# Propagation Attenuation Maps Based on Parabolic Equation Method +
## 6 Conclusions  
This paper focuses on a novel method of creating PAM as a crucial REM element, which allows for determining the ranges of radio network nodes. Our solution is based on the PAM determination in two stages. In the first stage, we determined the so-called sparse matrix for profiles outcoming radially from the TX. In the second stage, we used the interpolation method to calculate the full PAM matrix. The proposed approach is based on the DTED-based terrain profiles, PEM, and linear interpolation algorithm. Thereby, the developed solution considers the influence of topography on path loss calculation. The proposed algorithm was implemented in the REM for determining the radio ranges of tactical MANET nodes in the emerging military communication system. On the other hand, the proposed two-step approach to the PAM can be considered universal. This means that DTED, PEM, and linear interpolation can be replaced by others, which provide calculating the full matrix. In this paper, we have presented a detailed description of the PAM generation algorithm based on the PEM for a given terrain topography. Metrics for evaluating the algorithm effectiveness depending on the PAM size have been defined. They were the basis for the assessment of the proposed solution for various PAM. Analyzing the results presented in the paper, it can be concluded that in the \(R_{0}\) range up to about 3 km, over 50% of points in the PAM are calculated according to PEM. In the case of larger areas, it should be remembered that most of the points are interpolated, which affects the accuracy of determining the path loss values. These errors will get bigger with increasing distance from the TX. On the other hand, we presented a preliminary analysis of the PAM accuracy versus the angular resolution of the terrain profiles. The obtained results show that increasing \(\Delta\alpha\) reduces the accuracy of determining the attenuation. However, with a two-fold increase in \(\Delta\alpha\), the computation time decreases twice, and the mean estimation error is equal to 4 dB. The obtained results also showed that increasing \(\Delta\alpha\) from \(5^{\circ}\) to \(10^{\circ}\) only slightly increases the deviation of \(\Delta L\). The utilization of larger \(\Delta\alpha\) can be used in the initial stage of PAM  
Figure 15: RMSE of attenuation error for selected angular resolution of terrain profiles. determination for the preliminary visualization of the results. In the next step, the exact PAMs may be determined for the lower angular resolution of terrain profiles. Future work on PAM development will focus on assessing the impact of profile density on the path loss estimation accuracy, PAM utilization to evaluate the radio range of nodes (i.e., network coverage), comparison of the linear interpolation method with others (e.g., IDW or kriging), and PAM algorithm modification for the TX directional antennas. Conceptualization, M.K., K.M. and J.M.K. ; methodology, M.K., K.M. and J.M.K. ; software, M.K. ; validation, M.K. ; formal analysis, M.K., K.M. and J.M.K. ; investigation, M.K. and K.M. ; resources, M.K. ; data curation, M.K. ; writing--original draft preparation, M.K., K.M. and J.M.K. ; writing--review and editing, M.K., K.M. and J.M.K. ; visualization, M.K. and K.M. ; supervision, J.M.K. ; project administration, J.M.K. ; funding acquisition, J.M.K. All authors have read and agreed to the published version of the manuscript. This work was co-financed by the MILITARY UNIVERSITY OF TECHNOLOGY under Research Project no. UGB/22-740/2022/WAT on \"Modern technologies of wireless communication and emitter localization in various system applications\" and the POLISH MINISTRY OF DEFENSE under Research Grant no. GBMON/13-996/2018/WAT on \"Basic research in sensor technology field using innovative data processing methods\". Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to project restrictions.