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Enhancing physical layer security in wireless networks with cooperative approachesLiu, Weigang January 2016 (has links)
Motivated by recent developments in wireless communication, this thesis aims to characterize the secrecy performance in several types of typical wireless networks. Advanced techniques are designed and evaluated to enhance physical layer security in these networks with realistic assumptions, such as signal propagation loss, random node distribution and noninstantaneous channel state information (CSI). The first part of the thesis investigates secret communication through relayassisted cognitive interference channel. The primary and secondary base stations (PBS and SBS) communicate with the primary and secondary receivers (PR and SR) respectively in the presence of multiple eavesdroppers. The SBS is allowed to transmit simultaneously with the PBS over the same spectrum instead of waiting for an idle channel. To improve security, cognitive relays transmit cooperative jamming (CJ) signals to create additional interferences in the direction of the eavesdroppers. Two CJ schemes are proposed to improve the secrecy rate of cognitive interference channels depending on the structure of cooperative relays. In the scheme where the multipleantenna relay transmits weighted jamming signals, the combined approach of CJ and beamforming is investigated. In the scheme with multiple relays transmitting weighted jamming signals, the combined approach of CJ and relay selection is analyzed. Numerical results show that both these two schemes are effective in improving physical layer security of cognitive interference channel. In the second part, the focus is shifted to physical layer security in a random wireless network where both legitimate and eavesdropping nodes are randomly distributed. Three scenarios are analyzed to investigate the impact of various factors on security. In scenario one, the basic scheme is studied without a protected zone and interference. The probability distribution function (PDF) of channel gain with both fading and path loss has been derived and further applied to derive secrecy connectivity and ergodic secrecy capacity. In the second scenario, we studied using a protected zone surrounding the source node to enhance security where interference is absent. Both the cases that eavesdroppers are aware and unaware of the protected zone boundary are investigated. Based on the above scenarios, further deployment of the protected zones at legitimate receivers is designed to convert detrimental interference into a beneficial factor. Numerical results are investigated to check the reliability of the PDF for reciprocal of channel gain and to analyze the impact of protected zones on secrecy performance. In the third part, physical layer security in the downlink transmission of cellular network is studied. To model the repulsive property of the cellular network planning, we assume that the base stations (BSs) follow the Mat´ern hardcore point process (HCPP), while the eavesdroppers are deployed as an independent Poisson point process (PPP). The distribution function of the distances from a typical point to the nodes of the HCPP is derived. The noiselimited and interferencelimited cellular networks are investigated by applying the fractional frequency reuse (FFR) in the system. For the noiselimited network, we derive the secrecy outage probability with two different strategies, i.e. the best BS serve and the nearest BS serve, by analyzing the statistics of channel gains. For the interferencelimited network with the nearest BS serve, two transmission schemes are analyzed, i.e., transmission with and without the FFR. Numerical results reveal that both the schemes of transmitting with the best BS and the application of the FFR are beneficial for physical layer security in the downlink cellular networks, while the improvement due to the application of the FFR is limited by the capacity of the legitimate channel.

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Mathematical optimization techniques for cognitive radar networksRossetti, Gaia January 2018 (has links)
This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signaldependent clutter and noise. All algorithms are based on an iterative waveformfilter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and crosscorrelation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a maxmin optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signaldependent model was tested against existing worstcase and probabilistic methods. These methods appeared to be over conservative and generic for the considered signaldependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar crosssection and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for throughthewall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matchedillumination one, this thesis introduces robust optimization techniques that consider uncertainty on environmentrelated parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise.

