# Propagation Attenuation Maps Based on Parabolic Equation Method +
## 1 Introduction  
Currently, we are observing the development and implementation of the fifth-generation (5G) mobile network, i.e., 5G New Radio (NR) [1, 2]. At the same time, 5G standards are still being developed for other types of communication systems than terrestrial-wireless, such as satellite [3], wired, optical, hybrid [4], etc. This direction of development is so attractive that attempts are also made to replicate it in military communication systems [5, 6, 7, 8]. A few years ago, the first works and analyses began on the legitimacy of using 5G technologies for defense. 5G technologies are a set of radio and network technologies, i.e., in relation to the physical and higher layers of the ISO open systems interconnection (OSI) reference model, respectively. These technologies often also include technologies that were developed earlier, e.g., with the Long Term Evolution (LTE), LTE-Advance (LTE-A), or LTE-A Pro standards, and which are also implemented in the 5G NR. The most important 5G technologies include massive multiple-input-multiple-output (massive-MIMO), beamforming, millimeter waves, full-duplex communications, software-defined radio (SDR), radio resource management (RRM), dynamic spectrum access (DSA), interference mitigation, energy harvesting communications, ultra-dense network, self-organizing network (SON) [9, 10, 11, 12, 13]. In the military sector, work is underway to use the civilian 5G standard for military scenarios. On the other hand, selected 5G technologies are already implemented in the upcoming military systems. While wired and satellite military communications are often based on civilian solutions, wireless military communications, especially at the tactical level, are governed by different rules. In this case, the direct implementation of civil solutions, such as the LTE or 5G NR cellular telephony, is not possible. Tactical military networks are usually classified as mobile ad-hoc networks (MANETs) [14; 15]. In this case, there are no fixed base stations, and all network nodes act as mobile stations (MSs). MSs can move at different speeds and in any direction. Hence, the network organization and the coordination of all its elements are challenging. Some of the aforementioned 5G technologies, such as the RMM, DSA, or SON are already used in military communication systems today, regardless of the used radio resources. At the stage of planning, managing, and coordinating activities of military forces, the so-called battlefield management system (BMS) is used [16; 17]. In relation to communication systems, a radio environment map (REM) [18; 19] is usually the element of such a BMS. In this case, the REM is responsible for the planning, management, and coordination of the MANET nodes. On the other hand, the REM ensures the implementation of the RMM, DSA, and SON technologies. Propagation attenuation maps (PAMs) are crucial REM elements that allow for determining the ranges of radio network nodes. The PAMs may base on different propagation models. In this case, the use of statistical propagation models is usually insufficient [20]. Military operations can be conducted in various terrains. It requires that the PAM considers the terrain topography and the different clutter types such as vegetation, buildings, and the ground parameters (i.e., terrain type). In this case, the use of deterministic propagation models is a better solution [20]. This paper focuses on a novel algorithm for determining the PAM. The proposed solution is based on a parabolic equation method (PEM) and linear interpolation. This algorithm is implemented in a REM in the new Polish tactical communication system that used selected 5G technologies. In the next sections, we introduce important aspects related to the military use of 5G technologies, REM, and PEM. Full mobility of all MANET nodes and terrain variability, where the network operates, makes applying the ray-tracing method (RTM) [21] for its optimization and analysis challenging. A good solution for REMs is using measurement methods [22; 23].