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- Genre: Masters Thesis
Description
The ability to identify unoccupied resources in the radio spectrum is a key capability for opportunistic users in a cognitive radio environment. This paper draws upon and extends geometrically based ideas in statistical signal processing to develop estimators for the rank and the occupied subspace in a multi-user environment from multiple temporal samples of the signal received at a single antenna. These estimators enable identification of resources, such as the orthogonal complement of the occupied subspace, that may be exploitable by an opportunistic user. This concept is supported by simulations showing the estimation of the number of users in a simple CDMA system using a maximum a posteriori (MAP) estimate for the rank. It was found that with suitable parameters, such as high SNR, sufficient number of time epochs and codes of appropriate length, the number of users could be correctly estimated using the MAP estimator even when the noise variance is unknown. Additionally, the process of identifying the maximum likelihood estimate of the orthogonal projector onto the unoccupied subspace is discussed.
ContributorsBeaudet, Kaitlyn (Author) / Cochran, Douglas (Thesis advisor) / Turaga, Pavan (Committee member) / Berisha, Visar (Committee member) / Arizona State University (Publisher)
Created2014
Description
This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.
ContributorsNaik, Manjish Arvind (Author) / Cochran, Douglas (Thesis advisor) / Kovvali, Narayan (Committee member) / Kawski, Matthias (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis examines the application of statistical signal processing approaches to data arising from surveys intended to measure psychological and sociological phenomena underpinning human social dynamics. The use of signal processing methods for analysis of signals arising from measurement of social, biological, and other non-traditional phenomena has been an important and growing area of signal processing research over the past decade. Here, we explore the application of statistical modeling and signal processing concepts to data obtained from the Global Group Relations Project, specifically to understand and quantify the effects and interactions of social psychological factors related to intergroup conflicts. We use Bayesian networks to specify prospective models of conditional dependence. Bayesian networks are determined between social psychological factors and conflict variables, and modeled by directed acyclic graphs, while the significant interactions are modeled as conditional probabilities. Since the data are sparse and multi-dimensional, we regress Gaussian mixture models (GMMs) against the data to estimate the conditional probabilities of interest. The parameters of GMMs are estimated using the expectation-maximization (EM) algorithm. However, the EM algorithm may suffer from over-fitting problem due to the high dimensionality and limited observations entailed in this data set. Therefore, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are used for GMM order estimation. To assist intuitive understanding of the interactions of social variables and the intergroup conflicts, we introduce a color-based visualization scheme. In this scheme, the intensities of colors are proportional to the conditional probabilities observed.
ContributorsLiu, Hui (Author) / Taylor, Thomas (Thesis advisor) / Cochran, Douglas (Thesis advisor) / Zhang, Junshan (Committee member) / Arizona State University (Publisher)
Created2012
Description
This thesis considers the application of basis pursuit to several problems in system identification. After reviewing some key results in the theory of basis pursuit and compressed sensing, numerical experiments are presented that explore the application of basis pursuit to the black-box identification of linear time-invariant (LTI) systems with both finite (FIR) and infinite (IIR) impulse responses, temporal systems modeled by ordinary differential equations (ODE), and spatio-temporal systems modeled by partial differential equations (PDE). For LTI systems, the experimental results illustrate existing theory for identification of LTI FIR systems. It is seen that basis pursuit does not identify sparse LTI IIR systems, but it does identify alternate systems with nearly identical magnitude response characteristics when there are small numbers of non-zero coefficients. For ODE systems, the experimental results are consistent with earlier research for differential equations that are polynomials in the system variables, illustrating feasibility of the approach for small numbers of non-zero terms. For PDE systems, it is demonstrated that basis pursuit can be applied to system identification, along with a comparison in performance with another existing method. In all cases the impact of measurement noise on identification performance is considered, and it is empirically observed that high signal-to-noise ratio is required for successful application of basis pursuit to system identification problems.
ContributorsThompson, Robert C. (Author) / Platte, Rodrigo (Thesis advisor) / Gelb, Anne (Committee member) / Cochran, Douglas (Committee member) / Arizona State University (Publisher)
Created2012
Description
Scattering from random rough surface has been of interest for decades. Several
methods were proposed to solve this problem, and Kirchho approximation (KA)
and small perturbation method (SMP) are among the most popular. Both methods
provide accurate results on rst order scattering, and the range of validity is limited
and cross-polarization scattering coecient is zero for these two methods unless these
two methods are carried out for higher orders. Furthermore, it is complicated for
higher order formulation and multiple scattering and shadowing are neglected in these
classic methods.
Extension of these two methods has been made in order to x these problems.
However, it is usually complicated and problem specic. While small slope approximation
is one of the most widely used methods to bridge KA and SMP, it is not easy
to implement in a general form. Two scale model can be employed to solve scattering
problems for a tilted perturbation plane, the range of validity is limited.
A new model is proposed in this thesis to deal with cross-polarization scattering
phenomenon on perfect electric conducting random surfaces. Integral equation
is adopted in this model. While integral equation method is often combined with
numerical method to solve the scattering coecient, the proposed model solves the
integral equation iteratively by analytic approximation. We utilize some approximations
on the randomness of the surface, and obtain an explicit expression. It is shown
that this expression achieves agreement with SMP method in second order.
methods were proposed to solve this problem, and Kirchho approximation (KA)
and small perturbation method (SMP) are among the most popular. Both methods
provide accurate results on rst order scattering, and the range of validity is limited
and cross-polarization scattering coecient is zero for these two methods unless these
two methods are carried out for higher orders. Furthermore, it is complicated for
higher order formulation and multiple scattering and shadowing are neglected in these
classic methods.
Extension of these two methods has been made in order to x these problems.
However, it is usually complicated and problem specic. While small slope approximation
is one of the most widely used methods to bridge KA and SMP, it is not easy
to implement in a general form. Two scale model can be employed to solve scattering
problems for a tilted perturbation plane, the range of validity is limited.
A new model is proposed in this thesis to deal with cross-polarization scattering
phenomenon on perfect electric conducting random surfaces. Integral equation
is adopted in this model. While integral equation method is often combined with
numerical method to solve the scattering coecient, the proposed model solves the
integral equation iteratively by analytic approximation. We utilize some approximations
on the randomness of the surface, and obtain an explicit expression. It is shown
that this expression achieves agreement with SMP method in second order.
ContributorsCao, Jiahao (Author) / Pan, George (Thesis advisor) / Balanis, Constantine A (Committee member) / Cochran, Douglas (Committee member) / Arizona State University (Publisher)
Created2017
Description
Modern systems that measure dynamical phenomena often have limitations as to how many sensors can operate at any given time step. This thesis considers a sensor scheduling problem in which the source of a diffusive phenomenon is to be localized using single point measurements of its concentration. With a linear diffusion model, and in the absence of noise, classical observability theory describes whether or not the system's initial state can be deduced from a given set of linear measurements. However, it does not describe to what degree the system is observable. Different metrics of observability have been proposed in literature to address this issue. Many of these methods are based on choosing optimal or sub-optimal sensor schedules from a predetermined collection of possibilities. This thesis proposes two greedy algorithms for a one-dimensional and two-dimensional discrete diffusion processes. The first algorithm considers a deterministic linear dynamical system and deterministic linear measurements. The second algorithm considers noise on the measurements and is compared to a Kalman filter scheduling method described in published work.
ContributorsNajam, Anbar (Author) / Cochran, Douglas (Thesis advisor) / Turaga, Pavan (Committee member) / Wang, Chao (Committee member) / Arizona State University (Publisher)
Created2016