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Identification using Convexification and RecursionDai, Liang January 2016 (has links)
System identification studies how to construct mathematical models for dynamical systems from the input and output data, which finds applications in many scenarios, such as predicting future output of the system or building model based controllers for regulating the output the system. Among many other methods, convex optimization is becoming an increasingly useful tool for solving system identification problems. The reason is that many identification problems can be formulated as, or transformed into convex optimization problems. This transformation is commonly referred to as the convexification technique. The first theme of the thesis is to understand the efficacy of the convexification idea by examining two specific examples. We first establish that a l1 norm based approach can indeed help in exploiting the sparsity information of the underlying parameter vector under certain persistent excitation assumptions. After that, we analyze how the nuclear norm minimization heuristic performs on a lowrank Hankel matrix completion problem. The underlying key is to construct the dual certificate based on the structure information that is available in the problem setting. Recursive algorithms are ubiquitous in system identification. The second theme of the thesis is the study of some existing recursive algorithms, by establishing new connections, giving new insights or interpretations to them. We first establish a connection between a basic property of the convolution operator and the score function estimation. Based on this relationship, we show how certain recursive Bayesian algorithms can be exploited to estimate the score function for systems with intractable transition densities. We also provide a new derivation and interpretation of the recursive direct weight optimization method, by exploiting certain structural information that is present in the algorithm. Finally, we study how an improved randomization strategy can be found for the randomized Kaczmarz algorithm, and how the convergence rate of the classical Kaczmarz algorithm can be studied by the stability analysis of a related time varying linear dynamical system.

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Maximum Likelihood Identification of an Information Matrix Under Constraints in a Corresponding Graphical ModelLi, Nan 22 January 2017 (has links)
We address the problem of identifying the neighborhood structure of an undirected graph, whose nodes are labeled with the elements of a multivariate normal (MVN) random vector. A semidefinite program is given for estimating the information matrix under arbitrary constraints on its elements. More importantly, a closedform expression is given for the maximum likelihood (ML) estimator of the information matrix, under the constraint that the information matrix has prespecified elements in a given pattern (e.g., in a principal submatrix). The results apply to the identification of dependency labels in a graphical model with neighborhood constraints. This neighborhood structure excludes nodes which are conditionally independent of a given node and the graph is determined by the non zero elements in the information matrix for the random vector. A crossvalidation principle is given for determining whether the constrained information matrix returned from this procedure is an acceptable model for the information matrix, and as a consequence for the neighborhood structure of the Markov Random Field (MRF) that is identified with the MVN random vector.

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Statistical Guarantee for NonConvex OptimizationBotao Hao (7887845) 26 November 2019 (has links)
The aim of this thesis is to systematically study the statistical guarantee for two
representative nonconvex optimization problems arsing in the statistics community.
The first one is the highdimensional Gaussian mixture model, which is motivated by
the estimation of multiple graphical models arising from heterogeneous observations.
The second one is the lowrank tensor estimation model, which is motivated by
highdimensional interaction model. Both optimal statistical rates and numerical
comparisons are studied in depth.
In the first part of my thesis, we consider joint estimation of multiple graphical
models arising from heterogeneous and highdimensional observations. Unlike most
previous approaches which assume that the cluster structure is given in advance, an
appealing feature of our method is to learn cluster structure while estimating heterogeneous graphical models. This is achieved via a high dimensional version of Expectation
Conditional Maximization (ECM) algorithm. A joint graphical lasso penalty is
imposed on the conditional maximization step to extract both homogeneity and heterogeneity components across all clusters. Our algorithm is computationally efficient
due to fast sparse learning routines and can be implemented without unsupervised
learning knowledge. The superior performance of our method is demonstrated by extensive experiments and its application to a Glioblastoma cancer dataset reveals some
new insights in understanding the Glioblastoma cancer. In theory, a nonasymptotic
error bound is established for the output directly from our high dimensional ECM
algorithm, and it consists of two quantities: statistical error (statistical accuracy) and optimization error (computational complexity). Such a result gives a theoretical
guideline in terminating our ECM iterations.
In the second part of my thesis, we propose a general framework for sparse and lowrank tensor estimation from cubic sketchings. A twostage nonconvex implementation
is developed based on sparse tensor decomposition and thresholded gradient descent,
which ensures exact recovery in the noiseless case and stable recovery in the noisy
case with high probability. The nonasymptotic analysis sheds light on an interplay
between optimization error and statistical error. The proposed procedure is shown to
be rateoptimal under certain conditions. As a technical byproduct, novel highorder
concentration inequalities are derived for studying highmoment subGaussian tensors.
An interesting tensor formulation illustrates the potential application to highorder
interaction pursuit in highdimensional linear regression

