# Performance of Dense Wireless Networks in 5G and beyond Using Stochastic Geometry
## 5 Outage Analysis in the Presence of NLOS, Noise and Blockage
### Blockage  
In mmW and 6G sub-THz systems, the waves are prone to blockage due to static and dynamic blockage. Static blockage [61; 62; 63] is caused by structures such as buildings and trees; self-blockage [63; 64; 65] is caused by the body holding the UE; and dynamic blockage [63] is caused by moving objects, humans or vehicles. The behavior of blockages and their impact on the coverage probability and system performance are different. Some of the blockage effects can be modeled in closed form, while some others need numerical methods. Here, we limit the analysis of the paper to the numerical evaluation of the coverage probability in the presence of blockage. It is convenient to define a dummy binary variable \(\mu_{\ell}\) for the \(\ell\)-th path, which is \(\mu_{\ell}=0\) when the link is blocked and \(\mu_{\ell}=1\) when the link is free of any blockage, such that \(\mathit{Prob}(\mu_{\ell}=0)=P_{B}\) is invariant on every path, and \(P_{B}\) is the probability of blockage. The blockage per path can be incorporated into (48) as  
\[\mathbb{P}_{service}=\mathbb{P}_{I}\left(\check{I}_{tot}+\check{N}_{tot}<\frac {1}{T}\left(\sum\limits_{\ell=1}^{L}\frac{|\beta_{\ell}|^{2}\mu_{\ell}}{\check {I}_{\ell}\check{D}_{\ell}^{2p}}\right)^{2}\right), \tag{49}\]  
where \(\check{I}_{tot}=\sum\limits_{\ell=1}^{L}\check{\alpha}_{\ell}I_{\ell}\,\mu_{\ell}\) and \(\check{N}_{tot}=\sigma_{n}^{2}\sum\limits_{\ell=1}^{L}\check{\alpha}_{\ell}\) are the total interference and noise power computed respectively, after MRC at the AP, with \(\check{\alpha}_{\ell}=\mu_{\ell}\alpha_{\ell}\) being a scaling parameter for a given path, and it is obviously switched off by \(\mu_{\ell}\) when the path is blocked. The distribution of the aggregated interference power \(I\), can be achieved by considering that blockage modifies the average density of interferers to \(\lambda(1-P_{B})\). The goal is to assess the effect of the impact of blockage \(P_{B}\) on service probability. At each snapshot, one link can be either blocked or available. In order to calculate the service probability, taking into account the blockage probability, one must numerically evaluate (49), for \(\mathit{Prob}(\mu_{\ell}=0)=P_{B}\) for \(\forall\ell\). Figure 17 is the average service probability and Figure 18 is the number of UEs served; both figures are versus blockage probability \(P_{B}\) for small (\(\lambda=5\times 10^{-3}\,\mathrm{m}^{-2}\)) and large (\(\lambda=5\times 10^{-2}\,\mathrm{m}^{-2}\)) UE density, and a varying number of paths (\(L=1,4\)), and path loss (\(2b=2,2.8\)). In Figure 17, for a small \(\lambda\) and LOS path (\(L=1\)), the blockage probability reduces the service probability, while for \(L=4\), the service probability is more robust  
Figure 16: Average users served \(M_{s}\) within square area \(200\,\mathrm{m}\times 200\) m vs. UCA height \(h\), solid lines is the no NLOS (\(L=1\)), while dashed lines with marker are with NLOS for \(L=2,3,4\), with MRC and SC receivers for \(N_{c}=500,\lambda=10^{-3}\,\mathrm{m}^{-2}\); \(2b=2.6\), SIR threshold \([T]_{dB}=0\), \(R_{max}=400\,\mathrm{m}\), the normalized amplitude\(|\beta_{\ell}|=1\) for every path \(\ell\). even for large \(P_{B}\), and this is due to the diversity of the multipath against the interference. On the other hand, when \(\lambda=5\times 10^{-2}\,\mathrm{m}^{-2}\), a multipath channel with \(L=4\) severely degrades the performance. Numerical analysis shows the impact of the blockage on the service probability in Figure 17, and the average number of user served in Figure 18. The total number of users within a \(\Delta\times\Delta\) square-shaped area is \(M_{s}=\lambda\Delta^{2}P_{s}\). This means that for small \(P_{B}\) any increase of one decade of UE density results in a smaller variation in the number of users served.