# Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model
## 4 Simulation Results and Discussions  
_Fitting the Path Loss Model_  
The SEPLM is verified and validated for mmwave NLOS links with actual path loss measurement data at 28 GHz obtained through an open-source channel simulator NYUSIM [46]. NYUSIM generates static and independent samples of channel impulse responses for different separation distances between transmitter and receiver. The parameters fed into NYUSIM are listed in Table 2. A scatter plot of omnidirectional and directional path loss over the specified distance range is generated from a continuous run of simulations. For finding the best fit of the parameters \(\kappa\) and \(\zeta\), a linear mean-square estimate is employed [47], and details are provided in Appendix B. The directional, directional-best and omnidirectional path loss measurement data, along with the fitted SEPLM parameters, are shown in Figure 1(a)-c. It can be seen that, for the specified range, SEPLM can adequately describe the path loss characteristics of NLOS link and the path loss parameters are set differently according to the environment. The derived expressions for special cases of obstacle scaling factor \(\zeta=1\) and \(\zeta=2\) in Section 3 are evaluated numerically according to the parameters listed in Table 3. Although the derived expressions are mathematically complex in their generalized form, they are numerically computed easily using MATLAB. The numerical evaluation of derived expressions is also compared with simulation results. For simulation, the system model of Section 2 is produced by considering a circular area and the BSs are located uniform randomly over the entire area. Typical UE is placed at the origin. The coordinates of tagged BS from the origin are computed using minimum distance. The euclidean distance between interfering BSs and the tagged BS is computed. Depending on the distance, using the LOS probability function in (5), LOS and NLOS BSs are determined. The beamforming gains on desired and interfering links are then defined. Independent channel gains are modeled for each desired and interfering link by generating exponentially distributed fading power for LOS and NLOS channels. SIN \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(f\) & 28 GHz \\ \(B\) & 500 MHz \\ Scenario & UMi \\ Environment & NLOS \\ Lower-Upper bound of transmitter-receiver & 10–350 m \\ separation & 100 \\ Transmit Power & 30 dBm \\ Number of receiver locations & 100 \\ Other parameters & default \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input parameters to NYUSIM. Figure 2: Measured data of different path losses and fitted SEPLM parameters. (**a**) _Omnidirectional pathloss_ (**b**) _Directional pathloss_ (**c**) _Best-directional pathloss_. In Figure 3a,b, SINR coverage probability is plotted vs. the SINR threshold for a set of SEPLM parameters \(\kappa\) and \(\zeta\) to model different propagation environments. The analytical and simulation results are closely matched for two cell radii. An increasing value of \(\zeta\) is observed to cause a decrease in coverage probability due to increased path loss for higher values of \(\zeta\). Smaller values of \(\zeta\) represent an environment with sparse obstacles and few objects obstruct the link between UE and its serving BS. As a result, the probability of UE associating with the nearest BS with a minimum obstructed path is higher than the environment with dense obstacles (for higher values of \(\zeta\)), consequently, coverage probability decreases as \(\zeta\) increases. According to SEPLM, obstructions along with the path \(r\) scales as \(r^{\zeta}\) causing an attenuation \(\kappa\). As \(\zeta\) increases, the obstacles scale at a faster rate with distance causing more blockages and attenuation, hence the increased path loss. Since path loss directly affects received SINR, therefore SINR coverage probability is decreased. Figure 3 also explores the impact of varying cell radius on the coverage probability in varying \(\zeta\) environments.