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Although not considered for the first generation of European Galileo satellites, the use of C-Band frequencies for navigation purposes may be taken into account for a future generation of Galileo. For this reason, a frequency band of 20 MHz bandwidth (5,010-5,030 MHz) has been allocated in the course of the World Radio Communications Conference 2000 held in Istanbul, Turkey. The use of C-Band navigation signals offers both advantages and drawbacks. One example is the ionospheric path delay which is inversely proportional to the (squared) carrier frequency and is therefore significantly smaller at C-Band. On the other hand, the use of C-Band frequencies results in increased attenuation effects such as free space loss or rainfall attenuation. It is therefore necessary to provide a detailed analysis of the effects of C-Band frequencies on the navigation process. In order to assess the feasibility of using C-Band frequencies, various aspects of signal propagation and satellite signal tracking at C-Band are examined in the context of this article. In particular, aspects like free space loss, atmospheric effects, foliage attenuation, code and carrier tracking performance, code noise, phase noise and multipath are discussed with respect to their performance at C-Band. In order to allow comparison with the current GPS system, the performance at C-Band is compared to the L-Band performance under similar or identical conditions. The results of this analysis will finally be discussed with respect to their impact on satellite payload and receiver design.

Chapters 1-4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5-8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9-10 are the lecture notes of its further continuation "Geometry of Linear Matrix Inequalities" from the winter term 2021/2022.Because of the COVID-19 pandemic, I produced a series of accompanying screencasts of varying length where go in detail through the material. These can be found within a playlist of my Youtube Channel https://www.youtube.com/channel/UCcsp7yAQjJQHx3SN3aL_r1AOther material like the exercise sheets are available somewhere on my website:

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