## 4 Scanning Algorithm Using Omnidirectional Antenna at BS  
We first assess the performance of the GLRT detector for the case when an omnidirectional antenna is used at the BS. The parameters used for the PSS signal transmission are specified in Table 1. The value of \(T_{per}\) is chosen similar to that of current cellular networks while \(T_{sig}\) is chosen to keep a low total PSS overhead \(\left(T_{sig}/T_{per}=2\%\right)\) which is slightly higher than the overhead values of current systems (\(1.5\%\)). The values of false alarm probability used to estimate the threshold level of the GLRT detector are \(1.45\times 10^{-8}\), which are similar to that used in [21]. As will be shown in the next section, the choice of \(N_{slot}=25\) is necessary so that the BS antenna can cover the region of interest without any gaps. If \(N_{slot}<25\), the BS will likely not be able to cover the region, resulting in instability of the probability of misdetection. On the other hand, \(N_{slot}>25\) is not necessary and leads to a waste of transmitted power and resources. The SNR of the PSS signal is defined as  
\[SNR=\frac{P_{r}T_{sig}}{P_{noise}} \tag{12}\]  
where \(P_{r}\) is the received power at the receiver, \(T_{sig}\) is the duration of the signal, and \(P_{noise}\) is the noise power. It should be noted that the transmitted power for all BS antenna configurations (omni, \(4\times 4\), \(8\times 8\), etc.) are kept at the same level; i.e., \(P_{t}=50\) dBm. We will initially focus on LOS channels to present different scanning algorithms. For LOS channels, the omnidirectional path loss coefficient is calculated based on the Friis' transmission principles as in Equation (13). Later on in Section 6, we will investigate the impacts of more realistic scenarios for NLOS channels. \[PL_{linear,\ LOS}=10^{0.1(\alpha_{LOS}+10\beta_{LOS}log_{10}(R)+\xi)} \tag{13}\]  
where \(R\) is the distance between TX and RX, for LOS channels \(\alpha_{LOS}=61.4,\ \beta_{LOS}=2\), and the lognormal shadowing \(\xi=N\left(0,\sigma_{5}^{2}\right)\) with \(\sigma_{5}=5.8\) dB. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline PSS signal duration, \(T_{sig}\) & \(100\ \mathrm{\mu s}\) \\ PSS signal period, \(T_{per}\) & \(5\ \mathrm{ms}\) \\ False alarm probability, \(P_{FA}\) & \(1.45\times 10^{-8}\) \\ Number of slots, \(N_{slot}\) & \(25\ \mathrm{slots}\) \\ Carrier frequency, \(f_{c}\) & \(28\ \mathrm{GHz}\) \\ Transmitted Power, \(P_{t}\) & \(50\ \mathrm{dBm}\) \\ Noise level, \(P_{noise}\) & \(-159\ \mathrm{dBm}/\mathrm{Hz}\) \\ Signal-to-noise ratio (SNR) level & Vary as function of distance \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used for simulation on cell search procedure. Figure 3 shows the SNR levels for an omnidirectional transmitter as a function of distance between the BS and the UE in a LOS setting. As shown, for omnidirectional TX and \(4\times 4\) directional RX antennas with a noise power as specified in Table 1, the value of SNR levels at RX is \(-8\) dB when RX is located on radial contours 10 m away from TX, while the value drops to \(-28\) dB as RX is located on radial contours 600 m away from the TX. To demonstrate the concept, we focus on one facet of the hexagonal BS antenna structure in Figure 1, corresponding to a 60\({}^{\circ}\)-segment of cell. The performance for the other cell segments is similar assuming that: (i) the same antenna arrays will be employed in all cell segments, and (ii) channel characteristics are uniform across the coverage area. To assess the GLRT detector at different SNR levels, 46 different \(4\times 4\) directional UEs are distributed randomly over different radial contours corresponding to different PSS SNR contours.