# Performance Assessment and Comparison of Deployment Options for 5G Millimeter Wave Systems
## 3 Analytical Model  
For the considered scenario, we calculate the signal-to-noise ratio (SNR) at distance \(l\) m from the transmitter as (7)  
\[SNR(l,P_{0})=10 Log_{10}P+G_{tx}+G_{rx}-N-SNR_{marg}-SFM(P_{0})+ SCM\\ -10 lg\left(\sum_{i\in\{0,1\}}\sum_{j\in\{0,1\}}|1-i-p_{LoS}(l)||1- j-p_{l}(l)|PL(l,\alpha_{i},\beta_{j})\right), \tag{7}\] \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline
**Coefficient** & **LoS Value** & **NLoS Value** & **Description** \\ \hline \(\alpha\) & 2.1 & 3.19 & Building blockage coefficient \\ \hline \(\beta\) & 3.24 & 5.24 & Human blockage coefficient \\ \hline \end{tabular}
\end{table} 
Table 1: LoS coefficients. where \(P\) is the signal power in \(\mathrm{Wt}\), and \(G_{tx}\) and \(G_{rx}\) are gains in dB of the transmitter and the receiver, respectively, and \(N\) is the noise level in dB. Here \(\alpha_{i},\beta_{j}\) are the blockage coefficients from Table 1, and, thus, do not have dimension, \(i=0\) stands for the NLoS case, \(i=1\) stands for the LoS case for building blockages, and the same holds true for \(j\) in the case of human blockages. \(SNR_{marg}\) is the MCS margin in dB, given in accordance with [24]. This margin is implemented to take into account a situation where the signal is low enough to reach MCS 16, resulting in signal loss. \(SCM\) is [PERSON]'s capacity margin in dB, implemented to mitigate inaccuracy occurring due to using theoretical values derived from [PERSON]'s theorem, \(P_{0}\) is the outage probability, i.e., the acceptable probability of connection loss, and \(SFM\), calculated as (8), is the slow fading margin in dB. This margin takes into account possible signal variations due to the slow fading effect since we consider scenarios with building blockages. The latter parameter is given by  
\[SFM(P_{0})=\sigma_{SF}\sqrt{2}Errf^{-1}(2P_{0}), \tag{8}\]  
\(SNR_{marg}\) is the SNR value margin, and \(\sigma_{SF}\) is the shadow fading parameter dependent on the scenario. Here, we also consider a composite noise model, where the noise level is calculated as the sum of the internal and external noise, according to (9), i.e.,  
\[N=N_{int}+N_{ext}. \tag{9}\]  
Internal noise can be caused by cable losses, i.e., signal loss due to the cable length \(loss_{c}\), and the noise figure \(NF_{UE}\), defined by the UE device internal configuration. Thus, internal noise can be calculated as the sum of its components, as shown in (10), i.e.,  
\[N_{int}=loss_{c}+NF_{UE}. \tag{10}\]  
External noise sources (11) include thermal noise \(N_{0}\) and the interference margin \(I_{Marg}\) introduced to consider the worst-case scenario of signal interference between two different transmitters occurring on the cell edge. \[N_{ext}=N_{0}+I_{marg}. \tag{11}\]  
After implementing the blockage model, as specified in Section 2, we can calculate the transmitter coverage area with gain \(G_{tx}\) located at height \(h_{tx}\) that transmits a signal at a carrier frequency \(f\) to a receiver located at height \(h_{rx}\) with gain \(G_{rx}\). The coverage would be a three-dimensional distance from the transmitter to the receiver and, thus, is given by (12)  
\[r=\sqrt{l^{2}-(h_{tx}-h_{rx})^{2}}, \tag{12}\]  
where \(l\) is the distance between the transmitter and the receiver.