# Modeling of Downlink Interference in Massive MIMO 5G Macro-Cell +
## 4 Simulation Studies
### Analysis of SIR Confidence Intervals  
To analyze simulation result variability, we determined the confidence intervals against the average SIRs, \(SIR_{\text{avg}}\), presented in Sections 4.2 and 4.3. The obtained confidence intervals are depicted in Figures 11 and 12 for LOS and NLOS conditions, respectively. In  
Figure 10: CDFs of SIR for NLOS conditions and selected distances obtained for (**a**) the MPM and (**b**) the 3 GPP model.  
this case, considering the similarity of the results for various distances, we show the results only for \(D=100\) m.  
The confidence intervals of the SIR graphs were illustrated as \(SIR_{\mathrm{avg}}(\Delta\alpha)\pm\sigma_{SIR}(\Delta\alpha)\), where \(\sigma_{SIR}(\Delta\alpha)\) is a standard deviation for the selected separation angle, calculated based on 1000 values of the SIR set obtained during each Monte Carlo run. Using the Monte Carlo approach in the 3 GPP simulator allows these confidential intervals to be obtained simultaneously. Average results for the MPM simulator, illustrated in previous sections, were obtained based on the so-called single-simulation mode. In this case, we used a huge number of propagation paths. To analyze the confidence intervals for these average results, we also had to run the MPM simulator in Monte Carlo mode with a small number of random propagation paths.  
Figure 11: Exemplary SIRs with confidence intervals versus angle of beam separation for LOS conditions, \(D=100\) m, obtained for **(a)** the MPM and **(b)** the 3 GPP model.  
Figure 12: Exemplary SIRs with confidence intervals versus angle of beam separation for NLOS conditions, \(D=100\) m, obtained for **(a)** the MPM and **(b)** the 3 GPP model.  
Generally, we may see that the MPM results fall within the ambit of the 3 GPP confidence intervals. Under LOS conditions, both models' results are very convergent, as described in detail in Section 4.2. The obtained results of the confidence intervals further increase their similarity. In this case, a characteristic feature is a slight increase in the deviation with the increase in \(\Delta\alpha\). Under NLOS conditions, the SIR results for the MPM fall wholly within the ambit of the confidence intervals obtained for the 3 GPP model. For these propagation conditions, it is characteristic to keep the constant \(\sigma_{SIR}\) regardless of the separation angle.  
To compare error distribution of the simulation results, we calculated the mean standard deviation, \(\overline{\sigma}\), for the MPM: \(\overline{\sigma}_{LOS}^{MPM}=0.84\) dB and \(\overline{\sigma}_{NLOS}^{MPM}=1.83\) dB, and 3 GPP: \(\overline{\sigma}_{LOS}^{3 GPP}=0.94\) dB and \(\overline{\sigma}_{NLOS}^{3 GPP}=8.91\) dB, under LOS and NLOS conditions, respectively. In this case, SIR variability may be modeled as a Gaussian random variable with a standard deviation determined by the appropriate \(\overline{\sigma}\). Conversely, the average value of this random variable should be modeled using the averaged SIR described in Section 4.2 or Section 4.3. On the other hand, we can see the similarity of both simulators in their \(\overline{\sigma}\) values for LOS conditions. Under NLOS conditions, the values of \(\overline{\sigma}\) are definitely different. This may result from the fact that in the MPM, the scatterer locations are limited to the defined multi-elliptical structure related to the PDP. However, in the statistical 3 GPP channel model, the potential positions of the scatterers are characterized by more spatial variation.