## 4 Evaluation Results
### Transmission Rate and Allocated Bandwidth  
Given the allocated bandwidth, transmission rates under different MCS schemes can be obtained. In the frequency domain of NR system, a Resource Block (RB) is typically composed of 12 sub-carriers with interval of 15 kHz, which leads to a minimum scheduling unit of 180 kHz. Here, we use 540 kHz as the allocated bandwidth for URLLC traffic as an example.  
Figure 6 plots the theoretical transmission rate when \(k=256\) bits and \(\epsilon=10^{-3}\) under different MCS schemes. It is obvious that the transmission rate will be significantly improved when SNR increases or more efficient MCS scheme is applied. In addition, the curve with maker \"+\" is composed of those transmission rates after considering adaptive MCS selection with SNR thresholds given in Table 4. It can be seen that optimal rates can be achieved after applying adaptive MCS selection.  
For the considered periodical URLLC traffic, the maximum theoretical delay can be calculated out by Equation (13) based on the transmission rate given in Figure 7.  
In Figure 7, the maximum theoretical delay is more than 1 ms when SNR is below around \(-3\) dB. If the periodical URLLC traffic can tolerate a maximum delay of 1 ms and error probability of \(10^{-3}\), it means that more bandwidth should be allocated when SNR is  
Figure 6: Transmission rate (\(k=256\) bits, \(\epsilon=10^{-3}\), \(W=540\) kHz).  
Figure 7: Maximum delay (\(k=256\) bits, \(\epsilon=10^{-3}\), \(W=540\) kHz).  
below \(-3\) dB, while less bandwidth can be allocated when SNR is above \(-3\) dB in order to guarantee its QoS requirement and at the same time to consume as less system resource as possible.  
Based on Theorem 1 and Corollary 1, the minimum bandwidth derived theoretically under certain QoS requirement \((d_{0},\epsilon_{0})\) and certain SNR can be obtained as shown by the slashed lines in Figure 8, where the QoS constraint is \((d_{0}=1\) ms, \(\epsilon_{0}=10^{-3})\). The curves under fixed MCS schemes are plotted. In addition, the curve with marker \(+\) is composed of the minimum bandwidth among all MCS schemes considering adaptive MCS selection in different SNR ranges, and this curve can be used as admission region for QoS constraint of \((d_{0}=1\) ms, \(\epsilon_{0}=10^{-3})\).  
Simulation is also conducted to validate the theoretical analysis in this work. A simulation platform is established, where a typical deployment scenario is considered, i.e., an area of 19 cells (further divided into 57 sectors) with radius of 500 meters. Users with periodical URLLC traffic are uniformed deployed within the considered area, and user density is 10 users per sector, i.e., 570 users in total. All MCS schemes defined in [17] are used in the simulation, where the best suitable MCS scheme under different SNR will be selected in order to guarantee the QoS constraint of \((d_{0}=1\) ms, \(\epsilon_{0}=10^{-3})\). The solid line in Figure 8 is formed of the simulation results.  
Each step indicates one MCS scheme. It can be seen that the simulation results are slightly higher than the theoretical results, this is because the theoretical results are the lowest bound under ideal scenario and this also validates the theoretical analysis. In other words, the presented theoretical analysis framework can be relied on to obtain the admission region used for adaptive MCS selection and bandwidth allocation. Compared with simulation, theoretical model is more efficient and can be easily applied or extended to other scenarios.