# Unlicensed Spectrum Allocation for LTE and Wi-Fi Coexistence with HAP
## 5 Performance Evaluation
Therefore, the increase of STAs does not significantly impact the overall Wi-Fi throughput. Like LTE-U, the proposed method also finds an adequate \(\delta\) value to dynamically adjust the resources that Wi-Fi can obtain. The adjustment of \(\delta\) is closer to the optimal resource allocation, so it performs better than LTE-U. The NBS algorithm also calculates the period that LTE users can use the unlicensed band. The LTE users obtain more resources according to the time ratio calculated by NBS, so the Wi-Fi system's throughput performance is slightly worse. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{\(N_{UE}=20\), \(N_{STA}=5\)} & \multicolumn{3}{c}{\(N_{UE}=20\), \(N_{STA}=15\)} \\  & **Wi-Fi** & **LTE** & **Total** & **Wi-Fi** & **LTE** & **Total** \\ \hline Original & 25.7 & 28.1 & 53.8 & 18.8 & 30.1 & 48.8 \\ Proposed & 12.7 & 49.0 & **61.7** & 10.1 & 47.1 & **57.2** \\ \hline NBS & 8.6 & 51.4 & 60.0 & 6.1 & 49.1 & 55.2 \\ LAA & 14.1 & 41.1 & 55.2 & 8.1 & 32.4 & 40.5 \\ LTE-U & 10.3 & 48.0 & 58.3 & 9.0 & 43.4 & 52.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total throughput (Mbps). Figure 11: The throughput of Wi-Fi and LTE. We also examine the performance of each scheme with heavily loaded LTE in Figure 12. The number of LTE users is set to 50. When the LTE load is greater than the threshold \(Load_{LTE\_th}\), the Wi-Fi thresholds, \(P_{th}\) and \(Throughput_{th}^{WiFi}\), will be adjusted according to (5) and (6). As the load of LTE increases, the thresholds decrease to relax the conditions for LTE to use unlicensed bands. However, when the load of Wi-Fi is also very high, the Wi-Fi thresholds need to be adjusted back to normal values to protect Wi-Fi. We have results that resemble the patterns in Figure 11.  
In the next experiment, the Wi-Fi load is maintained at a low level, and the LTE load varies from low to high. As can be seen from Figure 13, since the mechanism proposed in this paper focuses on fairness, it will maximize the overall throughput while meeting the minimum Wi-Fi and LTE QoS requirements. Therefore, the decline in Wi-Fi throughput will be lower than that in NBS. The throughput will decline as the number of LTE users increases until the LTE load exceeds the threshold. In this scenario, the Wi-Fi load is very low, and the number of STAs is only 5. LTE users will benefit from accessing the unlicensed band. The proposed scheme will dynamically adjust the time ratio \(\delta\) when the LTE load exceeds the threshold to maximize the overall throughput. Therefore, the period for LTE to access the unlicensed band will increase, as well as the LTE throughput. Figure 12: Total throughput under a different number of stations with 20 LTE users. Figure 13: Total throughput under a different number of LTE users with 5 Wi-Fi stations. Next, we would like to assess how friendly the coexistence mechanisms are to Wi-Fi. The fairness indices for different schemes are examined [26]. [PERSON]'s fairness index [27; 28] is employed for the evaluation. The fairness index equation is given in (14). \[F=\frac{(\sum_{i=1}^{n}x_{i})^{2}}{n\times\sum_{t=1}^{n}x_{i}^{2}} \tag{14}\]  
\[x_{i}=\frac{Throughput_{i}}{Throughput_{i}^{opt}} \tag{15}\]  
where \(x_{i}\) represents the throughput proportion of entity \(i\), which can be expressed as the user throughput divided by the optimal user throughput in the network and \(n\) is the number of LTE users and Wi-Fi stations. For [PERSON]'s fairness index, the value of this fairness index is between 0 and 1, and the larger the value is, the fairer it is. There are 20 LTE users in this simulation, and the number of Wi-Fi stations increases from 5 to 25. The result is shown in Figure 13(a). As shown in the figure, as the number of users increases, both our proposed scheme and NBS can improve the fairness index. When the number of Wi-Fi stations is small, Wi-Fi is in a light load condition. Wi-Fi stations do not need too many resources. Therefore, the thresholds of Wi-Fi remained at a relatively low level.