## 3 Proposed Protocol Design Scheme
### Routing Strategies  
The proposed routing protocol strategies are divided into two stages: discovering possible candidates and selecting relay nodes. Candidate discovery is shown in Figure 2. A different icon shows each sensor node's remaining energy at a particular sensor node. With RF and acoustic modems installed at the water's surface, sink nodes do not need to care about running out of energy. Sinks that do not move about only need to broadcast their locations once during startup, which does not require significant energy. The transmitter sensor nodes are the nodes that hold the data packets. Every data packet carries the location of the sink node, relay node, and source sensor node. Before the data transmission, the \(si\) is the sender node, and the other nodes are the receiver nodes, as shown in Figure 2. The hello packets are transmitted by the \(si\) node with a minimum radius \(r_{min}\) including the position of itself \(si\) and the position of the \(st\) sink node. The cosine of the direction between the \(si\) and \(sj\) receiver will be calculated by the \(sj\) because it is the closest receiver of the transmitter. The advertisement packet with a radius of \(r_{j}\) will be transmitted by the \(sj\) if the cosine value is greater than 0. The radius \(r_{j}\) will be calculated as:  
\[r_{j}=MIN\left\{\left(1+\frac{e_{j}^{res}}{e_{j}^{max}}\right)\cdot r_{\min}, \ r_{max}\right\} \tag{11}\]  
Figure 2: Candidate discovery phase.  
Here, \(\varepsilon_{j}^{max}\) is the highest energy of the sensor node, and the \(\varepsilon_{j}^{res}\) is the starting energy of the sensor node. As a result, the range of \(r_{j}\) is \(r_{min}\) to \(2r_{min}\). Equation (11) shows that in an ideal situation, (\(r_{max}>2r_{min}\)), and that the starting energy of \(sj\) is complete, sufficient to fill the transmission circle of \(si\). Only an advertisement packet with a radius of \(r_{min}\). May reaches the \(si\) location in the worst-case scenario, the remaining energy in \(sj\) is nearly consumed. Furthermore, the advertisement packet contains data about \(sj\)'s location and residual energy.  
When \(sk\) collects the \(sj\) advertisement packet and \(si\) Hello packet, it extracts the residual energy and the position from these packets.  
The \(sk\) will go into sleep mode and will not transmit any packet to save the power because the residual energy of \(sk\) is lower than the \(sj\)'s. The hello and advertisement packets are also received by \(sq\) because its also in the receiver nodes. However, since the cosine of the angle here between routes from \(si\) to \(sq\) and from \(si\) to \(st\) is less than zero, \(sq\) will choose to go to sleep mode. Thus, \(sq\) is located at a preferred destination compared to other receivers. Although within the broadcast range of \(sj\), the receiver \(sh\) remains in sleep mode because \(sh\) cannot receive the hello packet sent by \(si\). After receiving \(si\)'s hello and \(sj\)'s advertising packet, the position and residual energy information are extracted from these packets. Upon receiving a courting packet, the sensor node that has gone into sleep mode will immediately wake up and find itself within the communication range.