## 6 Scanning the Coverage Area with Directional BS Antennas (NLOS Channels)  
While the same procedure described above can be applied for NLOS channels, the excess path loss encountered results in reduced coverage area. As mentioned earlier, we employ the empirical model given in [4; 28] to model NLOS channel behavior. The path loss is described by the empirical relationship given in Equation (14) as:  
\[PL_{linear,\ NLOS}=10^{0.1(\alpha_{NLOS}+10\beta_{NLOS}log_{10}(R)+\xi)} \tag{14}\]  
where for NLOS channels \(\alpha_{NLOS}=75.85\), \(\beta_{NLOS}=3.73\), and the lognormal shadowing \(\xi=N\big{(}0,\sigma_{\xi}{}^{2}\big{)}\) with \(\sigma_{\xi}=5.8\) dB. The NLOS path loss as a function of distance (solid blue line) is compared in Figure 10 to the LOS loss (dashed red line). We observe that as high as 30 dB excess loss can be experienced. Therefore, with the available antenna configuration specified in Table 2, it is necessary to reduce the cell size so that the detection of UEs inside the coverage region is guaranteed. If larger cell sizes need to be supported, larger antennas with finer scan steps; i.e., higher number of time slots, would need to be deployed. Since we want to keep the total number of slots \(N_{slot}=25\) and with the maximum antenna dimensions of 12 \(\times\) 12, the radius of the cell size under NLOS channels is chosen as R = 40 m to pose an equivalent problem to the LOS case discussed before. The procedure of choosing the  
Figure 9: Misdetection probability of the GLRT detector as a function of distance for different scanning strategies using 25 slots of search time under LOS conditions. appropriate scanning solutions is similar to the LOS case. Based on the required SNR (\(-13\) dB) as shown in Section 5.2, we can calculate the required power \(\left(P_{required}\right)\) at each receiver based on (12). As a result, the antenna dimensions as well as scanning directions at each time slots are designed to satisfy the required power received at each receiver in the region. Table 4 shows such a choice of antenna configuration and scanning position for the NLOS case. Figure 11 shows the received power at UEs distributed along the \(x\)-axis. Similarly, as in the LOS case, it is observed that with the appropriate array configurations directed towards points on the \(x\)-axis at 10, 15, 25 and 35 m, all UEs acquire the required power levels for high probability of detection. From these choices, the BS antenna is then scanned azimuthally to fully cover the area of interest. Figure 12 shows the color mapping of SNR levels after scanning for 25 slots. As similar to Section 5.2, we observe that the SNR levels within the entire area of interest are maintained at the required values; i.e., higher than \(-13\) dB, which allows us to keep a low value of \(P_{M}\) at the output of the GLRT detectors. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Slot \(n\)th** & **Target Contours (R)** & **Scanning Angle (\(\theta\))** & **Antenna** \\ \hline
1 st–2 nd slots & 10 m & \(-10^{\circ},10^{\circ}\) & \(8\times 8\) \\
3 rd–5 nd slots & 15 m & \(-15^{\circ},0^{\circ},15^{\circ}\) & \(8\times 8\) \\
6 th–15 th slots & 25 m & \(-20^{\circ},\)\(-15.56^{\circ},\)\(...,\)\(15.56^{\circ},20^{\circ}\) & \(8\times 8\) \\
16 th–25 th slots & 35 m & \(-20^{\circ},\)\(-15.56^{\circ},\)\(...,\)\(15.56^{\circ},20^{\circ}\) & \(12\times 12\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main beam direction and antenna configuration used for deterministic scanning solution under NLOS conditions. Figure 11: Received power levels along the \(x\)-axis for different array configurations under NLOS conditions. Figure 10: SNR levels for LOS and NLOS channels as a function of distance.