# Performance of Dense Wireless Networks in 5G and beyond Using Stochastic Geometry
## 3 CF of the Aggregated Interference in LOS
### Numerical Validation on Aggregated Interference
The amplitude \(\beta_{o}\) also considers the path-loss at distance \(1\) m: \(|\beta_{o}|=\sqrt{P_{tx}}\,4\pi F_{c}/c\) for \(c=3\times 10^{8}\) m/s and \(F_{c}\) is the carrier frequency (here \(F_{c}=28\) GHz). The mean interference power follows (26). It can be observed that for large thresholds \([T]_{dB}=\{4,5\}\), the average interference power is larger than the signal power, and the system is in outage for every AP height. For smaller thresholds, the AP serves the target UE for a range of AP heights. For example, at \([T]_{dB}=0\), the serving range of AP height is approximately \(1\) m \(<h<33\) m. At around \(h=1\) m, the difference of target UE signal power and mean aggregated interference is zero. For the AP height range \(1\) m \(<h<9\) m, this difference increases, and for the AP height range of \(9\) m \(\leq h<33\) m, the difference decreases, while for \(33\) m \(<h\), the user is in outage. Finally, for a better demonstration of the concave behavior of SIR vs. AP height, Figure 5 is plotted, for two groups of UE density \(\lambda=\{10^{-4},10^{-3}\}\)m\({}^{-2}\) and for the target UE distance of \(R_{0}=\{20,30,40\}\) m. Three SIR threshold \([T]_{dB}=\{5,10,15\}\) guidelines are plotted as horizontal lines. It can be observed that for \(\lambda=10^{-3}\), and a pre-defined threshold of \([T]_{dB}=5\), a target user located at \(R_{0}=40\) m is always in the outage, while the target users located at \(R_{0}=\{20,30\}\) m would experience a concave behavior vs. the AP height \(h\). Once the analytical model has been validated, one might investigate the \(N_{c}\) vs. \(N_{v}\) arrangement of UcyIA for a given total number of antennas \(N_{c}N_{v}\) (e.g., for the same complexity of the radio frequency circuitry). The cylinder arrangement of the UcyIA can be tall (\(N_{c}<N_{v}\)), fat (\(N_{c}>N_{v}>1\)) or just a ring (\(N_{v}=1\)), and the optimum array geometry for service probability depends on different parameters, such as the SIR threshold (\(T\)), path-loss exponent (\(b\)), the antenna (or users) height \(h\), and the directivity of every antenna element (not considered here). The metric used herein is the ratio of the served users in a  
Figure 4: Received power and mean aggregated interference power vs. AP height \(h\), for a target UE located at \(R_{0}=20\) m equipped with a uniform circular array (UCA) with \(N_{c}=128\) that has average power gain \(\tilde{G}_{c}^{2}=0.012\). Parameters: SIR threshold \([T]_{dB}=\{0,1,2,3,4,5\}\), interferer density \(\lambda=5\times 10^{-3}\) m\({}^{-2}\), path-loss exponent \(2b=2.4\), central frequency \(F_{c}=28\) GHz, and transmit power \([p_{\mathrm{rx}}]_{dBm}=20\), \(|\beta_{o}|=\sqrt{P_{tx}}\,4\pi F_{c}/c\), \(R_{max}\rightarrow\infty\). certain area (\(2\pi\lambda\int_{0}^{R}P_{s}(r)rdr\)) to the total average users (\(\pi\bar{R}^{2}\lambda\)), assumed here to be PPP distributed, which is also referred as average service probability  
\[\bar{P}_{\rm s}=\frac{2\int_{0}^{R}P_{s}(r)rdr}{\bar{R}^{2}}. \tag{32}\]  
In the following examples, we maintain the total number of antennas \(N_{\rm c}\times N_{\rm v}=256\), changing the ratio of UCA and vertical antennas. Figure 6 illustrates the number of users served vs. the antenna ratio \(\log_{2}(N_{\rm c}/N_{\rm p})\), varying the path-loss exponent \(2b=\{2,24,2.8,3.2,3.6\}\) for a medium UE density \(\lambda=10^{-3}\)m\({}^{-2}\) and an extremely large UE density \(\lambda=5\times 10^{-2}\)m\({}^{-2}\). It can be seen that, in the case of a smaller UE density, it is preferable to use a UCA. In the case of a very large UE density, a UcylA would be preferred. This is because for a smaller UE density, there are not many interferers that are far from the AP, while their power is largely attenuated w.r.t interferers located closer to the AP. Thus, UCA outperforms by creating a narrower main lobe toward the interested UE, nullifying most of the other UEs located close to the AP but in different azimuths. However, when \(\lambda\) is large, there are too many far-away interferers.