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 Title
 Stochastic modeling of routing protocols for cognitive radio networks
 Creator
 Soltani, Soroor
 Date
 2013
 Collection
 Electronic Theses & Dissertations
 Description

Cognitive radios are expected torevolutionize wireless networking because of their ability tosense, manage and share the mobile available spectrum.Efficient utilization of the available spectrum could be significantly improved by incorporating different cognitive radio based networks. Challenges are involved in utilizing the cognitive radios in a network, most of which rise from the dynamic nature of available spectrum that is not present in traditional wireless networks. The set of available...
Show moreCognitive radios are expected torevolutionize wireless networking because of their ability tosense, manage and share the mobile available spectrum.Efficient utilization of the available spectrum could be significantly improved by incorporating different cognitive radio based networks. Challenges are involved in utilizing the cognitive radios in a network, most of which rise from the dynamic nature of available spectrum that is not present in traditional wireless networks. The set of available spectrum blocks(channels) changes randomly with the arrival and departure of the users licensed to a specific spectrum band. These users are known as primary users. If a band is used by aprimary user, the cognitive radio alters its transmission power level ormodulation scheme to change its transmission range and switches to another channel.In traditional wireless networks, a link is stable if it is less prone to interference. In cognitive radio networks, however, a link that is interference free might break due to the arrival of its primary user. Therefore, links' stability forms a stochastic process with OFF and ON states; ON, if the primary user is absent. Evidently, traditional network protocols fail in this environment. New sets of protocols are needed in each layer to cope with the stochastic dynamics of cognitive radio networks.In this dissertation we present a comprehensive stochastic framework and a decision theory based model for the problem of routing packets from a source to a destination in a cognitive radio network. We begin by introducing two probability distributions called ArgMax and ArgMin for probabilistic channel selection mechanisms, routing, and MAC protocols. The ArgMax probability distribution locates the most stable link from a set of available links. Conversely, ArgMin identifies the least stable link. ArgMax and ArgMin together provide valuable information on the diversity of the stability of available links in a spectrum band. Next, considering the stochastic arrival of primary users, we model the transition of packets from one hop to the other by a SemiMarkov process and develop a Primary Spread Aware Routing Protocol (PSARP) that learns the dynamics of the environment and adapts its routing decision accordingly. Further, we use a decision theory framework. A utility function is designed to capture the effect of spectrum measurement, fluctuation of bandwidth availability and path quality. A node cognitively decides its best candidate among its neighbors by utilizing a decision tree. Each branch of the tree is quantified by the utility function and a posterior probability distribution, constructed using ArgMax probability distribution, which predicts the suitability of available neighbors. In DTCR (Decision Tree Cognitive Routing), nodes learn their operational environment and adapt their decision making accordingly. We extend the Decision tree modeling to translate video routing in a dynamic cognitive radio network into a decision theory problem. Then terminal analysis backward induction is used to produce our routing scheme that improves the peak signaltonoise ratio of the received video.We show through this dissertation that by acknowledging the stochastic property of the cognitive radio networks' environment and constructing strategies using the statistical and mathematical tools that deal with such uncertainties, the utilization of these networks will greatly improve.
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 Title
 Highdimensional learning from random projections of data through regularization and diversification
 Creator
 Aghagolzadeh, Mohammad
 Date
 2015
 Collection
 Electronic Theses & Dissertations
 Description

Random signal measurement, in the form of random projections of signal vectors, extends the traditional pointwise and periodic schemes for signal sampling. In particular, the wellknown problem of sensing sparse signals from linear measurements, also known as Compressed Sensing (CS), has promoted the utility of random projections. Meanwhile, many signal processing and learning problems that involve parametric estimation do not consist of sparsity constraints in their original forms. With the...
Show moreRandom signal measurement, in the form of random projections of signal vectors, extends the traditional pointwise and periodic schemes for signal sampling. In particular, the wellknown problem of sensing sparse signals from linear measurements, also known as Compressed Sensing (CS), has promoted the utility of random projections. Meanwhile, many signal processing and learning problems that involve parametric estimation do not consist of sparsity constraints in their original forms. With the increasing popularity of random measurements, it is crucial to study the generic estimation performance under the random measurement model. In this thesis, we consider two specific learning problems (named below) and present the following two generic approaches for improving the estimation accuracy: 1) by adding relevant constraints to the parameter vectors and 2) by diversification of the random measurements to achieve fast decaying tail bounds for the empirical risk function.The first problem we consider is Dictionary Learning (DL). Dictionaries are extensions of vector bases that are specifically tailored for sparse signal representation. DL has become increasingly popular for sparse modeling of natural images as well as sound and biological signals, just to name a few. Empirical studies have shown that typical DL algorithms for imaging applications are relatively robust with respect to missing pixels in the training data. However, DL from random projections of data corresponds to an illposed problem and is not wellstudied. Existing efforts are limited to learning structured dictionaries or dictionaries for structured sparse representations to make the problem tractable. The main motivation for considering this problem is to generate an adaptive framework for CS of signals that are not sparse in the signal domain. In fact, this problem has been referred to as 'blind CS' since the optimal basis is subject to estimation during CS recovery. Our initial approach, similar to some of the existing efforts, involves adding structural constraints on the dictionary to incorporate sparse and autoregressive models. More importantly, our results and analysis reveal that DL from random projections of data, in its unconstrained form, can still be accurate given that measurements satisfy the diversity constraints defined later.The second problem that we consider is highdimensional signal classification. Prior efforts have shown that projecting highdimensional and redundant signal vectors onto random lowdimensional subspaces presents an efficient alternative to traditional feature extraction tools such as the principle component analysis. Hence, aside from the CS application, random measurements present an efficient sampling method for learning classifiers, eliminating the need for recording and processing highdimensional signals while most of the recorded data is discarded during feature extraction. We work with the Support Vector Machine (SVM) classifiers that are learned in the highdimensional ambient signal space using random projections of the training data. Our results indicate that the classifier accuracy can be significantly improved by diversification of the random measurements.
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