# Directional Paging for 5G Communications Based on Partitioned User ID
## 3 Proposed PIDP Paging
### PIDP System Model  
For PIDP analysis, we first consider the number of POs configured by the network (evaluated using Equation (6). Subsequently, We can evaluate the UE per PO (\(U_{PIDP}\)) based on the paging rate. Let \(R_{pag}\) be the paging rate, defined as the number of UE to be paged per second. The paging rate can be established by accounting for various factors, for instance paging arrival rate, number of gNBs in a tracking area, user density per cell, type of paging scheme, etc. [10]. \(U_{PIDP}\) can be evaluated as:  
\[U_{PIDP}=\frac{R_{pag}\times L_{DRX}}{N_{PIDP}} \tag{7}\]  
where \(L_{DRX}\) is the length of the IDRX cycle in seconds. The paging message in every PO is comprised of the UE ID of all the UE configured in the PO along with RRC overhead bits (\(\epsilon_{RRC}\)), CRC bits (\(\epsilon_{CRC}\)) and PDCCH (\(\epsilon_{PC}\)) bits. In PIDP, only the partial UE ID (\(N2\): UE ID Part 2 in Figure 3) is included per UE in every PO. Moreover, in the directional  
Figure 4: Configuration of paging occasions (POs) and the distribution of UE over POs in PIDP for \(N1=2\). interface, the same paging message needs to be transmitted over multiple beams. If \(B_{n}\) is the number of beams, then the bits to be transmitted per PO (\(b_{PID}\)) are computed as:  
\[b_{PID}=B_{n}\times\bigg{(}U_{PID}\times N2+\epsilon_{CRC}+\epsilon_{RRC}+ \epsilon_{PC}\bigg{)}. \tag{8}\]  
We can calculate the bits that need to be transmitted per second (\(b_{s}\)) in PIDP as:  
\[b_{s}=\text{ {Bits to be transmitted per PO }}\times\text{POs per IDRX cycle}\]  
\[b_{s} =b_{PID}\times\frac{N_{PID}}{L_{DRX}} \tag{9}\] \[=B_{n}\times\bigg{(}U_{PID}\times N2+\epsilon_{CRC}+\epsilon_{ RRC}+\epsilon_{PC}\bigg{)}\times\frac{2^{N1}}{L_{DRX}}\]  
If \(\eta_{s}\) is the downlink cell edge spectral efficiency in bits/s/Hz and \(\Omega_{w}\) is the system bandwidth in Hz, then the maximum number of bits, \(b_{max}\), that can be transmitted in every second is calculated as:  
\[b_{max}=\eta_{s}\times\Omega_{w}. \tag{10}\]  
Subsequently, we can evaluate the percentage of system capacity used in the PIDP mechanism (\(C_{PIDP}\)) when the partial UE ID is used for directional paging in 5G communications as:  
\[C_{PIDP}=\bigg{(}\frac{\text{ {Bits required to be transmitted per PO in PIDP}}}{\text{ Maximum number of bits that can be transmitted per PO}}\bigg{)}\times 100\]  
\[C_{PIDP} =\frac{b_{s}\times 100}{b_{max}} \tag{11}\] \[=\bigg{(}100\times B_{n}\times(U_{PIDP}\times N2+\epsilon_{CRC}+ \epsilon_{RRC}+\epsilon_{PC})\times\frac{2^{N1}}{L_{DRX}}\bigg{)}\bigg{/} \bigg{(}\eta_{s}\times\Omega_{w}\bigg{)}.\]  
To ascertain the gains due to PIDP, we also evaluate the percentage of system capacity required when the full UE ID is transmitted for each UE in every PO for directional paging. Moreover, when the full UE ID (comprised of N bits) is transmitted, the network needs to configure only a limited number of POs depending on the paging rate and the maximum possible paging capacity [10]. Let \(PO_{N}\) be the minimum number of POs per second required for directional paging that includes the full user ID. We can evaluate \(PO_{N}\) as:  
Figure 4:0  
where \(Cap_{Max}\) is the maximum paging capacity defined as bits available for paging per time slot of duration \(T\) seconds. The value of \(Cap_{Max}\) is based on the number of bits that is available for transmitting the IDs of paged UE in a time slot for a given carrier with a certain carrier bandwidth. \(Cap_{Max}\) can be evaluated as:  
Figure 4:1  
Similar to Equation (9), we can evaluate bits to be transmitted per second \(b_{sDP}\) for directional paging with the full user ID for \(PO_{N}\) number of POs as:  
Figure 4:2Subsequently, we can evaluate the percentage of system capacity used in directional paging when the full UE ID is included in the paging message as:  
Figure 4:3 Figure 4:4  
We also evaluate the effect of the PIDP proposal on the power savings at the base station. Fewer time slots for paging would facilitate the base station to sleep, resulting in power saving.