# RECRP: An Underwater Reliable Energy-Efficient Cross-Layer Routing Protocol +
## 4 Simulation
### Results and Analysis  
Figure 5 shows the optimal transmission frequency between two nodes at different distances when the transmission power was 90 dB re \(\upmu\)Pa. The optimal transmission frequency here means that the expected energy consumption for successfully transmitting a data packet is the smallest. It can be seen that as the distance increased, the optimal transmission frequency decreased. When the distance exceeded 27 km, since the SNR was smaller than the threshold we set, the data could not be correctly decoded within the available frequency ranges, so there was no such optimal transmission frequency. Figure 6 shows the transmission power and the expected retransmission times as a function of distance in order to ensure energy efficiency. It can be seen that as the transmission distance increased, the transmission power of the RECRP also increased, and the number of retransmissions of the data \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Value** & **Variable** & **Value** \\ \hline \(k\) & 1 & \(k_{1}\) & \(\mathcal{N}(0.001\pi,0.0001\pi)\) \\ \(k_{4}\) & 0.015 & \(k_{2}\) & \(\mathcal{N}(0.01\pi,0.001\pi)\) \\ \(k_{5}\) & 0.01 & \(k_{3}\) & \(\mathcal{N}(0.02\pi,0.002\pi)\) \\ \(\lambda\) & \(\mathcal{N}(1,0.1)\) & \(v\) & \(\mathcal{N}(0.1,0.01)\) m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ocean current variables. Figure 5: Optimal frequency with 90 dB re \(\upmu\)Pa transmission power. packet and the ACK packet increased as the distance increased. Since data messages are longer than ACK messages, the probability that the data message is correctly transmitted is less than that of ACK packets. Therefore, the retransmission of ACK packets was much less than that of data packets. As shown in Figure 7, it is easy to observe that RECRP had a higher delivery rate than DBR and HH-VBF. This is because we calculate relative velocity and distance through Doppler effect and RSSI, and dynamically select the appropriate power \(P\) and frequency \(f\) to choose the next hop. We can easily observe that the delivery rate got higher as the number of nodes increased. By setting a random sending time, RECRP achieves a lower probability of collisions. Additionally, we adopt a communication voids avoidance mechanism. Together with that, RECRP achieved a higher delivery rate than DBR and HH-VBF. DBR uses the global flooding mechanism, so the initial delivery rate was higher than HH-VBF, as the number of nodes increased, the collisions happened more frequently and the delivery rate became lower than HH-VBF. Figure 8 illustrates energy consumption with different numbers of nodes. Its clear that the energy consumption per node of RECRP was much lower than DBR and HH-VBF. This is because we estimated the distance between nodes and selected the appropriate transmit power \(P\) and channel frequency \(f\)  
Figure 6: Transmission power and retransmission times with minimized energy cost. ACK: data response packet. Figure 7: Delivery ratio with different numbers of nodes. DBR: depth-based routing; HH-VBF: hop-by-hop vector-based forwarding; RECRP: reliable energy-efficient cross-layer routing protocol. The delivery rate is guaranteed, and the retransmission times were reduced. Our single-copy mechanism also avoids redundant packets to achieve the goal of prolonging the network lifetime. As the number of nodes increased, the retransmission times increased. The reason that the energy consumption was still smaller than DBR and HH-VBF is that RECRP has a lower probability of collisions and the transmission power \(P\) required for RECRP is relatively minimized. It is easy to observe that the energy per node per message of HH-VBF was higher than DBR. This is because the working mechanism of HH-VBF is to select nodes in the virtual pipeline. The candidate nodes are smaller than DBR, which adopts the flooding method, so the probability of successful forwarding becomes smaller, which leads to more retransmissions and larger total energy consumption.