Author's `Characterization of subgradients: 1` (31 leaves) in pocket / Bibliography: leaves 229-231 / 231 leaves : 1 port ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, 1986

Thesis (M. Sc.)--University of Canterbury, 2009. / Typescript (photocopy). "5th February 2009." Includes bibliographical references (leaves 66-69). Also available via the World Wide Web.

Thesis (PhD)--University of Stellenbosch, 2007. / Bibliography. Also availabe via the Internet.

Nessa dissertação estudamos Sistemas Dinâmicos do ponto de vista da Otimização Ergódica. Analizamos o problema da maximização da integral de potenciais com respeito a probabilidades invariantes pela dinâmica. Mostramos que toda medida ergódica e unicamente maximizante para algum potencial. Verificamos que o conjunto de potenciais com exatamente uma medida maximizadora e residual. Esses resultados são obtidos atrav es de técnicas da Teoria Ergódica e Análise Convexa. / In this thesis we study dynamical systems trough the viewpoint of ergodic optimization. We analyze the problem of maximizing integrals of potentials with respect to invariant probabilities. We show that every ergodic measure is uniquely maximizing for some potential. We also verify that the set of potentials with exactly one maximizing measure is residual. This results are obtained through techniques of ergodic theory and convex analysis.

Title: Nonconvex stochastic programming problems - formulations, sample approximations and stability Author: RNDr. Martin Branda Author's e-mail address: branda@karlin.mff.cuni.cz Supervisor: Doc. RNDr. Petr Lachout, CSc. Supervisor's e-mail address: lachout@karlin.mff.cuni.cz Abstract: We deal with problems where integer variables may appear, hence no assumptions on convexity are made throughout this thesis. The goal of Chapter 2 is to introduce stochastic programming problems and to outline the most important tasks connected with solving the problems. In Chapter 3, we compare basic formulations of static stochastic programming problems with chance constraints, with integrated chance constraints and with penalties in the objective function. We show that the problems are asymptotically equivalent under mild conditions. We discuss solving the problems using sample approximation techniques and extend some results on rates of convergence. All the formulations and corresponding sample approximations are compared on an investment problem with real features with Value at Risk constraint, integer allocations and transaction costs. Then, stability of financial decision models where two-stage mixed-integer value function appears as a loss variable is studied. In Chapter 4, we study qualitative properties of the...

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 signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation 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 max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section 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 through-the-wall 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 matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related 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.

Nessa dissertação estudamos Sistemas Dinâmicos do ponto de vista da Otimização Ergódica. Analizamos o problema da maximização da integral de potenciais com respeito a probabilidades invariantes pela dinâmica. Mostramos que toda medida ergódica e unicamente maximizante para algum potencial. Verificamos que o conjunto de potenciais com exatamente uma medida maximizadora e residual. Esses resultados são obtidos atrav es de técnicas da Teoria Ergódica e Análise Convexa. / In this thesis we study dynamical systems trough the viewpoint of ergodic optimization. We analyze the problem of maximizing integrals of potentials with respect to invariant probabilities. We show that every ergodic measure is uniquely maximizing for some potential. We also verify that the set of potentials with exactly one maximizing measure is residual. This results are obtained through techniques of ergodic theory and convex analysis.

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 non-instantaneous channel state information (CSI). The first part of the thesis investigates secret communication through relay-assisted 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 multiple-antenna 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 hard-core 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 noise-limited and interference-limited cellular networks are investigated by applying the fractional frequency reuse (FFR) in the system. For the noise-limited 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 interference-limited 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.

Alongside the ever increasing traffic demand, the fifth generation (5G) cellular network architecture is being proposed to provide better quality of service, increased data rate, decreased latency, and increased capacity. Without any doubt, the 5G cellular network will comprise of ultra-dense networks and multiple input multiple output technologies. This will make the current centralised solutions impractical due to increased complexity. Moreover, the amount of coordination information that needs to be transported over the backhaul links will be increased. Distributed or decentralised solutions are promising to provide better alternatives. This thesis proposes new distributed algorithms for wireless networks which aim to reduce the amount of system overheads in the backhaul links and the system complexity. The analysis of conflicts amongst transmitters, and resource allocation are conducted via the use of game theory, convex optimisation, and auction theory. Firstly, game-theoretic model is used to analyse a mixed quality of service (QoS) strategic non-cooperative game (SNG), for a two-user multiple-input single-output (MISO) interference channel. The players are considered to have different objectives. Following this, the mixed QoS SNG is extended to a multicell multiuser network in terms of signal-to-interference-and-noise ratio (SINR) requirement. In the multicell multiuser setting, each transmitter is assumed to be serving real time users (RTUs) and non-real time users (NRTUs), simultaneously. A novel mixed QoS SNG algorithm is proposed, with its operating point identified as the Nash equilibrium-mixed QoS (NE-mixed QoS). Nash, Kalai-Smorodinsky, and Egalitarian bargain solutions are then proposed to improve the performance of the NE-mixed QoS. The performance of the bargain solutions are observed to be comparable to the centralised solutions. Secondly, user offloading and user association problems are addressed for small cells using auction theory. The main base station wishes to offload some of its users to privately owned small cell access points. A novel bid-wait-auction (BWA) algorithm, which allows single-item bidding at each auction round, is designed to decompose the combinatorial mathematical nature of the problem. An analysis on the existence and uniqueness of the dominant strategy equilibrium is conducted. The BWA is then used to form the forward BWA (FBWA) and the backward BWA (BBWA). It is observed that the BBWA allows more users to be admitted as compared to the FBWA. Finally, simultaneous multiple-round ascending auction (SMRA), altered SMRA (ASMRA), sequential combinatorial auction with item bidding (SCAIB), and repetitive combinatorial auction with item bidding (RCAIB) algorithms are proposed to perform user offloading and user association for small cells. These algorithms are able to allow bundle bidding. It is then proven that, truthful bidding is individually rational and leads to Walrasian equilibrium. The performance of the proposed auction based algorithms is evaluated. It is observed that the proposed algorithms match the performance of the centralised solutions when the guest users have low target rates. The SCAIB algorithm is shown to be the most preferred as it provides high admission rate and competitive revenue to the bidders.

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