## 5 Performance Evaluation
### Simulation Results
The influence of the shadowing is twofold, as explained in Section 4.2. On one hand, the distances are usually underestimated, so the transmission power calculated from them to reach the receiver with the desired \(snr\) has to be corrected with the correction margin given at Figure 2. On the other hand, even when the optimum transmission power is used, the final \(snr\) at the receiver may not be the desired one due to the effects of shadowing. To counteract this effect, we have corrected the number of transmitted packets with the factor given at Figure 3. The average results of 5000 simulations are shown in Figure 9. Figure 9(a) shows the average energy consumption of the three strategies for each localization interval and Figure 9(b) shows the average number of received packets at the furthest node. It can be seen that the proposed strategy gives the lowest energy consumption (about 54% the energy consumption of strategy #2) and, at the same time, guarantees that, at least, the average number of received packets at the furthest node is \(n=5\). These results were obtained for localization packets of length \(l=4\) bytes. Table 3 shows the energy consumption of the proposed strategy for other values of \(l\) and Table 4 shows the average number of received packets at the furthest neighbor. It can be seen that the length of the localization \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{l}=\) 4 & \(\mathbf{l}=\) 10 & \(\mathbf{l}=\) 20 & \(\mathbf{l}=\) 40 \\ \hline Highest \(P_{TX}\) & 3.20 & 8.00 & 16.00 & 32.00 \\ \(P_{TX}\) calculated from \(d\) & 1.26 & 2.98 & 5.87 & 11.58 \\ Proposed strategy & 0.60 & 1.79 & 4.24 & 9.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average energy consumption (in \(\mu\) J) of the three strategies for different packet lengths. packets has an effect on the performance of the proposed strategy: the longer the packet is, the lower is the gain in energy consumption with respect to other strategies. This is because when \(l\) increases, the optimum \(snr\) increases as well and gets closer to 1 (\(SNR=0\) dB), so the difference in energy consumption with respect to strategy #2 decreases. In any case, the proposed strategy always assures a given number of received packets, in contrast to strategy #2 and, moreover, entails energy savings with respect to other strategies. As explained before, the number of received packets at the furthest neighbor determines the accuracy of the distance estimation at these nodes. The accuracy of the distance estimations in closer neighbors \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(l=4\) & \(l=10\) & \(l=20\) & \(l=40\) \\ \hline Highest \(P_{TX}\) & 4.98 & 4.96 & 4.93 & 4.90 \\ \(P_{TX}\) calculated from \(d\) & 4.89 & 4.76 & 4.58 & 4.32 \\ Proposed strategy & 5.28 & 5.31 & 5.33 & 5.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average number of received packets at the furthest neighbor. \begin{table}
\begin{tabular}{l c c c} \hline \hline \(l=4\) & \(l=10\) & \(l=20\) & \(l=40\) \\ \hline
54\% & 73\% & 92\% & 110\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy consumption of the proposed strategy expressed in % with respect to strategy #2. Figure 9: Average energy consumption and average number of received packets at the furthest node of the three strategies for each localization interval for an environment with shadowing. will be at least as good as the one at the furthest neighbor. In order to better understand the behavior of the proposed transmission strategy, we have represented in Figures 10 and 11 the relation between the average energy consumption and the accuracy of the distance estimations for TOA and RSS measurements respectively, obtained from the previous realistic simulations for different values of \(n\).