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Distributed model predictive control based consensus of general linear multiagent systems with input constraintsLi, Zhuo 16 April 2020 (has links)
In the study of multiagent systems (MASs), cooperative control is one of the most fundamental issues. As it covers a broad spectrum of applications in many industrial areas, there is a desire to design cooperative control protocols for different system and network setups.
Motivated by this fact, in this thesis we focus on elaborating consensus protocol design, via model predictive control (MPC), under two different scenarios: (1) general constrained linear MASs with bounded additive disturbance; (2) linear MASs with input constraints underlying distributed communication networks.
In Chapter 2, a tubebased robust MPC consensus protocol for constrained linear MASs is proposed. For undisturbed linear MASs without constraints, the results on designing a centralized linear consensus protocol are first developed by a suboptimal linear quadratic approach. In order to evaluate the control performance of the suboptimal consensus protocol, we use an infinite horizon linear quadratic objective function to penalize the disagreement among agents and the size of control inputs. Due to the nonconvexity of the performance function, an optimal controller gain is difficult or even impossible to find, thus a suboptimal consensus protocol is derived. In the presence of disturbance, the original MASs may not maintain certain properties such as stability and cooperative performance. To this end, a tubebased robust MPC framework is introduced. When disturbance is involved, the original constraints in nominal prediction should be tightened so as to achieve robust constraint satisfaction, as the predicted states and the actual states are not necessarily the same. Moreover, the corresponding robust constraint sets can be determined offline, requiring no extra iterative online computation in implementation.
In Chapter 3, a novel distributed MPCbased consensus protocol is proposed for general linear MASs with input constraints. For the linear MAS without constraints, a prestabilizing distributed linear consensus protocol is developed by an inverse optimal approach, such that the corresponding closedloop system is asymptotically stable with respect to a consensus set. Implementing this prestabilizing controller in a distributed digital setting is however not possible, as it requires every local decision maker to continuously access the state of their neighbors simultaneously when updating the control input. To relax these requirements, the assumed neighboring state, instead of the actual state of neighbors, is used. In our distributed MPC scheme, each local controller minimizes a group of control variables to generate control input. Moreover, an additional state constraint is proposed to bound deviation between the actual and the assumed state. In this way, consistency is enforced between intended behaviors of an agent and what its neighbors believe it will behave. We later show that the closedloop system converges to a neighboring set of the consensus set thanks to the bounded state deviation in prediction.
In Chapter 4, conclusions are made and some research topics for future exploring are presented. / Graduate / 20210331

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ITEM RESPONSE MODELS AND CONVEX OPTIMIZATION.Lewis, Naama 01 May 2020 (has links)
Item Response Theory (IRT) Models, like the one parameter, two parameters, or normal Ogive, have been discussed for many years. These models represent a rich area of investigation due to their complexity as well as the large amount of data collected in relationship to model parameter estimation. Here we propose a new way of looking at IRT models using Iprojections and duality. We use convex optimization methods to derive these models. The KullbackLeibler divergence is used as a metric and specific constraints are proposed for the various models. With this approach, the dual problem is shown to be much easier to solve than the primal problem. In particular when there are many constraints, we propose the application of a projection algorithm for solving these types of problems. We also consider reframing the problem and utilizing a decomposition algorithm to solve for parameters as well. Both of these methods will be compared to the Rasch and 2Parameter Logistic models using established computer software where estimation of model parameters are done under Maximum Likelihood Estimation framework. We will also compare the appropriateness of these techniques on multidimensional item response data sets and propose new models with the use of Iprojections.

