Propagation Model for Ground-to-Aircraft Communications in the Terahertz Band with Cloud Impairments  
[PERSON]  
1 Applied Informatics and Probability Theory Department, Peoples' Friendship University of Russia 1117198 Moscow, Russia 1  
[PERSON]  
1 Applied Informatics and Probability Theory Department, Peoples' Friendship University of Russia 1117198 Moscow, Russia 1  
[PERSON]  
1 Applied Informatics and Probability Theory Department, Peoples' Friendship University of Russia 112  
the authors in [8] analyzed the usage of aircraft as relaying nodes in space-aircraft-ground communications. Direct space-to-ground communications in the THz band are considered in [10]. However, they did not account for propagation specifics of ground-to-aircraft links. Propagation models for different altitudes are proposed in [9]. However, the authors do not account for the attenuation caused by cloud formations. There are also multiple models assessing this type of channel at other frequencies that do not have THz-specifics such as atmospheric absorption and specific cloud attenuation [11; 12], and a plethora of papers recently addressed UAV-to-ground channels, see [13]. In this paper, we advocate for ground-to-aircraft communications. The ultimate goal of such a system is Internet access provisioning for passengers and usage of aircraft as relaying points in space-aircraft-ground communications similarly to [10]. The advantages of utilizing ground-mounted stations instead of satellites are much smaller latency and virtually no limitations on complexity and emitted power of ground-mounted communicating units. In order to design such kind of system and to decide upon its operational parameters, a propagation model is required. Two unique impairments that need to be taken into account when designing the ground-to-aircraft THz propagation models are altitude-dependent atmospheric absorption and attenuation by the clouds. The former component is well-described in literature for fixed altitude and is known to produce exponential attenuation on top of conventional power-law free space losses [14; 15]. Cloud impairments are much more difficult to account for due to different types of clouds and their physical and chemical properties [16; 17]. Over the past few years, many research groups have focused their efforts on obtaining an extended description of weather effects in the THz band. In particular, the THz attenuation and channel degradation are caused by atmospheric compounds in clouds (particularly, water vapor), airborne particles (such as dust, fog, clouds, and rain), and refractive index in-homogeneity which are caused by air turbulence and related scintillation. However, there are still no studies accounting for these effects in propagation modeling for ground-to-aircraft communications. The aim of the paper is to develop an analytical propagation model for ground-to-aircraft communications in the THz frequency band. Specifically, by accounting for the specifics of atmospheric absorption as well as cloud impairments, we deliver a closed-form expression for received signal strength at the aircraft. To this aim, we utilize the tools of stochastic geometry by estimating the overall attenuation caused by crossing the clouds at multiple levels. The developed model may serve as a first-order approximation when designing ground-to-aircraft communications systems operating in the THz frequency band. The main contributions of our study are:  
* Detailed overview and classification of the types of clouds, their impairments for THz propagation, and the associated procedure for calculating attenuation induced by a single cloud;
* Analytical propagation model allowing to assess the impairments produced by atmospheric absorption and cloud attenuation in different weather conditions and geographical regions;
* Numerical results showing that the path loss heavily depends on the type of the weather in Earth regions with differences reaching 30-50 and 10-30 dB. The rest of the paper is organized as follows.