# Cross-Cycled Uplink Resource Allocation over NB-IoT
## 4 Performance Evaluation
### Simulation Results  
Figure 4 shows the effect of adjusting the number of UEs on the consumption of subframes under the three combinations of \(R_{max}\) and \(G\) values. Because more UEs will have more data requirements, the consumption of NPUSCH subframes also increases as the number of UEs increases. Compared with the three different combinations of \(R_{max}\) and \(G\) values, the performance improvement of the proposed \(CNPIRA\) is more evident under \(R_{max}=8\) and \(G=2\). When the NP length is shorter, a higher percentage of subframes in an NP (i.e., \(\frac{R_{max}}{R_{max}\times\mathbb{C}}\)%) cannot be used under the \(ES\) and \(LAURA\) algorithms. \(CNPIRA\) can efficiently use the NPUSCH subframes of the next NP to increase the subframe utilization, especially when more NPUSCH start subframes reside in the next NP. The proposed algorithm can respectively outperform \(LAURA\) about 69%, 53%, and 32% in Figure 4a-c, in terms of the consumed subframes. Compared with \(ES\), \(CNPIRA\) can obviously reduce more subframe consumption. The proposed algorithm not only consumes fewer subframes but can also be adopted for more \(R_{max}\) and \(G\) values. When \(R_{max}=8\) and \(G=1.5\), Figure 5 only shows our proposed \(CNPIRA\), because the \(ES\) and \(LAURA\) algorithms are not available in this case while the proposed algorithm is still workable. This is because the two baselines cannot meet the data repetition requirements of all the UEs and are explained in detail in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(m\)} & & & & & \multicolumn{3}{c}{\(\boldsymbol{l^{h}}\)} \\ \cline{2-10}  & **1** & **2** & **3** & **4** & **5** & **6** & **8** & **10** \\ \hline
1 & 16 & 32 & 56 & 88 & 120  
In Figure 6, because the two baselines do not consider cross-cycled resource allocation to use subframes of the next NP, they can only use three subframes (i.e., subframes 10-12 marked by red color) in an NP, which are not sufficient to satisfy the data repetition requirements of all UEs. By contrast, our proposed algorithm can utilize a total of 12 subframes marked by the red and yellow colors, where subframes 1-9 cannot be used by the next NP limited to the NB-IoT resource allocation protocol. Therefore, the proposed algorithm can be flexibly applied for more \(R_{max}\) and \(G\) values, especially for smaller \(R_{max}\) and \(G\) values. Resource allocation algorithms operating under smaller \(R_{max}\) and \(G\) values generally can consume fewer subframes. The number of consumed subframes in Figure 5 is slightly lower than that in Figure 3(a). Figure 7 shows the impacts of adjusting the number of UEs on the resource utilization under different \(R_{max}\) and \(G\) values. Resource utilization is defined as the number of consumed subcarriers divided by the total number of subcarriers. For the three combinations of \(R_{max}\) and \(G\) values, as the number of UEs increases, the resource utilization will slightly decrease because more UEs should compete for the limited radio resources. Figure 7 demonstrates that the proposed algorithm considers cross-cycled resource allocation so  
Figure 4: Effect of the UE numbers on the number of consumed subframes under different \(R_{max}\) and \(G\) values. (**a**) \(R_{max}=8\) and \(G=2\). (**b**) \(R_{max}=16\) and \(G=1.5\). (**c**) \(R_{max}=16\) and \(G=2\). Figure 5: Effect of the UE numbers on the number of consumed subframes under \(R_{max}=8\) and \(G=1.5\). Figure 6: An illustration for using the subframes of the next NP. that the resource utilization is always higher than 80%, while the resource utilization of the _ES_ and _LAURA_ algorithms is lower than 30%, 40%, and 55% in Figure 7a-c, respectively. The two baselines waste a proportion of the subframes in each NP, resulting in lower resource utilization. Moreover, the waste proportion will be higher when the NP length is shorter.