# Characterization of Dynamic Blockage Probability in Industrial Millimeter Wave 5G Deployments
## 7 Conclusions  
In this paper, motivated by the usage of 5G private NR systems in industrial deployments, we proposed a methodology to evaluate the LoS blockage probability for UE-UE and BS-UE communications scenarios. The proposed methodology is based on the use of photogrammetry to obtain transparency probability of individual machines and stochastic geometry to determine the blockage probability in specific deployments characterized by a certain density of industrial machines. This methodology can be utilized in system-level mathematical or simulation-based performance assessment and of mmWave 5G NR deployments in the industrial environment.  
We also investigated in detail the blockage probability as a function of industrial deployments. Specifically, we have shown that direct UE-UE communications are feasible in sparse machine deployments (less than 0.1 machine/m\({}^{2}\)) or at small communications distances (less than 5-10 m). Otherwise, BS-UE communications need to be utilized. In this case, BS height is a critical parameter affecting LoS blockage probability. Specifically, by improving the BS height from 4 m to 10 m allows the the blockage probability to be decreased by 20-30% depending on other system parameters. Furthermore, UE height produces more impact on the blockage probability as compared to machine height. In real deployments, one needs to ensure that the height of communications modules at UEs is maximized. Finally, random machine heights affect blockage probability more heavily, by 10-20% more, as compared to constant heights.  
We specifically note that the model proposed in our study accounts for LoS blockage probability only. In practice, the received signal strength dictates whether communication  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Machine Name** & **Width** & **Length** & **Transparency**, \(\kappa\) \\ \hline
**BS array** & \(R_{M}\) & \(R_{T,1}\) & \(R_{T,2}\) \\ \hline RG2 & 0.85 & 0.85 & 0.9983 \\ \hline Quantec & 3.2 & 3.2 & 0.9896 \\ \hline Iiwa 1 & 0.9 & 0.9 & 0.9932 \\ \hline Iiwa 2 & 3.8 & 3.8 & 0.9974 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dimensions and calculated transparency of machines.  
Figure 10: Blockage probability in deployments with considered machines.  
is feasible or not. We envision that the proposed model can be utilized together with other radio part model specific for a given technology such as modulation and coding schemes [31], propagation models [32], antenna models [33; 34], etc., to produce the received signal strength at BS or UE. An overview of these models can be found in [35].  
Conceptualization, V.B., E.M. ([PERSON]) and K.S.; methodology, E.M. ([PERSON]); software, A.K., D.I.; validation, [PERSON] ([PERSON]), E.M. ([PERSON]), V.B. and K.S.; formal analysis, V.B.; investigation, [PERSON] ([PERSON]), V.B.; resources, A.K.; data curation, D.I.; writing--original draft preparation, [PERSON] ([PERSON]), V.B., Y.G. and K.S.; writing--review and editing, D.I.; visualization, A.K.; supervision, K.S.; project administration, V.B., Y.G. and K.S.; funding acquisition, K.S. All authors have read and agreed to the published version of the manuscript.  
Sections 3-5 were written by [PERSON] under the support of the Russian Science Foundation, project no. 22-29-00222. This paper has been supported by the RUDN University Strategic Academic Leadership Program (recipients [PERSON], Sections 1, 2 and 6).  
Not applicable.