## 5 Performance Evaluation
### Simulation Results  
We have run a set of simulations to evaluate the energy consumption of the proposed strategy in several scenarios. In these simulations, the performance of the proposed strategy is also compared with other two strategies: (1) sending \(n\) packets with the highest transmission power available by hardware and (2) sending \(n\) packets with a transmission power that depends on the estimated inter-node distance: \(P_{TX}(dBm)=-A+10\eta\log\tilde{d}/d_{0}+N_{RX}(dBm)\), which is the most common strategy when power adaptation is used (note that this is equivalent to using a transmission power such that the \(SNR\) at the receiver is 0 dB). In these simulations, we considered networks composed of reference nodes and mobile nodes. In order to estimate the position of the mobile nodes, each reference node transmits packets to them. These nodes measure the RSS of the received packets and calculate their distance to each of the reference nodes. With these range estimations and the known positions of the reference nodes, the mobile nodes are able to calculate their own positions. As soon as they have an estimated value of their physical position, they can send packets to other nodes with the information about their estimated position and act themselves as reference nodes. Consequently, every node of the network will transmit packets to and receive packets from every other node within its communications range. Considering the transmission strategy proposed in the previous section for a single link, we applied it to the whole network by finding at each node the optimum transmission strategy (\(P_{TX}^{*}\) and \(T^{*}\)) for its furthest neighbor (closer neighbors will be guaranteed to receive at least the same average number of packets). The transmission power \(P_{TX}\) is adaptively modified, by estimating from Equation (3) the value necessary to achieve the desired \(SNR^{*}\) at the furthest neighbor. As an estimate of the distance between the transmitter and its furthest neighbor  
Figure 8: Experimental RSS measurements for different distances between two MICAz nodes. The log-normal channel model curve fitting is also represented. is needed, the method is refined iteratively: first, the transmission power is set to an initial (high) value and a preliminary distance estimation is obtained; then, the transmission power is modified according to the distance estimation. First, we simulated a network composed of four reference nodes deployed randomly in a 15 \(\times\) 15 m\({}^{2}\) room and one mobile node that stays in the center of the room during 20 seconds. The localization is done every second (\(T_{0}=1\) s) and the desired accuracy is such that \(n=5\). The communication channel was simulated using the log-normal model in Equation (2) with \(A=-65\) dB, \(\eta=2.5\), \(d_{0}=1\) m and \(\sigma=0\) dB (ideal channel without shadowing). Packet reception was modeled with Equation (1), using \(W=2\) Mhz and \(v_{b}=250\) kbps. The average energy consumption of 5000 simulations (50 different node placements, 100 simulations for each placement), which stays constant after the first localization interval, is shown in Table 2 for different values of the packet length. On the other hand, in this ideal simulation environment, the three strategies guarantee that the average number of received packets is \(n=5\) at the furthest node during the whole simulation. It can be seen that the proposed strategy gives the lowest energy consumption (about 47% the energy consumption of strategy #2 for \(l=4\)) and, at the same time, guarantees that the average number of received packets is \(n=5\) at the furthest node. The length of the localization packets also has an influence in the energy consumption: the gain of the proposed method with respect to the other two is higher for lower values of \(l\). Next, to simulate a more realistic scenario, we added shadowing with \(\sigma=2\) dB and node movement to the previous simulation. We simulated a 7m-radius circular trajectory centered in the simulated area.