## 1 Introduction
Moreover, for certain issues, e.g., interference assessment, the use of simple models may provide sufficient accuracy for the analysis results. In this paper, we continue our previous research presented in [21; 22; 23]. Inter-beam interference evaluations for the sub-6 GHz downlink using the real 3 GPP massive MIMO [30] and Gaussian patterns are presented in [21] and [22], respectively. Similar studies for the sub-millimeter-wave downlink and uplink scenarios and real 3 GPP antenna patterns are shown in [23]. In these cases, the MPM [31; 32] was used for modeling radio channels, and in [22; 23], we additionally used the 3 GPP channel model [24] to compare the results. The obtained signal-to-interference ratio (SIR) results for the Gaussian and 3 GPP patterns showed some discrepancies for line-of-sight (LOS) and non-LOS (NLOS) conditions. It resulted from considering only the main lobe in the simplified pattern model. Under LOS conditions for the 3 GPP pattern, the extremes in the SIR graphs versus the beam separation angle occurred for angles that are multiples of the antenna half-power beamwidth (HPBW) for both the MPM and 3 GPP models. The results in [14] depict a similar effect. These differences motivated us to analyze other simple pattern models and develop their modifications to obtain a more accurate SIR assessment. In this paper, we show a modification of simple antenna pattern models. This approach is limited to considering the change in directivity of the real antenna pattern, which occurs with a change in the direction of the main lobe. The proposed solution is independent of the antenna system's type, structure, and analytical description (e.g., [33; 34]) or beamforming technique. This paper is also devoted to the evaluation methodology of interference between the serving (i.e., useful) and adjacent beams. However, here, the main problem focuses on assessing the possibility of simplifying the complex patterns of real antenna systems [35] using simple models such as the Gaussian, Cosine, and Sinc [28; 29]. In the case of real antennas with beam control, both the parameters and shapes of the beams change with the change in their orientation [22; 30]. This fact significantly increases the numerical complexity of conducting simulation tests and analytical evaluation of the interference level from the co-channel beams. This paper shows that the proposed modification of simple models provides consistent results of the interference level assessment in relation to the actual antenna beam pattern. The simplicity of the proposed amendment only considers the change in the antenna beam directivity proportional to the change in this parameter for the real beam. Changing the beam orientation while maintaining its shape significantly simplifies the simulation test procedure and enables the assessment of the influence of its individual elements on the level of interference induced in the receiving antenna. The procedure presented in the paper uses the modification of simple models of antenna beam patterns to analyze the level of interference occurring in radio links with multi-beam antenna systems. This method of evaluating the effects of individual antenna beams on the received serving signal determines the originality and novelty of the developed solution. The main contributions in this paper are as follows:  
1. We introduce a novel modification of the simple antenna pattern model, which is based only on the knowledge of the real antenna system pattern and is independent of its type, structure, and analytical description. 2. We evaluate the pattern approximation accuracy of the modified and non-modified models against the 3 GPP reference pattern model. 3. From the interference evaluation viewpoint, we proposed assessing the effectiveness of simple pattern models based on SIR errors instead of pattern mapping errors, taking the real antenna pattern (i.e., the 3 GPP beam pattern in the case of our studies) as a reference. 4.