# Energy-Efficient BWP Configuration for Multi-Slice Users
## 3 System Model  
The system model is represented in Figure 1.  
As can be seen, we consider a fixed random number of users \(N_{users}\) and a single next generation NodeB (gNB) with a total band \(B_{total}\) which corresponds to the amount of bandwidth owned by a 5G operator. The gNB covers an area with radius \(R\). Additionally, it operates on the \(f_{operator}=3.5\) GHz frequency (Frequency Range 1) in Time-Division Duplex (TDD) mode. As for the users, they are randomly distributed in the gNB coverage area within the radius \(R\) where each user is connected to two slices: eMBB and URLLC. Each slice will have a dedicated number of radio resources. Additionally, three bandwidth parts are considered for each slice: the first BWP denoted by BWP 1 consists of the band attributed to the eMBB slice and uses numerology 1 (the lower numerology) with a band \(B_{eMBB}\) MHz, the second BWP denoted by BWP 2 is the band attributed to the URLLC slice using numerology 2 (a higher numerology) with a band \(B_{URLLC}\) MHz. Note that users selecting the multi-numerology BWP configuration will scan both these BWPs (BWP 1 and BWP 2) consecutively to retrieve the data for each slice. The third BWP denoted by BWP 3 is the one shared between both slices using numerology 1 with a band \(B_{mixed}\) with \(B_{eMBB}+B_{URLLC}+B_{mixed}\leq~{}B_{total}\). This particular BWP (BWP 3) is scanned by users affected with a single numerology for both services. Each UE \(u\) has a given volume of data \(V_{u,s}\) to retrieve for each service \(s\) and remain in the network until the total data volume for both services is consumed. A fair queuing scheduling is applied at the level of each BWP where the BWP radio resources are attributed equally among users. For each user, we calculate the throughput to determine at a later stage the user's sojourn time in the network. The throughput of UE \(u\) for service \(s\) is computed as follows:  
\[Thr_{u,s}=\frac{AllocPRB_{u,s}\times Bits\_per\_PRB_{u}}{D} \tag{1}\]  
where \(AllocPRB_{u,s}\) is the number of allocated PRBs to UE \(u\) for service \(s\) from its attached BWP during a TII with duration \(D\). Furthermore, \(Bits\_per\_PRB_{u}\) is the number of bits per PRB that depends on the modulation and coding rate of the UE, which in turn are based on its Signal-to-Interference-plus-Noise Ratio (SINR). It is calculated as follows:  
\[Bits\_per\_PRB_{u}=12\times 14\times\log_{2}(MO_{u})\times CR_{u} \tag{2}\]  
In (2), the PRB is considered to be composed of 12 subcarriers in the frequency domain and 14 OFDM symbols in the time domain, which explains the displayed values. In addition, \(MO_{u}\) is the modulation order and \(CR_{u}\) is the coding rate of the considered UE. As for the number of allocated PRBs to the UE for service \(s\), it depends on the total number of PRBs \(TotPRB_{bwp}\) allotted to its attached BWP \(bwp\), which is linked to the service \(s\) and  
Figure 1: System model.  
the total number of connected users to this particular BWP \(N_{users,bwp}\), since a fair resource scheduling is applied:  
\[AllocPRB_{u,s}=\frac{TotPRB_{bwp}}{N_{users,bwp}} \tag{3}\]  
As for the total number of PRBs available at each BWP, it is determined by Table 5.3.2-1 from [17] depending on the attributed BWP band and numerology.  
Such performance indicators will be used to devise the cost function presented hereafter and used to stir adequately the BWP selection configuration in centralized and distributed approaches.