Reconstruction of the Antenna Near-Field

Cílem disertační práce je navrhnout efektivně pracující algoritmus, který na základě bezfázového měření v blízkém poli antény bude schopen zrekonstruovat komplexní blízké pole antény resp. vyzařovací diagram antény ve vzdáleném poli. Na základě těchto úvah byly zkoumány vlastnosti minimalizačního algoritmu. Zejména byl analyzován a vhodně zvolen minimalizační přistup, optimalizační metoda a v neposlední řadě i optimalizační funkce tzv. funkcionál. Dále pro urychlení celého minimalizačního procesu byly uvažovány prvotní odhady. A na závěr byla do minimalizačního algoritmu zahrnuta myšlenka nahrazující hledané elektrické pole několika koeficienty. Na základě předchozích analýz byla navržená bezfázová metoda pro charakterizaci vyzařovacích vlastností antén. Tato metoda kombinuje globální optimalizaci s obrazovou kompresní metodou a s lokální metodou ve spojení s konvečním amplitudovým měřením na dvou površích. V našem případě je globální optimalizace použita k nalezení globálního minima minimalizovaného funkcionálu, kompresní metoda k redukci neznámých proměnných na apertuře antény a lokální metoda zajišťuje přesnější nalezení minima. Navržená metoda je velmi robustní a mnohem rychlejší než jiné dostupné minimalizační algoritmy. Další výzkum byl zaměřen na možnosti využití měřených amplitud pouze z jednoho měřícího povrchu pro rekonstrukci vyzařovacích charakteristik antén a využití nového algoritmu pro rekonstrukci fáze na válcové geometrii.The aim of this dissertation thesis is to design a very effective algorithm, which is able to reconstruct the antenna near-field and radiation patterns, respectively, from amplitude-only measurements. Under these circumstances, the properties of minimization algorithm were researched. The selection of the minimization approach, optimization technique and the appropriate functional were investigated and appropriately chosen. To reveal the global minimum area faster, the possibilities in the form of initial estimates for accelerating minimization algorithm were also considered. And finally, the idea to represent the unknown electric field distribution by a few coefficients was implicated into the minimization algorithm. The designed near-field phaseless approach for the antenna far-field characterization combines a global optimization, an image compression method and a local optimization in conjunction with conventional two-surface amplitude measurements. The global optimization method is used to minimize the functional, the image compression method is used to reduce the number of unknown variables, and the local optimization method is used to improve the estimate achieved by the previous method. The proposed algorithm is very robust and faster than comparable algorithms available. Other investigations were focused on possibilities of using amplitude from only single scanning surface for reconstruction of radiation patterns and the application of the novel phase retrieval algorithm for cylindrical geometry.

A Stochastic Approach to the Construction of One-Dimensional Chaotic Maps with Prescribed Statistical Properties

We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power of our method.Comment: to appear in Physics Letters

Possible dynamical determination of mtm_t, mbm_b and $m_{\tau}

Motivated by four-dimensional superstring models, we consider the possibility of treating the Yukawa couplings of the Minimal Supersymmetric Standard Model (MSSM) as dynamical variables of the effective theory at the electroweak scale. Assuming bottom-tau unification, we concentrate on the top and bottom Yukawa couplings, and find that minimizing the effective potential drives them close to an effective infrared fixed line. Requiring an acceptable bottom-top mass ratio leads in principle to an additional constraint on the MSSM parameter space. As a by-product, we give new approximate analytical solutions of the renormalization group equations for the MSSM parameters.Comment: 18 pages, 4 effective figures, plain LATEX (no special macros, to be run twice

Asymptotics of Nonlinear LSE Precoders with Applications to Transmit Antenna Selection

This paper studies the large-system performance of Least Square Error (LSE) precoders which~minimize~the~input-output distortion over an arbitrary support subject to a general penalty function. The asymptotics are determined via the replica method in a general form which encloses the Replica Symmetric (RS) and Replica Symmetry Breaking (RSB) ans\"atze. As a result, the "marginal decoupling property" of LSE precoders for $b$-steps of RSB is derived. The generality of the studied setup enables us to address special cases in which the number of active transmit antennas are constrained. Our numerical investigations depict that the computationally efficient forms of LSE precoders based on "$\ell_1$-norm" minimization perform close to the cases with "zero-norm" penalty function which have a considerable improvements compared to the random antenna selection. For the case with BPSK signals and restricted number of active antennas, the results show that RS fails to predict the performance while the RSB ansatz is consistent with theoretical bounds.Comment: 5 pages; 2 figures; to be presented at ISIT 201

Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements

We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical examples show stable reconstruction of the dielectric permittivity function $\varepsilon$ for random noise level using these measurements