# The Analysis of Experimental Deployment of IGLUNA 2019 Trans-Ice Longwave System
## 5 Transmission Performance Comparison of Propagation Models
### Proposed Propagation Models  
Frequencies used for these transmissions belong to the upper part of the low frequency band (30-300 kHz), designated internationally for longwave (LW) radio broadcasting services. The propagation of these frequencies can be described by many formulas [25; 26; 27], among which the purely theoretical ones possess significant amounts of inaccuracies and remain barely useful for practical implementations [26]. The solution to these issues is the choice of formulas based on long-lasting experimental research on the RF propagation and reception, which include the natural (and difficult in simulation) characteristics of the terrestrial propagation environment. Such formulas had been formed by many researchers and institutions-including the CCIR (Comite Consultatif International des Radiocommunications, currently ITU-R) [28] and EBU (European Broadcasting Union, also UER-Union Europe de Radiodifusion) [29]. Figure 13: The idealized range pattern of the Klein Matterhorn LW radio experiment. The CCIR had issued a series of graphs with curves describing the E field intensity (RMS) in relation to the distance for ground wave and ground properties as parameters (conductivity and specific electric permeability) [28]. From the graph depicting curves for the conductivity of 1 mS/m and \(\varepsilon_{\tau}=4\) (the closest values to those calculated above), an interesting property can be read--the actually-achieved maximal distance is described by the curve belonging to the frequency nearly twice lower (2000 km for 150 kHz, versus 1000 km for 300 kHz). The UER ground wave formula (but for vertical antenna), used to calculate approximate E field strength (RMS) in the LW broadcasting range, is presented as follows [28]:  
\[E\left[\frac{mV}{m}\right]=\ \frac{300r^{2}\sqrt{P_{\Sigma}G}}{\left(r^{2}+4Z_{ eff.}^{2}\right)^{\frac{3}{2}}} \tag{4}\]  
\[Z_{eff.}=a\left[\frac{\sin\left(\frac{\mathcal{I}_{H}}{2}+\varphi_{0}\right)} {\sin\varphi_{0}}-1\right] \tag{5}\]  
where \(r\) is the distance (km), \(P_{\Sigma}\) is the radiated power (kW), in this case: 0.000426 kW (A-class A3E-SC), \(G\) is the antenna gain (here assumed 1), \(Z_{eff. }\) is the effective height of the reflective layer of the ionosphere, \(a\) is the mean Earth's radius (6378.14 km), and \(\varphi_{0}\) is the angle of incidence on the ground wave on the reflective layer of the ionosphere, estimated using [28] at 82.16\({}^{\circ}\). For the ionospheric wave (emitted by a vertical antenna at night hours with the middle of the distance experiencing midnight at local time, magnetic declination of 61\({}^{\circ}\) and Wolf number equal to 0), the UER gives the following empirical formula [28]:  
\[E\left[\frac{\mu V}{m}\right]=\frac{10233}{\sqrt{r}}\sqrt{P_{\Sigma}G}\cdot e^ {-8.94\cdot 10^{-4}}\lambda^{-0.26}r \tag{6}\]  
with \(\lambda\) being the transmitted wavelength [km]. As the performed experiments were carried out in an untypical setting for a longwave broadcasting-vertical loop antenna, nearly 4 km above sea level, diamagnetic surroundings, singular obstacles on the signal's way, very low power-formulas describing the propagation of surrounding frequency bands are also considered for comparison, regardless of their constraints (the same rule was applied for the formulas mentioned above). Four such formulas were taken into consideration. The Austin-Cohen formula [28; 29] is often used to calculate the E field intensity in the VLF and lower LF frequency ranges, with the leading influence of the ionospheric wave; best applicable for sea-dominated distances. The formula is given as:  
\[E\left[\frac{mV}{m}\right]=\frac{300}{r}\sqrt{P_{\Sigma}G}\sqrt{\frac{\alpha} {\sin\alpha}}e^{-\frac{0.0014r}{\lambda^{0.0}}} \tag{7}\]  
with \(\alpha\) being the central angle (angle measured on the planet's great circle) between the transmission and reception points; here equal to 18.66\({}^{\circ}\).