# Full-Duplex MAC Protocol for CSMA/CA-Based Single-Hop Wireless Networks
## 4 Numerical Simulation and Analysis  
According to the discussion in Section 3.1, when each node in the network works in the FD and HD modes (the former adopts the proposed FD MAC protocol, and the latter adopts the traditional CSMA/CA protocol), we use different values of \(n\) and \(W\). The values of \(\pi_{T1}\) and \(\pi_{T}\) are shown in Figure 8.  
As shown in Figure 8, in general, the largest difference between the values of \(\pi_{T}\) and \(\pi_{T1}\) (in \(n=5\) and \(W=64\) case) was about 20%. As the size of \(W\) increased, both the values of \(\pi_{T1}\) and \(\pi_{T}\) decreased because after a node sends the frame over, regardless of whether the transmission is successful, it will randomly select a back-off count in the contention window and enter the corresponding back-off state. According to the state transition diagrams as shown in Figures 6 and 7, if the size of \(W\) increases, then the optional number of the back-off counts will increase and the node may select a larger back-off count. At this time, the \"way\" from the back-off states to the transmission state becomes longer. In other words, the probability that originally belongs to the transmission state is allocated to the back-off states. Figure 8: “Active” transmission probabilities for the proposed FD MAC protocol and the traditional CSMA/CA protocol versus the different values of \(n\) and \(W\). For the HD node, according to Equation (1), the value of \(\pi_{T}\) is independent of \(n\). However, for the FD node, when the size of \(W\) remains unchanged, the value of \(\pi_{T1}\) will increase as \(n\) increases. We used the \(W=8\) case for example. When \(n=5\), we have \(\pi_{T1}=0.1768\), but when \(n=10\), we have \(\pi_{T1}=0.2005\). This condition occurs because, according to the system model, the node which \"actively\" sends the frame randomly selects its destination among all the other nodes. Then, the two nodes communicate in FD_1 or FD_3 mode. At this time, a node will be present in the \(T_{2}\) state. According to Equations (7)-(11), if the value of \(n\) increases, then the probability (\(\beta_{1}\) and \(\beta_{2}\)) that the node is selected as the destination will decrease. Furthermore, the node will be less likely in the \(T_{2}\) state (in the simulation, when \(n=5\), we have \(\pi_{T2}=0.089\), but when \(n=10\), we have \(\pi_{T2}=0.0409\)) and more likely in the \(T_{1}\) state. Note that when \(n\) increases to a large value, the probability that the node is in the \(T_{2}\) state is very small. The value of \(\pi_{T1}\) approaches \(\pi_{T}\). In the simulation, when \(n=30\), the value of \(\beta\) (\(\beta_{1}+\beta_{2}\)) equaled \(6.17\times 10^{-4}\). Accordingly, the value of \(\pi_{T2}\) was only \(4.8\times 10^{-4}\). When the size of \(W\) is large, although the value of \(\beta\) will decrease as \(n\) increases, given the probability that the node is in the back-off states increases and \(\pi_{T2}\) can be solved by \(\beta\) multiplying the sum of \(\pi_{Si}(i=1,\,\ldots,\,W-1)\), both the values of \(\pi_{T2}\) and the difference between \(\pi_{T1}\) and \(\pi_{T}\) will increase. When the communication modes as shown in Figure 1b-d appear in the network, if the protocol operates as shown in Figure 4, then neither of the two nodes initiates \"passive\" transmission, \(\beta_{2}\) does not exist, and \(\beta=\beta_{1}\). In fact, we lose the probability that the node jumps from the back-off states to the \(T_{2}\) state. The value of \(\pi_{T2}\) will decrease. Hence, the values of \(\pi_{T1}\) in such cases are slightly larger than those shown in Figure 8. In the simulation, when \(n=5\) and \(W=8\), here \(\pi_{T1}=0.1841\), but in the above case, \(\pi_{T1}=0.1768\). When we keep the value of \(W\) unchanged and only increase the value of \(n\), the value of \(\pi_{T1}\) in such cases will be closer to \(\pi_{T}\). For simplicity, we did not provide a comparison of the values of \(\pi_{T1}\) in the two cases in detail.