# Traffic Offloading in Unlicensed Spectrum for 5G Cellular Network: A Two-Layer Game Approach
## 4 Coalition Game
### Merge-and-Split Based Coalition Formation Algorithm
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline slot time & 9 \(\mu\)s & Unlicensed bandwidth & 20 MHz \\ PHY header of WiFi packet & 224 bits & Station transmission probability \(\tau\) & 0.05 \\ PHY header of WiFi packet & 224 bits & AWGN noise power & \(-174\) dBm\(/\)Hz \\ SIFS & 16 \(\mu\)s & WiFi slot time size, \(\sigma\) & 20 \(\mu\)s \\ DIFS & 34 \(\mu\)s & ACK & 112 bits + 224 bits \\ WiFi maximum backoff state \(m^{(WF)}\) & 6 & Channel bit rate for WiFi & 300 Mbps \\ \hline \hline \end{tabular}
\end{table} 
Table 1: WiFi system parameters. collision probability and the delay in WiFi. In addition, the trade-off between aggressiveness and fairness of LAA can be adjusted by varying \(T_{on}\). In addition, the throughput of LAA is obviously better than that of WiFi and the proposed mechanism can greatly improve the throughput of both LAA and WiFi due to collision avoidance at the instant start of \"on\" period. For example, when \(T_{on}:T_{off}=1:1\) and the number of aggregated packets is 15, the system throughput of WiFi and LAA can increase about 65.93% and 24.76%, respectively, after using the devised approach. Next, the impact of WiFi AP throughput vs. the changing of station numbers before and after coalition forming is presented in Figures 5 and 6. Firstly, we assume that the AP1 is turned off and has no data waiting for transmission. There are only AP2, AP3 and other APs working in the network. The throughput of AP2 and AP3 before and after coalition forming is shown in Figure 5. The AP3 is a heavy-loaded AP, so AP3 has the motivation to form a coalition with other APs which has less stations. When the station number in AP2 is less than \(n^{*}\), both APs could benefit from coalition forming based on merged rule. However, when the number of stations in AP2 is above the \(n^{*}\), no benefit could get from the coalition anymore and the coalition between AP2 and AP3 would be broken based on the splitting rule. Then, AP2 and AP3 would find other APs for cooperation. Moreover, to get insight of the each AP throughput changes after coalition formed, we add the AP1 in the game and the throughput changes of APs before and after coalition forming is shown in Figure 6. As assumed that AP1 is light-loaded and AP3 is heavy-loaded, consequently, after the coalition forming, parts of AP3 data are offloaded to AP1 and AP2 while the number of AP2 stations is less than \(n^{*}\). We further assume AP2 and AP3 have the equal channel condition, equal priority and equal distance to AP1, so when \(n\) is larger than \(n^{*}\), AP1 will accept the transferred stations from AP2 and AP3 alternatively based on the Algorithm 1. In addition, with the increasing number of AP2 stations, AP2 and AP3 would share the benefit from AP1's help. However, once the AP1 station number is over \(n^{*}\) (including stations transferred from AP2 and AP3), it would maintain its current station number and does not continue receiving loads any more. At this time, the AP1 throughput could maintain the maximum value while the throughput in AP2 and AP3 would drop due to the increased station number. Even so, AP2 and AP3 could get profits from the coalition because some

Figure 4: The modified LBT-based CSAT. data are carried by AP1, which can benefit from the coalition to reach the optimal station numbers and maximum throughput. Accordingly, the impact of changing the encourage factor \(\alpha\) of the WiFi coalition is shown in Figure 7. \(\beta\) is the discount factor which has effects on the motivation of a AP joining the coalition. A lager \(\beta\) means a stronger motivation. While the average station number is less than \(n^{*}\), the encourage factor \(\alpha\) is negative, which means more stations could be transferred to this coalition in this period. On the contrary, when the average station number is larger than \(n^{*}\), \(\alpha\) is positive and increased with the increasing number of stations in AP2.