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Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 136-140).

Estuda-se a relação entre vários conceitos de estabilidade (permanência, estabilidade assintótica e V L-estabilidade) para a equação de Lotka-Volterra e certas propriedades algébricas da Matriz de Interação. Analisa-se os pontos de equilibrio saturados. / We show a relation of several different concepts of stability (permanence, asymptotic stability and VL-stability) for the Lotka-Yolterra equations and certain algebraic properties of the Interaction Matrix. We analize the saturated equilibrium points.

Estuda-se a relação entre vários conceitos de estabilidade (permanência, estabilidade assintótica e V L-estabilidade) para a equação de Lotka-Volterra e certas propriedades algébricas da Matriz de Interação. Analisa-se os pontos de equilibrio saturados. / We show a relation of several different concepts of stability (permanence, asymptotic stability and VL-stability) for the Lotka-Yolterra equations and certain algebraic properties of the Interaction Matrix. We analize the saturated equilibrium points.

Estuda-se a relação entre vários conceitos de estabilidade (permanência, estabilidade assintótica e V L-estabilidade) para a equação de Lotka-Volterra e certas propriedades algébricas da Matriz de Interação. Analisa-se os pontos de equilibrio saturados. / We show a relation of several different concepts of stability (permanence, asymptotic stability and VL-stability) for the Lotka-Yolterra equations and certain algebraic properties of the Interaction Matrix. We analize the saturated equilibrium points.

Cette thèse est consacrée à l'exploitation des propriétés de non circularité et de non gaussianité des signaux en traitement d'antennes.Dans une première partie de cette thèse, nous nous intéressons au contexte de la formation de voies (beamforming) pour la réception d'un signal utile inconnu, dont le vecteur directionnel est connu, corrompu par un bruit potentiellement non circulaire et/ou non gaussien. Dans des études récentes, un beamformer MVDR (Minimum Variance Distortionless Response) linéaire au sens large WL (Widely Linear) exploitant la non circularité au second ordre (SO) des interférences a été introduit et analysé. Cependant, ce beamformer demeure sous optimal pour la réception d'un signal utile non circulaire au SO, du moment où il n'exploite pas la non circularité de ce dernier. C'est ainsi, que notre contribution a porté principalement sur l'introduction, l'étude de performances et la mise en \oe uvre d'un beamformer MVDR WL. Ce dernier, basé sur une décomposition orthogonale originale du signal utile introduisant une contrainte supplémentaire, prend en considération la non circularité du signal utile et celle des interférences. L'étude des performances de ce beamformer a montré que ce dernier améliore toujours les performances en présence de signaux non circulaires. Dans le même contexte et pour la réception de signaux non gaussiens, nous avons introduit et étudié un beamformer MVDR non linéaire de Volterra. Ce beamformer dont les contraintes s'adaptent à la non circularité des brouilleurs, a été étudié à l'ordre trois sous sa forme équivalente GSC. Cette structure, dite complète, prend en compte conjointement des propriétés de non circularité et de non gaussianité des brouilleurs. L'analyse des performances en gains en SINR de ce récepteur est donnée pour la réception d'un signal réel corrompu par des brouilleurs non gaussiens et non circulaires d'ordre deux et quatre. Cette analyse a montré que la prise en considération de ces propriétés améliore toujours les performances. Dans une deuxième partie nous nous intéressons au contexte de détection selon deux volets: Le premier volet consiste en la détection d'un signal utile réel connu de paramètres inconnus, noyé dans un bruit total potentiellement non circulaire au SO et de matrice de covariance inconnue. Ainsi, suivant une approche basée sur le test de rapport de vraisemblance généralisé GLRT (Generalized Likelihood Ratio Test), de nouveaux récepteurs pour la détection d'un signal réel connu avec différents ensembles de paramètres inconnus ont été récemment introduits. Néanmoins, les performances de ces récepteurs, n'ont été que partiellement étudiées. Notre contribution a porté sur l'étude des distributions exactes et asymptotiques des statistiques associées au LRT et au GLRT sous H_0 et H_1. Cette étude a permis de donner les expressions théoriques exactes des probabilités de détection et de fausse alarme des récepteurs LRT, et celles asymptotiques pour certains récepteurs GLRT. Nous avons aussi complété cette analyse par des simulations Monte-Carlo en courbes ROC (Receiver Operating Characterisics) pour l'ensemble des détecteurs GLRT. Le deuxième volet, consiste en la détection de non circularité au SO de signaux aléatoires mono et multidimensionnels complexes. Nous avons donné la distribution asymptotique du GLR de non circularité sous H_0 et H_1 dérivé sous l'hypothèse de distribution gaussienne mais utilisée sous une distribution arbitraire non nécessairement gaussienne des données. Ces données considérées sont indépendantes, mais non nécessairement identiquement distribuées, ce qui permet de traiter des situations pratiques où les données non circulaires sont perturbées par un résidu de fréquence et un bruit additif gaussien circulaire. Cette analyse a été aussi complétée par des courbes ROC. / This thesis is devoted to the study of exploiting the properties of non-circularity and non-Gaussianity of signals in array processing. In the first part of this thesis, we focus on beamforming technics in the context of the reception of an unknown signal, whose steering vector is known, corrupted by potentially non-circular and/or non-Gaussian noise. In recent studies, a widely linear minimum variance distortionless response beamformer (WL MVDR) exploiting the second order (SO) non-circularity of interference was introduced and analyzed. However, this beamformer remains suboptimal for the reception of a non-circular useful signal, since it does not exploit the non-circularity of this latter. Thus, our contribution has focused on the introduction, the performances analysis and the implementation of a WL MVDR Beamformer. This latter, based on an original orthogonal decomposition of the useful signal, take into account the SO non-circularity of both useful signal and interferences. The new performances analysis of this new beamformer has shown that it always improves the performance of the well known Capon beamformer and the WL MVDR beamformer introduced recently, this in the presence of non-circular signals. In the same context and for receiving non-Gaussian signals, we introduced and studied a nonlinear MVDR Beamformer based on comlexe Volterra filters. This Beamformer, which adapt the constraints to the non circularity of jammers, has been studied in the third order by its equivalent GSC form. The performance analysis of this beamformer are shown in term of SINR Gains for the recepetion of non-Gaussian and SO (until to fourth order) non-circular. It is shown that taking into account of these properties always improves performance. In the second part, we focus on two parts of detection: The first part consists of the detection a known signal, with unknown parameters, corrupted by a total noise potentially SO noncircular with unknown covariance matrix. Thus, following Generalized Likelihood Ratio Test approach, new receivers for the detection a real known signal with different sets of unknown parameters have been recently introduced. Nevertheless, the performances analysis of these receptors have only been partially studied. Our contribution has focused on the study of exact and asymptotic distributions of statistics associated with the LRT and GLRT under H$_0$ and H$_1$. This study has given theoretical expressions of probabilities of correct detection and false alarm. We also supplemented this analysis with Monte Carlo simulations and given receiver operating characterisics ROC curves. In the second part, we consider the problem of testing impropriety (i.e., second-order noncircularity) of a complex valued random variable based on the generalized likelihood ratio test (GLRT) for Gaussian distributions. Asymptotic (w.r.t. the data length) distributions of the GLR are given under the hypothesis that data are proper or improper, and under the true, not necessarily Gaussian distribution of the data. The considered data are independent but not necessarily identically distributed: assumption which has never been considered until now. This enables us to deal with the practical important situations of noncircular data disturbed by residual frequency offsets and additive circular noise. The receiver operating characteristic (ROC) of this test is derived as byproduct, an issue previously overlooked. Finally illustrative examples are presented in order to strengthen the obtained theoretical results.

