# An Optimal Resource Allocation Scheme with Carrier Aggregation in 5G Network under Unlicensed Band
## 4 Problem Formulation
Initialize \(\gamma\), \(\xi\) with \(\rho_{s}(\gamma,\xi)\leq 1\) and \(0\leq\gamma,\xi\leq 1\) begin  Obtain \(b_{w}\) from (29). if\(\sum b_{w}=B\)then  Stop; else \(b_{w



## 5 Numerical Results

We investigate a 5G network under an unlicensed band with a CA feature within one MBS cell coverage with dimensions 1 km \(\times\) 1 km \(\times\) 1 km. The parameters for simulation are summarized in Table 2.

Figure 7 shows the comparison between the peak data rate for rate-sensitive UE with a CA feature and that without a CA feature, which results in superior performance in improving mean achievable peak data rate for rate-sensitive UE. In the figure, the peak data rate for rate-sensitive UE with a CA feature keeps increasing as \(\xi\) increases. Meanwhile, the peak data rate reaches the maximum point as \(\gamma\) reaches the optimal value \(\gamma^{*}\), and then decreases as \(\gamma\) keeps increasing due to the shortage of spectrum resource to match the allocated power resource. Figure 8 shows the comparison between mean packet transmission delay for delay-sensitive UE with a CA feature and that without a CA feature, which results in superior performance in decreasing mean packet transmission delay for delay-sensitive UE. \(\eta\) is 0.5 in Figures 7 and 8. In the figure, the mean packet transmission delay for delay-sensitive UE with a CA feature reaches the minimum value as the \(\gamma\) is the maximum and the \(\xi\) is the minimum. In the figure, the variation tendency of mean packet transmission delay is faster with the change in \(\gamma\) as compared to that of \(\xi\), which means that the delay-sensitive UE is more sensitive to the spectrum resource. \begin{table}
\begin{tabular}{c c} \hline
**Definition** & **Value** \\ \hline \(\delta_{m}\) & 1/km\({}^{2}\) \\ \hline \(\delta_{s}\) & 1000/km\({}^{2}\) \\ \hline \(\delta_{w}\) & 1000/km\({}^{2}\) \\ \hline \(\delta_{u}\) & 10,000/km\({}^{2}\) \\ \hline Total spectrum & 1000 MHz \\ \hline Total power & 100 mW \\ \hline Step size \(\theta\) & 0.05 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 7: Comparison of peak data rate for rate-sensitive UE with CA and without CA. Figure 9 shows system satisfaction as a function of unlicensed spectrum allocation ratios \(\gamma\) for various power allocation ratio \(\xi\). The value of system satisfaction reaches its maximum when \(\gamma\) is optimal and the value of optimal \(\gamma\) increases with the power allocation ratio \(\xi\) increasing. Also, the value of system satisfaction drops rapidly after the \(\gamma\) reaches the optimal point due to the influence on the rate-sensitive UE. The value of system satisfaction increases as \(\xi\) increases due to the rate-sensitive UE being more sensitive to power allocation. As shown in the figure, the proposed scheme achieves superior system satisfaction with \(\xi^{*}\) as compared to that when \(\xi\) is other values achieved by utilizing the Monte Carlo simulation. Figure 10 shows system satisfaction in Figure 9 as a function of power allocation ratio \(\xi\) for various unlicensed spectrum allocation ratios \(\gamma\). This shows that the optimal value of spectrum allocation ratio \(\xi\) for the maximum system satisfaction keeps changing as the power allocation ratio \(\xi\) increases. When the \(\xi\) is small, the corresponding \(\gamma\) with the smallest value contributes to the maximum system satisfaction since the rate-sensitive UE needs more spectrum resources to compensate for the shortness of power resource. As the power resource allocation ratio \(\xi\) increases, the optimal value of \(\gamma\) for the maximum system satisfaction decreases, which is due to the optimal point of \(\gamma\), as shown in Figure 9. As shown in the figure, the proposed scheme achieves superior system satisfaction with \(\gamma^{*}\) than that when \(\gamma\) is other values achieved by utilizing the Monte Carlo simulation. Figure 8: Comparison of packet transmission delay for delay-sensitive UE with CA and without CA.