# A Joint Strategy for Fair and Efficient Energy Usage in WLANs in the Presence of Capture Effect
## 4 Results and Analysis  
In this Section, we perform experiments using ns-2 simulator [32]. Table 2 shows the values used for various parameters during mathematical calculations and simulation of the IEEE 802.11g type of WLAN. Network consists of 30 nodes and an AP. All 30 nodes were randomly scattered around AP in a circle with a radius of 100 m and they transmitted data frames of size \(L=1000\) bytes. Figure 3 shows the energy efficiency of WLAN when the number of nodes in network is fixed as 30. The traffic load varied from 100 to 1500 frames/s and the channel was error free, i.e., \(P_{e}=0\). We took three different values for the capture threshold, i.e., \(Z_{0}=\) {\(\infty\), 10 dB, 6 dB}. When \(Z_{0}=\infty\), capture did not occur. In such situation, the network gave the lowest energy efficiency as compared to the other two values of \(Z_{0}\). In contrast, the network was more energy efficient when \(Z_{0}=6\) dB, which shows that capture happened more frequently than when \(Z_{0}=10\) dB. Figure 3 also shows that, initially, the energy efficiency values were close to each other when the network was lightly loaded, that is, \(\lambda=100\) frames/s, because the probability of two or more than two frames arriving simultaneously  
in same time slot was very low. This indicates that capture was not very effective in unsaturated conditions. As the network approached mild saturated conditions such as \(\lambda=500\) frames/s or above the effect of capture was more obvious. While in mild saturated condition, that is, \(\lambda=\{500\)\(\sim\)1500\(\}\) frames/s, energy efficiency remained almost the same in the presence of capture, it started decreasing more steeply in the absence of capture, that is, when \(Z_{0}=\infty\). The simulation results (abbreviated as Sim in the legend of Figure 3) matched the results obtained from the analytical model (abbreviated as Mod in the legend of Figure 3) and thereby validated the accuracy of our analytical model. Figure 4 shows energy efficiency of WLAN when the number of nodes in network is 30, \(Z_{0}=\{\infty\), 10 dB, 6 dB\(\}\), \(\lambda=1500\) frames/s and \(P_{e}=\{0\), 0.1, 0.2, 0.3\(\}\). As previously stated, \(Z_{0}=\infty\) corresponds to the absence of capture and therefore gives the lowest energy efficiency. Energy efficiency decreased more when channel was not ideal, i.e., when \(P_{e}=0.3\). Furthermore, in the presence of capture, for example, for the same values of \(Z_{0}=10\) dB, 6 dB, the network gave lower energy efficiency when \(P_{e}=0.3\) as compared to the case when \(P_{e}=0.1\). However, energy efficiency in the presence of capture was still higher than the case when there was no capture effect in the network. This experiment indicates that taking into account channel condition is important for the study of capture effect. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Data rate & 54 Mbps \\ Control rate & 6 Mbps \\ PHY header & 20 \(\upmu\)s \\ MAC header & 272 bits \\ ACK frame & 112 bits \\ Slot time \(\sigma\) & 9 \(\upmu\)s \\ \(CW_{min}\) & 15 \\ Maximum backoff stage (m) & 5 \\ Transmit power (\(P_{tx}\)) & 2000 mW \\ Receive power (\(P_{rx}\)) & 1000 mW \\ Idle power (\(P_{idle}\)) & 1000 mW \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for experiments. Figure 3: Energy efficiency in presence of capture against varying offered load. Figure 5 shows the effect of three different values of capture threshold, i.e., \(Z_{0}=\) [20 dB, 10 dB, 6 dB], frame error rate, \(P_{e}=\) [0, 0.1, 0.2] when \(N=\) 30 and when the network was fully saturated, i.e., \(\lambda=\infty\). At first, it can be seen in the figure that energy efficiency is always high when channel is ideal, i.e., \(P_{e}=0\) irrespective of the underlying value of capture threshold.