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by Fan Chun-Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 90-[91]). / Abstract also in Chinese. / Chapter CHAPTER 1: --- INTRODUCTION --- p.1 / Chapter CHAPTER 2: --- BACKGROUND OF INJECTION LOCKING --- p.3 / Chapter 2.1 --- Basics of Injection Locking --- p.3 / Chapter 2.2 --- Analytical Methods for Injection Locking --- p.6 / Chapter 2.2.1 --- Analysis of Fundamental Mode Injection Locking --- p.6 / Chapter 2.2.2 --- Analysis of Ha rmonic/Subharmonic Injection Locking --- p.9 / Chapter 2.4 --- Numerical Methods --- p.11 / Chapter CHAPTER 3: --- THE VOLTERRA SERIES METHOD FOR NONLINEAR CIRCUIT ANALYSIS --- p.13 / Chapter 3.1 --- Volterra Expansion --- p.14 / Chapter 3.2 --- Evaluation of Nonlinear Transfer Function --- p.16 / Chapter 3.2.1 --- Probing Method --- p.16 / Chapter 3.2.2 --- Nonlinear Current Method --- p.17 / Chapter 3.2.3 --- Higher order nonlinear current --- p.20 / Chapter 3.2.4 --- Voltage response by using nonlinear transfer function --- p.20 / Chapter 3.3 --- Advantage of Volterra Series --- p.21 / Chapter 3.4 --- Volterra Series Simulator(VSS) Implementation --- p.22 / Chapter 3.4.1 --- Admittance Matrix Formulation --- p.22 / Chapter 3.4.2 --- Evaluation of Nonlinear Response --- p.26 / Chapter 3.4.3 --- Local Cache and Global Cache --- p.26 / Chapter 3.4.4 --- Components Library --- p.27 / Chapter 3.4.5 --- Verification of Simulator --- p.27 / Chapter CHAPTER 4: --- VOLTERRA SERIES GENERAL INJECTION-LOCKED OSCILLATOR FORMULATION --- p.28 / Chapter 4.1 --- Volterra Series Approach to Analysis of Autonomous System --- p.29 / Chapter 4.1.1 --- Chua and Tang's work --- p.29 / Chapter 4.1.2 --- Cheng and Everard's work --- p.29 / Chapter 4.1.3 --- Huang and Chu 's work --- p.30 / Chapter 4.2 --- A Novel Approach --- p.33 / Chapter 4.3 --- Derivation of Determining Equation --- p.35 / Chapter 4.4 --- Injection Lock vector and circuit synthesis --- p.38 / Chapter 4.5 --- Modification to Volterra Series Simulator (VSS) --- p.40 / Chapter CHAPTER 5: --- CIRCUIT MODELING AND PARAMETER EXTRACTION --- p.42 / Chapter 5.1 --- Forward-Bias Gate Measurement --- p.42 / Chapter 5.2 --- Low FREQUENCY S-PARAMETER MEASUREMENT --- p.50 / Chapter 5.3 --- Parameter Extraction from High Frequency S-Parameter Data --- p.52 / Chapter 5.3.1 --- Direct Extraction Method --- p.52 / Chapter 5.3.2 --- Estimation of lead inductance --- p.56 / Chapter 5.4 --- Large Signal Characterization and Extraction --- p.59 / Chapter 5.4.1 --- Large Signal Model --- p.59 / Chapter 5.4.2 --- Extraction of g2 and g3 --- p.60 / Chapter 5.5 --- Equivalent circuit model for inductor and capacitor --- p.67 / Chapter CHAPTER 6: --- APPLICATION TO 1/3 ANALOG FREQUENCY DIVIDER --- p.68 / Chapter 6.1 --- Oscillator design by negative resistance approach --- p.68 / Chapter 6.2 --- Simulation of Free Running Oscillation by VSS --- p.73 / Chapter 6.3 --- Simulation of injection locked oscillator by VSS --- p.75 / Chapter 6.4 --- Injection Locking Experiment --- p.77 / Chapter 6.5 --- Injection Lock Vector --- p.80 / Chapter CHAPTER 7: --- CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK --- p.85 / Chapter 7.1 --- Conclusions --- p.85 / Chapter 7.2 --- Recommendations for Future Work --- p.86 / APPENDIX 1: REFERENCES --- p.87 / APPENDIX 2: PUBLICATION --- p.91

