# Modeling of Downlink Interference in Massive MIMO 5G Macro-Cell +
## 4 Simulation Studies  
### Assumptions  
In the simulation studies, we considered a scenario illustrated in Figure 4[38]. In this case, the macro-cell gNodeB (Tx) with the mMIMO antenna array generates two beams in the selected sector, i.e., reference and interfering beams marked in green and red colors, respectively. Their directions determined the angle of beam separation, \(\Delta\alpha\). The UE (Rx) is in an area of the reference beam at distance \(D\). Directions of the UE (purple color) and reference gNodeB beams provide their alignment. We assessed the DL SIR versus \(\Delta\alpha\) between the serving and unwanted beams for various distances \(D\) in an urban macro (UMa) deployment scenario. For more realistic results, we used practical patterns for the UE and gNodeB beams, and simulation assumptions developed by the 3 GPP and ITU in [29, 30]. The gNodeB was equipped with an antenna array of \(8\times 8\) elements that generate two analyzed beams in the selected sector. The UE beam with HPBWs equal to \(90^{\circ}\) and \(65^{\circ}\) on the horizontal and vertical planes, respectively, is generated by a single antenna element. Figure 5 depicts the 3D pattern of the reference beam [38]. The patterns of the UE (purple dashed line), reference (green line), and interference (red dotted line) beams in the azimuth plane are shown in Figure 6[38]. In this case, the exemplary interfering beam is presented for \(\Delta\alpha=30^{\circ}\). Figure 4: Spatial scenario of simulation studies [38]. The main simulation parameters are summarized in Table 1, whereas details of assumed channel models are as follows:  
* in case of the MPM:
* PDPs are based on tapped-delay line (TDL) models from the 3 GPP standard [28] (pp. 77-78, Tables 7.7.2-2, 7.7.2-4), i.e., TDL-D and TDL-B for LOS and NLOS conditions, respectively;
* these TDLs correspond an UMa scenario and normal-delay profile, i.e., rms delay spread (DS) is equal to \(\sigma_{\mathrm{ T}}=363\) ns [28] (pp. 80, Table 7.7.3-2);
* in the TDL-D for LOS conditions, the Rician factor is defined as \(\kappa=13.3\) dB [28] (pp. 78, Table 7.7.2-4);
* local scattering described by the von Mises distribution [39] with an intensity coefficient equal to \(\gamma=60\);
* in case of the 3 GPP model:
* New Radio (NR) UMa LOS and NLOS statistical channel models with parameters from [28] (Section 7.5);
* Monte Carlo simulation methodology with 1000 repetitions of statistical channel model realizations. Figure 5: 3D pattern of reference beam [38]. Figure 6: Patterns of users’ equipment (UE), reference, and exemplary interfering beams in the azimuth plane [38]. The angular spread characteristics for the UMa channel are determined by the 3 GPP [28] using the inverse Gaussian and Laplacian functions for the azimuth and zenith spreads, respectively. The mean and standard deviation values for these distributions are given in [28] (pp. 42-44, Table 7.5-6 Part-1). Therefore, the Monte Carlo simulation methodology is required to obtain a statistically representative set of results. Two separate simulation tools have been used to obtain results for the MPM and 3 GPP model. In the MPM's case, we use our own simulator developed in a MATLAB environment. It is based on analysis of propagation paths between the Tx and Rx, scattered on the multi-elliptical geometry, according to the block diagram depicted in Figure 2. Since 2015, the MPM and its simulator are developing [27; 34]. In the first version, isotropic/omnidirectional pattern antennas were considered [34]. Next, we introduced the Gaussian pattern for the transmitting [35] and then for the receiving antennas [33]. In this case, the transmitting pattern is used to determine the path direction probability. In contrast, the receiving pattern is using for spatial filtering of the paths reaching to the Rx, similarly to the 3 GPP model. In the last version of the simulator used in this research, we replaced the Gaussian patterns with realistic patterns based on3 GPP recommendation [30].