## 5 Scanning the Coverage Area with Directional BS Antennas (LOS Channels)
### Deterministic Scanning Algorithm  
For the deterministic approach, the exhaustive method was shown to be effective in [22; 23; 24]. While this method presents a low misdetection probability at UEs, it is considered too cumbersome in practice since the BS antenna needs to scan both in angular and radial spaces. In this paper, we propose an optimized deterministic scanning pattern employing directional antennas at the BS. This step will be considered as stage 2 of the iterative method in [22; 23; 24]. The objective is to use adaptive directional antennas to cover the regions where the omnidirectional transmission suffers from high misdetection \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Slot \(n\)th** & **Target Contours (R)** & **Scanning Angle (\(\theta_{l}\))** & **Antenna** \\ \hline \hline Case 1 & 1 st–25 th slots & Random & Random & \(8\times 8\) \\ \hline \multirow{4}{*}{Case 2} & 1 st slot & 43 m & \(0^{\circ}\) & \(4\times 4\) \\  & 2 nd–4 th slots & 96 m & \(-18^{\circ},0^{\circ},18^{\circ}\) & \(4\times 4\) \\  & 5 th–10 th slots & 161 m & \(-25^{\circ},-15^{\circ},...,15^{\circ},25^{\circ}\) & \(8\times 8\) \\  & 11 th–25 th slots & 502 m & \(-27^{\circ},-23.15^{\circ},...,23.15^{\circ},27^{\circ}\) & \(12\times 12\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main beam direction and antenna configuration used for deterministic scanning solution under LOS conditions. Figure 6: (a) Random beam locations on ground for the 25 time slots; (b) Corresponding coverage with random scan pattern using an \(8\times 8\) directional antenna. rate due to propagation loss. This way, the misdetection rate can be reduced for UEs residing far away from the BS by improving the SNR levels. Furthermore, to maximize the performance of the search process, we propose the use of an adaptive array antenna to reduce the total scanning time while keeping the coverage capability the same and misdetection rate low. Based on the misdetection probability rates for the omnidirectional antenna in Figure 4, we realize that to keep the misdetection rate \(P_{M}\) low for each slot of search time, the SNR level received at the UEs should be at least \(-13\) dB. With the required SNR values, we can calculate the required power \(\left(P_{required}\right)\) at each receiver based on (12). Therefore, the specific antenna configuration at each time slot is based on the required SNR level at a target area to acquire a low value of \(P_{M}\). Furthermore, we assume the BS antenna can only scan in one direction at a time. The BS will then need to scan multiple slots to guarantee good SNR levels anywhere within the segment. The array can be scanned to different directions by applying the necessary phase excitations to the array elements as described in (2) while the transmitted power is fixed. Figure 7 shows the received power at UEs distributed along the \(x\)-axis. It is observed that with the appropriate array configurations directed towards points on the \(x\)-axis at 43 m, 96 m, 161 m and 502 m, all UEs acquire the required power levels for high probability of detection. From the choices in Figure 7, the BS antenna is then scanned azimuthally to fully cover the area of interest. This is where the total of \(N_{slot}\) is equal to 25. Figure 8a shows the color mapping of SNR levels after scanning for one slot within 43 m. For all of the UEs located within 43 m of BS, they will acquire a low misdetection rate since the powers received at these UEs are higher than the required power. Figure 8b shows the color mapping of the next three slots as the BS scans to the 96 m contour using a 4 \(\times\) 4 array antenna. As observed, three beams with an azimuthal scan step of \(\Delta\theta_{l}=18^{\circ}\), cover the radial range between 43 and 200 m with the required received power.