Digital predistortion is one of the most cost effective ways among all linearization techniques. However, most of the existing designs treat the power amplifier as a memoryless device. For wideband or high power applications, the power amplifier exhibits memory effects, for which memoryless predistorters can achieve only limited linearization performance. In this dissertation, we propose novel predistorters and their parameter extraction algorithms. We investigate a Hammerstein predistorter, a memory polynomial predistorter, and a new combined model based predistorter. The Hammerstein predistorter is designed specifically for power amplifiers that can be modeled as a Wiener system. The memory polynomial predistorter can correct both the nonlinear distortions and the linear frequency response that may exist in the power amplifier. Real-time implementation aspects of the memory polynomial predistorter are also investigated. The new combined model includes the memory polynomial model and the Murray Hill model, thus extending the predistorter's ability to compensate for strong memory effects in the power amplifier. The predistorter models considered in this dissertation include both even- and odd-order nonlinear terms. By including these even-order nonlinear terms, we have a richer basis set, which offers appreciable improvement. In reality, however, the performance of a predistortion system can also be affected by the analog imperfections in the transmitter, which are introduced by the analog components; mostly analog filters and quadrature modulators. There are two common configurations for the upconversion chain in the transmitter: two-stage upconversion and direct upconversion. For a two-stage upconversion transmitter, we design a band-limited equalizer to compensate for the frequency response of the surface acoustic wave (SAW) filter which is usually employed in the IF stage. For a direct upconversion transmitter, we develop a model to describe the frequency-dependent gain/phase imbalance and dc offset. We then develop two methods to construct compensators for the imbalance and dc offset. These compensation techniques help to correct for the analog imperfections, which in turn improve the overall predistortion performance.