## 5 Performance Evaluation
### Energy Consumption  
In underwater acoustic channels the energy costs of acoustic modes are as: \(Tx>Rx>Idle\gg Sleep\), so a significant portion of energy is spent during packet transmission [2]. In contrast, energy costs for terrestrial radio modems are: \(Tx\)\(\sim\)\(Rx\)\(\sim\)\(Idle\gg Sleep\)[53]. Therefore, in USN, localization protocols are expected to avoid excessive overhead and establish localization with the least possible number of messages. Moreover, for a mobile UWSN, localization should be repeated periodically which also increases the energy consumption and decreases the network lifetime. Hence, to calculate the energy consumption, we use the average number of received and transmitted bits and energy per bit values of a Micro-modem. Figure 9 shows the energy consumption for RLS. It is obvious that this value is increased by increasing the number of sensor nodes. Energy spent per node localization is defined as the total amount of energy consumption including transmit and receive for both anchors and sensors. RLS anchor nodes consume low amounts of acoustic modem receive power and low RF transmit power, so the energy consumption for anchors is very low and increasing the percentage of anchors parallel with enlarging the ordinary nodes, decreases the energy spent per node for localization. Figure 8: Mean error ratio for RLS. Figure 9: Energy consumption per node for localization. In RLS, according to Figure 4, the number of transmitted bits by detector sensor is equal to 80 bps, so the energy consumption for sending and receiving one packet is calculated based on [50]:  
\[E_{Tx}=P_{Tx}\times\frac{packet-size}{data-rate} \tag{13}\]  
\[E_{Rx}=P_{Rx}\times\frac{packet-size}{data-rate} \tag{14}\]  
where \(E_{Tx}\) and \(E_{Rx}\) are the energy consumption for sending and receiving one packet, respectively. Transmitted and received power are shown by \(P_{Tx}\) and \(P_{Rx}\), respectively. Energy spent per node localization is defined as the total amount of energy consumption including transmit and receive for both anchors and sensors, so we can formulate it as follows:  
\[Total_{Energy- Consumption}=\frac{E_{TA}+E_{TS}+E_{RA}+E_{RS}}{localized\ node-num} \tag{15}\]  
where \(E_{TA}\) and \(E_{TS}\) are the energy consumption for transmitting by anchor and sensor, respectively. Energy consumption for receiving a message for anchor and sensor is shown by \(E_{RA}\) and \(E_{RS}\), respectively. It is extracted from Equation (15) that a significant portion of energy is spent during transmission by ordinary sensors. Anchor's transmission in RLS occurs by RF signals with very low energy consumption and it is negligible, so to calculate the energy consumption, we use the number of transmitted bits. It is obvious from Equation (13) that energy consumption will be reduced by decreasing the transmitted packet size. Our proposed scheme can reduce the energy consumption of localization in comparison with energy efficient methods like SLMP [8], which is a prediction-based scheme, via decreasing the message size. In SLMP [8], the localization message structure has some extra fields such as Location and Speed vector compared to the RLS message format (Figure 4). Moreover, this localization message could be sent by both anchor nodes and localized ordinary nodes [8]. As another comparison for energy consumption of RLS and ARTL In [50], the packet size and the data rate for ARTL are 400 bits and 1,000 bps, respectively. Like RLS, this method also utilizes the Micro-modem [44]. It is obvious that RLS with an event-driven report decrease significantly the message size and the transmitted data bits. The calculated \(E_{Tx}\) in ARTL is 14 J. It is calculated that \(E_{Tx}\) for our method based on Table 2 is around 35 J, but for data rates higher than 80 bps Micro-modems require additional coprocessor data to be recorded [44], so the ARTL method employing the Micro-modem can achieve lower energy consumption than our method, but it requires an additional coprocessor which adds extra cost and complexity.