilities.

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  • 2014-05

Multiple-Channel Detection in Active Sensing

Description

The problem of detecting the presence of a known signal in multiple channels of additive white Gaussian noise, such as occurs in active radar with a single transmitter and multiple

The problem of detecting the presence of a known signal in multiple channels of additive white Gaussian noise, such as occurs in active radar with a single transmitter and multiple geographically distributed receivers, is addressed via coherent multiple-channel techniques. A replica of the transmitted signal replica is treated as a one channel in a M-channel detector with the remaining M-1 channels comprised of data from the receivers. It is shown that the distribution of the eigenvalues of a Gram matrix are invariant to the presence of the signal replica on one channel provided the other M-1 channels are independent and contain only white Gaussian noise. Thus, the thresholds representing false alarm probabilities for detectors based on functions of these eigenvalues remain valid when one channel is known to not contain only noise. The derivation is supported by results from Monte Carlo simulations. The performance of the largest eigenvalue as a detection statistic in the active case is examined, and compared to the normalized matched filter detector in a two and three channel case.

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  • 2013-05

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Edge Detection from Non-Uniform Fourier Data via a Modified Method of Convolutional Gridding

Description

The recovery of edge information in the physical domain from non-uniform Fourier data is of importance in a variety of applications, particularly in the practice of magnetic resonance imaging (MRI).

The recovery of edge information in the physical domain from non-uniform Fourier data is of importance in a variety of applications, particularly in the practice of magnetic resonance imaging (MRI). Edge detection can be important as a goal in and of itself in the identification of tissue boundaries such as those defining the locations of tumors. It can also be an invaluable tool in the amelioration of the negative effects of the Gibbs phenomenon on reconstructions of functions with discontinuities or images in multi-dimensions with internal edges. In this thesis we develop a novel method for recovering edges from non-uniform Fourier data by adapting the "convolutional gridding" method of function reconstruction. We analyze the behavior of the method in one dimension and then extend it to two dimensions on several examples.

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  • 2013-05

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Validity of down-sampling data for regularization parameter estimation when solving large-scale ill-posed inverse problems

Description

The solution of the linear system of equations $Ax\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel is considered. The solution by means

The solution of the linear system of equations $Ax\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel is considered. The solution by means of Tikhonov regularization in which $x$ is found to as the minimizer of $J(x)=\{ \|Ax -b\|_2^2 + \lambda^2 \|L x\|_2^2\}$ introduces the unknown regularization parameter $\lambda$ which trades off the fidelity of the solution data fit and its smoothing norm, which is determined by the choice of $L$. The Generalized Discrepancy Principle (GDP) and Unbiased Predictive Risk Estimator (UPRE) are methods for finding $\lambda$ given prior conditions on the noise in the measurements $b$. Here we consider the case of $L=I$, and hence use the relationship between the singular value expansion and the singular value decomposition for square integrable kernels to prove that the GDP and UPRE estimates yield a convergent sequence for $\lambda$ with increasing problem size. Hence the estimate of $\lambda$ for a large problem may be found by down-sampling to a smaller problem, or to a set of smaller problems, and applying these estimators more efficiently on the smaller problems. In consequence the large scale problem can be solved in a single step immediately with the parameter found from the down sampled problem(s).

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  • 2014-05

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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

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.

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  • 2014-05

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Statistically Based Registration in Sensor Networks

Description

In recent years, networked systems have become prevalent in communications, computing, sensing, and many other areas. In a network composed of spatially distributed agents, network-wide synchronization of information about the

In recent years, networked systems have become prevalent in communications, computing, sensing, and many other areas. In a network composed of spatially distributed agents, network-wide synchronization of information about the physical environment and the network configuration must be maintained using measurements collected locally by the agents. Registration is a process for connecting the coordinate frames of multiple sets of data. This poses numerous challenges, particularly due to availability of direct communication only between neighboring agents in the network. These are exacerbated by uncertainty in the measurements and also by imperfect communication links. This research explored statistically based registration in a sensor network. The approach developed exploits measurements of offsets formed as differences of state values between pairs of agents that share a link in the network graph. It takes into account that the true offsets around any closed cycle in the network graph must sum to zero.

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  • 2014-05

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Multi-Static Space-Time-Frequency Channel Modeling

Description

Radio communication has become the dominant form of correspondence in modern society. As the demand for high speed communication grows, the problems associated with an expanding consumer base and limited

Radio communication has become the dominant form of correspondence in modern society. As the demand for high speed communication grows, the problems associated with an expanding consumer base and limited spectral access become more difficult to address. One communications system in which people commonly find themselves is the multiple access cellular network. Users operate within the same geographical area and bandwidth, so providing access to every user requires advanced processing techniques and careful subdivision of spectral access. This is known as the multiple access problem. This paper addresses this challenge in the context of airborne transceivers operating at high altitudes and long ranges. These operators communicate by transmitting a signal through a target scattering field on the ground without a direct line of sight to the receiver. The objective of this investigation is to develop a model for this communications channel, identify and quantify the relevant characteristics, and evaluate the feasibility of using it to effectively communicate.

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  • 2015-12

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Edge Detection from Spectral Phase Data

Description

The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local,

The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.

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  • 2016-05

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Electromagnetic Models of Electric Field Imaging

Description

The field of computed tomography involves reconstructing an image from lower dimensional projections. This is particularly useful for visualizing the inner structure of an object. Presented here is an imaging

The field of computed tomography involves reconstructing an image from lower dimensional projections. This is particularly useful for visualizing the inner structure of an object. Presented here is an imaging setup meant for use in computed tomography applications. This imaging setup relies on imaging electric fields through active interrogation. Models designed in Ansys Maxwell are used to simulate this setup and produce 2D images of an object from 1D projections to verify electric field imaging as a potential route for future computed tomography applications. The results of this thesis show reconstructed images that resemble the object being imaged using a filtered back projection method of reconstruction. This work concludes that electric field imaging is a promising option for computed tomography applications.

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  • 2016-12