## 1 Introduction  
### Radio Waves Propagation in the Ionosphere  
Research on the propagation of radio waves in the immediate surroundings of the Earth began at the turn of the 19 th and 20 th centuries, with the appearance of the first attempts to use these waves as an information carrier. In the 1930s the first extraterrestrial sources of radio waves were discovered by [PERSON] [1], which initiated the research of these cosmic signals' nature. The big development of radio wave research from extraterrestrial sources began in the mid\(-\)1950s and continues to this day. The base for the great success of radio astronomy was the huge advance of radio and radar techniques, as well as the introduction of unusual observation techniques that allow for the multiplication of resolution and sensitivity capacities while maintaining the small size of the system's individual elements. Today these techniques are commonly referred to as interferometry, including large-scale VLBI (Very Large Baseline Interferometry) techniques (see, e.g., [2]). On the other hand, radio astronomers quickly realized that the existence of the ionosphere layer has a great impact on the propagation of radio waves in the Earth's atmosphere, especially in the long-wavelength regime. For centimeter waves, changes caused by minor ionospheric disturbances cause fluctuations in the signal path by up to a dozen centimeters, which changes with a typical timescale of a few milliseconds. This was an evident obstacle blocking the development of radio astronomy on meter waves in the second half of the last century, however today it became an opportunity to implement radio astronomy techniques (as in the 1960s, VLBI methods in geodesy and geodynamics) in the study of propagation of radio signals through the turbulent ionized medium [3; 4], as well as the Earth's ionosphere. This affects the accuracy of currently used geodetic techniques associated with observations of Global Navigation Satellite Systems (GNSS) signals (see Figure 1). These relations were shown already in the concept phase of the LOFAR (LOw Frequency ARay) instrument [5], which is an important part of our work. However, at high radio frequencies (over 4 GHz) the ionosphere impact on the astronomical radio signals from galactic and extragalactic sources (e.g., supernova remnants (SNR) or quasars) is negligible, the LOFAR operational frequency range (of 10-240 MHz) could be seriously disrupted. The current investigation of the ionospheric scintillations within the bright point radio sources observations was shown by [PERSON] et al. [6]. On the way from the source to the detection system, radiation encounters the interstellar medium (ISM) (see e.g., [3; 4]), an interplanetary ionized matter and the Earth's ionosphere [7; 8]. This gives an incredible opportunity to obtain information on the condition of the ionized medium, including the state and dynamic of the ionosphere. Recent works confirm this state of research completely and show that the precision of ionosphere parameter determination far exceeds that of GNSS-related signal systems (see e.g., [9]). At some point we come to a situation in which the propagation of radio waves through the ionosphere is not only a stimulus for the study of the ionosphere itself, but also begins to influence the development of other branches of scientific research. A variety of observational infrastructure and research methods have been developed over the last few decades (see Figure 1), the aim of which is to diagnose the ionosphere through the study of radio wave propagation, which perfectly complements the strictly astrophysical observations. In order to study wave propagation a number of radio-based terrestrial  
Figure 1: Schematic representation of the interconnectedness of the close environments of the Earth and its research, and its connection to radio waves from distant sources discussed in this document. systems, such as the European Incoherent Scatter Scientific Association (EISCAT) and the ionosonde networks, have been created.