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Towards Energy Efficient Cognitive Radio SystemsAlabbasi, AbdulRahman 14 July 2016 (has links)
Cognitive radio (CR) is a cuttingedge wireless communication technology that adopts several existing communication concepts in order to efficiently utilize the spectrum and meet the users demands of high throughput and realtime systems. Conventionally, high throughput demands are met through adopting broadband and multiantenna technologies such as, orthogonal frequency division multiplexing (OFDM) and MultiInput MultiOutput (MIMO). Whereas, realtime application demands are met by analyzing metrics which characterize the delay limited channels, such as, outage probability over blockfading channels. Being an environmental friendly technology, energy efficiency metrics should be considered in the design of a CR application. This thesis tackles the energy efficiency of CR system from different aspects, utilizing different measuring metrics and constrains.
Under the singleinput singleoutput (SISO) OFDM we minimized the energy per goodbit (EPG) metric subject to several power and Quality of Service (QoS) constraints. In this approach, the minimum EPG metric is optimized via proposing two optimal and suboptimal resource allocation schemes. We consider several parameters as optimization variables, such as, power policy, sensing threshold, and channel quality threshold. We also captured the impact of involving the media access control (MAC) layers parameters, such as, frame length, in the minimization of a modified EPG metric. Also, a MAC protocol, i.e., hybrid automatic repeat request (HARQ),
and the associated power consumption of the retransmission mechanism is considered in the formulation of the problem. In this context, the optimal power and frame length are derived to minimize the modified EPG while considering several spectrumsharing scenarios, which depend on sensing information. In MIMO based CR system, we maximized capacity to power ratio (CPR) (as an energy efficiency (EE) metric) subject to several power and QoS constraints. In this context, the impact of sensing information with imperfect channel state information (CSI) of the secondary channel has been considered. To realize a CR system with realtime applications we minimized the outage probability over M blockfading channel with several longterm and shortterm energy constrains. We derive the minimum outage region and the associated optimal power. Tractable expressions to lower and upper bound the outage probability are derived. We then analyze the impact of utilizing the sensing process of primary user activity.

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An open source object oriented platform for rapid design of high performance path following interiorpoint methodsChiş, Voicu January 2008 (has links)
<p> Interior point methods (IPMs) is a powerful tool in convex optimization. From
the theoretical point of view, the convex set of feasible solutions is represented
by a socalled barrier functional and the only information required by the
algorithms is the evaluation of the barrier, its gradient and Hessian. As a
result, IPM algorithms can be used for many types of convex problems and
their theoretical performance depends on the properties of the barrier. In
practice, performance depends on how the data structure is exploited at the
linear algebra level. In this thesis, we make use of the objectoriented paradigm
supported by C++ to create a platform where the aforementioned generality
of IPM algorithms is valued and the possibility to exploit the data structure
is available. We will illustrate the power of such an approach on optimization
problems arrising in the field of Radiation Therapy, in particular Intensity
Modulated Radiation Therapy. </p> / Thesis / Master of Science (MSc)

30 
Computational Experience and the Explanatory Value of Condition Numbers for Linear OptimizationOrdónez, Fernando, Freund, Robert M. 25 September 2003 (has links)
The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a test bed for condition number computation and analysis. Our computational results indicate that 72% of the NETLIB suite problem instances are illconditioned. However, after preprocessing heuristics are applied, only 19% of the postprocessed problem instances are illconditioned, and log C(d) of the finitelyconditioned postprocessed problems is fairly nicely distributed. We also show that the number of IPM iterations needed to solve the problems in the NETLIB suite varies roughly linearly (and monotonically) with log C(d) of the postprocessed problem instances. Empirical evidence yields a positive linear relationship between IPM iterations and log C(d) for the postprocessed problem instances, significant at the 95% confidence level. Furthermore, 42% of the variation in IPM iterations among the NETLIB suite problem instances is accounted for by log C(d) of the problem instances after preprocessin

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