## 5 MPM-Based Interference Assessment
### Simulation Study Assumptions  
The simulation tests aimed to assess the possibility of simplifying the complex patterns of real antenna systems [33] by using simple models such as the Gaussian or Sinc patterns. The studies focused on determining the SIR relationship with the separation angle \(\Delta\alpha\). The simulations were carried out for the distance \(D=100\) m between the Tx (gNodeB) and Rx (UE). The carrier frequency was fixed at 28 GHz, typical for the 5G micro- and pico-cells, where multiple sub-arrays and beamforming technologies are planned for implementation.  
We adopted the 3 GPP recommendations [30], and non-modified or modified simple antenna patterns to model the Tx antennas. The Rx antenna consists of a single element with a main lobe HPBW of about \(90^{\circ}\).  
In our scenario, we assumed that the Tx was generating two beams (serving and interfering) in the selected sector that were operating in the same sub-band (frequency channel). Thus, the SIR assessment comes down to determining the \(P_{S}\) and \(P_{I}\) powers induced in the Rx antenna that come from the signals generated by the serving and interfering beams, respectively. The SIR definition based on the PAS for two beams is as follows:  
\[\begin{array}{l}SIR(\Delta\alpha)\left(\begin{matrix}\mathrm{W}\\ \mathrm{W}\end{matrix}\right)=\frac{P_{s}(\Phi_{0S}=0^{\circ})}{P_{I}(\Phi_{0 I}=\Delta\alpha)}\\ SIR(\Delta\alpha)\left(\begin{matrix}\mathrm{dB}\end{matrix}\right)=P_{s} \left(\Phi_{0S}=0^{\circ}\right)\left(\mathrm{dBm}\right)-P_{I}(\Phi_{0I}= \Delta\alpha)\left(\mathrm{dBm}\right)\end{array} \tag{14}\]  
To assess the accuracy of the SIR approximation, we used the measure \(\Delta SIR\) defined as:  
\[\Delta SIR(\Delta\alpha)\left(\mathrm{dB}\right)=\left|10\log_{10}\left(\frac{ SIR_{Model}(\Delta\alpha)\left(\mathrm{W}/\mathrm{W}\right)}{SIR_{3 GPP}(\Delta\alpha) \left(\mathrm{W}/\mathrm{W}\right)}\right)\right| \tag{15}\]  
The serving (reference) Tx and Rx beams were aligned, i.e., directed to each other (\(\alpha_{T}=0^{\circ}\) and \(\alpha_{R}=180^{\circ}\), see Figure 8). In relation to the direction of the cell sector center, the reference and interfering Tx beams are oriented in \(\Phi_{0S}\) and \(\Phi_{0I}\) directions, respectively (see Figure 9). Thus, the separation angle of the beams is defined as:  
\[\Delta\alpha=\Phi_{0S}-\Phi_{0I} \tag{16}\]  
Figure 9: Spatial scenario for downlink simulation studies [22].  
Then, the interfering beam orientation in relation to the Tx-Rx direction was equal to \(\Delta\alpha\). In our tests, the direction of the reference Tx beam overlapped with the cell sector center, i.e., \(\Phi_{05}=0^{\circ}\). Hence, we considered the change in separation angle in the ranges of \(0^{\circ}\div 60^{\circ}\) which corresponds to half of a 120\({}^{\circ}\) sector. The tests were carried out for LOS and NLOS conditions.  
In the simulation studies, the following assumptions were made:  
* An illustrative spatial scenario, as shown in Figure 9;
* Carrier frequency is equal to \(f_{\rm c}=28\) GHz;
* PDPs are based on tapped-delay line (TDL) models from the 3 GPP TR 38.901 standard [24], i.e., the TDL-B and TDL-D for NLOS and LOS conditions, respectively; these TDLs are adopted for analysis and RMS delay spread, \(\sigma_{\rm T}\), for so-called the normal-delay profile and urban macro (UMa) scenario, i.e., \(\sigma_{\rm T}=266\) ns;
* The Rician factor defining the direct path component in the scenario for LOS conditions is appropriate for TDL-D [24], i.e., \(\kappa=13.3\) dB;
* The intensity coefficients of the local scattering components, i.e., the 2D von Mises distribution parameters, are equal to \(\gamma=60\);
* The distance between the TX and RX is equal to \(D=100\) m;
* The range of changes in the beam separation angle is [\(0^{\circ}\), \(60^{\circ}\)] with step size of \(0.1^{\circ}\) in the azimuth plane.