## 3 Proposed Schemes
### Cooperative Delay Minimization Routing (CoDMR) Scheme  
The CoDMR scheme introduces cooperative routing to the DMR scheme to make it CoDMR. Cooperative routing adds reliability to information transfer over the channel by involving a single relay node, in addition to the source and destination. This process is further explained as below. Data Forwarding and Cooperation:  
In CoDMR protocol, the data packets are forwarded into two ways i.e., direct communication and relaying or cooperative communication as shown in Figure 6. In direct communication, when one or more source nodes have one or more minor sink nodes inside their communication range, the former advance the information to the latter. However, if the minor sink nodes are beyond the communication range of the source nodes, then cooperative routing is applied, makes DMR as the CoDMR scheme. In the CoDMR algorithm, to ensure a reliable data delivery, the source node chooses the destination node, from the set of the neighbour nodes, which is closest to the minor sink. The node having lowest distance with respect to minor sink node is considered the destination node. A node that is second closest to the minor sink node is nominated as a relay node. The source node broadcasts the information packets towards the destination and the relay node. The destination checks the BER of the information packet, if BER is lower than the desired threshold value then it forwards the information directly to the minor sink node. However, if BER exceeds the threshold value, then it sends a request to the relay node to send the same information. The relay node then forwards the information along with the acknowledgement towards the destination node. Each destination node utilizes a diversity scheme to merge the two received packets (form source node and relaying). Fixed ratio combine (FRC) is used as a diversity technique instead of maximal ratio combine (MRC) because MRC requires the full channel state information (CSI), which is challenging in underwater environment as the channel fluctuates rapidly due to ocean currents and marine life. The received packets at the destination node, by using a single relay, can be designated as [26]. \[Y_{d}=K_{1}Y_{sd}+K_{2}Y_{rd} \tag{3}\]  
Figure 5: DMR packet forwarding operation. The \(Y_{d}\) represents the merge of the two information packets reached at the destination node. The \(Y_{sd}\) is the packet secured by the destination node directly from source node. Also, \(Y_{rd}\) is the received packet from relay to destination. The variables \(K_{1}\) and \(K_{2}\) are the weighted constant ratios of the two links. These weights constant are the function of channel coefficients and can be express as [26]. \[\frac{K_{1}}{K_{2}}=\frac{\sqrt{P_{1}G_{sd}}}{\sqrt{P_{2}G_{rd}}} \tag{4}\]  
where \(P_{1}\) and \(P_{2}\) are the two links power from the source towards the destination and from source in the direction of relay node, respectively. The symbol \(G_{sd}\) indicates the channel gain from source towards the destination and \(G_{rd}\) shows the channel gain in the direction of the destination node from the source node. In case of the special type of amplify and forward cooperation, the optimal value of the weight constant ratios is 2:1 and can be represent as [27]. \[K_{1}=\frac{\sqrt{P_{1}G_{sd}}}{\sigma_{0}} \tag{5}\]  
\[K_{2}=\frac{\sqrt{P_{2}G_{rd}}}{\sigma_{0}} \tag{6}\]  
Here \(\sigma_{0}\) shows the signal variance, if the packet is transmitted with an average power of unity, the signal to noise ratio (SNR) can be computed through FRC as [27]. \[\rho=\frac{P_{1}|G_{sd}|^{2}+P_{2}|G_{rd}|^{2}}{\sigma_{0}} \tag{7}\]  
Figure 6: Cooperation model. The information combined at destination is further evaluated for the extraction of the desired information packets. The destination then advances the information to an in-range minor sink node or this process is repeated unless the information is received by one of the minor sink nodes.