# Directional Paging for 5G Communications Based on Partitioned User ID
## 4 Performance Analysis and Results  
The numerical analysis of PIDP is conducted using MATLAB while considering the combined effect of: the reduction in the UE ID size (with respect to \(N2\)) and re-configurations of POs (with respect to \(N1\) and the paging rate). In directional communication, the paging resource overhead increases with the number of TX beams since the transmission of the paging message takes place over all the beams. Hence, in this section, we present the performance analysis of PIDP with respect to variations in the UE ID size, paging rate and the effect of the number of TX beams. Various parameters utilized for the analysis of the proposed PIDP mechanism are given in Table 3. In the PIDP performance analysis, the downlink cell edge spectral efficiency is considered as paging is a broadcast communication and is intended to be received by all UE (near the cell edge, as well as at the cell center). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Full UE ID Size (N) & 40 bits [26] \\ Cropped UE Size (N2) & 28, 30, 32, 34, 36, 38 bits \\ Paging Rate, (\(R_{pag}\)) & 1600–6400 UE/s [26] \\ Number of Beams (\(B_{n}\)) & 16, 32, 64, 128 beams [8] \\ System Bandwidth, (\(\Omega_{w}\)) & 100 MHz [5] \\ Cell Edge Spectral Efficiency, (\(\eta_{s}\)) & 0.225 bits/s/Hz [27] \\ CRC + PDCCH + RRC bits & 64 bits [28] \\ (\(\epsilon_{CRC}+\epsilon_{RRC}+b_{PDCCH}\)) & 0.2 ms [29] \\ Time Slot Duration (T) & 0.0  
We first present the advantage of the PIDP mechanism with respect to variations in number of beams (16, 32, 64 and 128 beams). Figure 5a,b delineates the percentage of system capacity required when the UE ID size reduces by 20% (\(N2=32\)) and by 5% (\(N2=38\)), respectively, for the PIDP mechanism. Figure 5a,b also shows the comparison of the PIDP mechanism with the percentage of paging capacity required in directional paging with transmission incorporating the full UE ID (\(N=40\)) for the paging rate of 6400 UE/s. As the number of beams increases, the paging resource requirement increases since the paging needs to be transmitted over multiple beams (in turn, multiple time slots). However, the increase in \(C_{PIDP}\) is less compared to directional paging with the full UE ID, \(C_{DP}\). For instance, while directional paging requires almost 73.87% of the system capacity, the requirement reduces to only around 62.9% of system capacity in PIDP for \(N2=32\) and 64 TX beams. As expected, by reducing the number of bits, the paging resource requirement decreases despite the reconfigurations of the number of POs. The reduction in system capacity with \(N2=32\), shown in Figure 5a, is more prominent compared to \(N2=38\) in Figure 5b. The effect of the decrease in \(N2\) is consolidated in Figure 5c. Figure 5c demonstrates the effect of the decrease in the number of bits of the UE ID per UE (\(N2\)) that are included in the paging message for the paging rates of 6400 UE/s when the transmission is executed over 64 TX beams. As the number of bits reduces, the percentage of system capacity initially reduces. However, it shows an overwhelming increase as the bits keep on reducing beyond a threshold (\(N2=30\)) in the case of 64 TX beams and 6400 UE/s PR. This is because the network has to configure  
Figure 5: (a) Percentage capacity vs. the number of beams (32 bits); (b) percentage capacity vs. the number of beams (38 bits); (c) Percentage capacity vs. the cropped UE ID size; (d) Percentage capacity vs. the paging rate. more POs (Equation (6)) as \(N2\) decreases (\(N1\) increases) to ensure that it is able to uniquely page a UE even though a lesser number of bits is transmitted in the paging message. The impact of variations in paging rate (UE/s) on the percentage of the system capacity required for paging transmission is highlighted in Figure 5d for both the PIDP mechanism and directional paging with full UE ID transmission. In Figure 5d, the paging rate variations are shown for 16, 64 and 128 number of beams.