Μοντελοποίηση διάδοσης ραδιοκυμάτων στην ιονόσφαιρα και την τροπόσφαιρα με τη χρήση της μεθόδου πεπερασμένων στοιχείων

Abstract

All wireless communication systems are based on radiowave propagation between transmitter and receiver and are highly affected by the propagation medium. The current work, deals with the effects caused to radiowaves, as they propagate through the ionospheric and tropospheric media The variations of the tropospheric and ionospheric refractive indices lead to various phenomena on the propagating waves, like phase variations, refraction and attenuation. The knowledge and the ability to predict such phenomena can result in the design of more reliable communication systems by contributing to the understanding of the relation between the medium and the radiowave propagation characteristics. In this thesis, starting from Maxwell’s equations and the wave equation, a complete model of radiowave propagation is developed. The propagation medium is modeled through the refractive index, while the differential wave equations are solved using the Finite Element Method (FEM). The methodology and the corresponding equations are properly defined and adapted, in order to solve this large-domain propagation problem. The current study is divided into two main sections, the one dealing with ionospheric propagation and the other dedicated to the tropospheric propagation, emphasizing the tropospheric ducting phenomena. The approach to these propagation problems is not identical, mainly due to the differences in the refractive index and the wave equations in the ionospheric and topospheric media. In the troposphere, the propagation is governed by a parabolic equation and the refractive index is a function of pressure, temperature and relative humidity. In the ionosphere, the index of refraction is a function of the electron density, the wave frequency and the electron collisions, while the propagation obeys the normal wave equation. Thus, in the ionospheric propagation, parameters such as phase advance, attenuation, refraction and reflection are calculated. In the tropospheric section, emphasis is given to the refraction and attenuation of the waves, caused by ducting conditions. Additionally, the availability of a large amount of data from the Hellenic National Meteorological Service (HNMS), gave the opportunity for further studies of the tropospheric ducting phenomena and the refractivity variations over the Hellenic region. In Appendix 1, the basic elements of the structure and morphology of the ionosphere are presented. The chapter starts with a short description of the ionospheric layers, followed by a presentation of the mathematical and empirical electron density models. The next paragraphs contain a complete analysis of various propagating phenomena, such as Faraday rotation, phase advance, Doppler shift and scintillations. Also, the ionization mechanism is explained and the plasma dielectric constant is extracted, together with the Maxwell’s equations for the ionosphere. Using elements from the magneto-ionic theory, the electron density and collision frequency formulas are determined and the ionospheric refractive index is calculated. The wave equation for vertical and horizontal polarization is analyzed and a preliminary solution is obtained using the Wentzel, Kramers και Brillouin (WKB) method. All the basic elements and equations of chapter 1, are used later on, in chapter 4, for the complete modeling of radiowave propagation in the ionosphere, using the FEM. In Appendix 2, the morphology of the troposphere is described, together with it’s its effects on wave propagation. Fundamental elements of the tropospheric medium, such as refractive index, refractivity and modified refractivity index are defined here. Also, the conditions of the standard and non-standard atmosphere are described and emphasis is given to the trapping conditions and waveguide types that occur. Finally, a short description of the most important modeling methodologies is presented, including ray tracing, mode theory and parabolic equation models.