## 1 Introduction  
In fifth-generation (5G) New Radio (NR) wireless systems, the use of the millimeter wave range makes it possible to introduce new technologies that significantly contribute to increasing the management efficiency of the available radio resources [1, 2, 3, 4]. Thanks to the beamforming and beam direction control system, the massive multiple-input-multiple-output (MIMO) system is an example of technology that enables the spatial separation of network users using the links of the same gNodeB base station [5, 6, 7]. However, the practical use of this technology requires solving an additional problem related to the need to assess the limitations of mutual orientations of the individual beams of the antenna system. This is due to the presence of inter-beam interference that degrades the quality of information transmission on individual links. The widespread use of the inter- or co-channel spectral resources by adjacent beams causes inter-beam interference occurrence [8, 9]. Thisphenomenon is the impetus for developing mechanisms and methods of inter-beam interference mitigation, suppression, or cancellation (e.g., [10; 11; 12]). On the other hand, in 5G and beyond networks, this goal is also achieved by implementing new technologies such as ultra-dense network [13; 14], device-to-device [15], full duplex, non-orthogonal multiple access [16; 17]. These solutions provide inter-beam interference minimization and are crucial for increasing the coverage and spectral efficiency of the network. Numerous works illustrating empirical [8; 18] or simulation studies [13; 14; 19; 20; 21; 22; 23] show the importance of analyzing inter-beam interference in mobile networks. In inter-beam interference research, the orientation, parameters, and shape of individual antenna beam patterns are of crucial importance. Real antenna patterns or simple models may be used in simulation studies. Currently, to ensure an acceptable level of inter-channel interference, the simulation procedure according to the 3 rd Generation Partnership Project (3 GPP) standard [24] is widely used. As a result, we can evaluate the required angular separation between the individual antenna beams. However, in this case, the assessment of inter-beam interference is limited only to multi-element array antennas. In the case of other types of multi-beam antennas, such as [25; 26; 27], this approach will significantly differ from the analysis method with 3 GPP. There is also a need to develop a methodology for assessing inter-beam interference that will be independent of the type (design) of the antenna system and will only use knowledge of its parameters and patterns. Additionally, the procedure's high structural and numerical complexity and the inability to deviate from strictly determined research scenarios make it impossible to assess the level of inter-beam interference under any environmental conditions. The complexity of the analytical description of the antenna patterns and the variability in their parameters that occur with the change in their directions is an additional factor that makes it difficult to assess the required angular separation between the beams. Simple antenna pattern models (e.g., Gaussian, Cosine, Sinc [28; 29]), which primarily consider the influence of the antenna's main lobe, are used to conduct rough calculations and simulations in which the antenna pattern should be considered. The results of such calculations/simulations are usually used at the initial stage of research or analysis, to estimate the trend of changes in the analyzed parameters and phenomena rather than exact results, e.g., at the initial stage of the spatial design of networks. Then, a statistical approach to model the environment (i.e., buildings, terrain) is used, which also does not produce accurate results typical of the deterministic scenario. The main advantage of using simple models is a shorter computation time. Implementing real or more realistic antenna pattern models requires more time and computational resources.