## 4 Next Forwarding Node Selection in UWSNs
### Physical Distance  
The distance calculation is another important metric that have been utilized in some routing protocols. In non-localization routing protocols, routing protocols calculate the physical distance using two different mechanisms using becoming messages provided by the sink. The following paragraphs discuss the localization routing protocols belonging to this subcategory in detail. Figure 12: The use of super nodes in MRP. Different from H\({}^{2}\)-DAB and 2H-ACK, another localization-free routing protocol using physical distance has been proposed by [PERSON] et al. [50], named Energy-Efficient Routing Using Physical Distance and Residual Energy (ERP\({}^{2}\)R). This protocol consists of two phases, namely cost establishment and data forwarding. Selecting the next forwarding nodes here involves sending beaconing messages from the sink that include the node ID, residual energy, and cost (physical distance to the sink), as shown in Figure 13. Then, each node that receives this message starts calculating the time to arrival to the sink (ToA) and updates the packets by adding its cost to the sink and residual energy. Then, it rebroadcasts this message with its node ID to its neighboring nodes; after receiving this message, the neighboring nodes start calculating their physical distance to this node and add their distance to the sender's distance, and so on. During the data forwarding phase, the nodes with smallest physical distance than sender are eligible to forward the packets. Then, the node with the highest residual energy forwards the data packets. ERP\({}^{2}\)R has some advantages. It does not require localization information for identifying the node's position. Moreover, a multi-sink structure has been used in this protocol, which helps improve the performance of the protocol. Furthermore, the use of residual energy along with physical distance helps balance the energy between nodes. However, ERP\({}^{2}\)R also has some disadvantages. The first phase should be updated with a short interval of time, which leads to high network overhead. Moreover, this protocol does not solve the communication void problem. Furthermore, ERP\({}^{2}\)R does not utilize link quality for selecting the next forwarding nodes, whereas the use of link quality, along with residual energy and physical distance, helps improve the packet delivery ratio along with reducing the total energy consumption. A physical distance location-free routing protocol named Reliable and Energy Efficient Routing Protocol (R-ERP\({}^{2}\)R) has been proposed as an extension version of an energy-efficient routing protocol for UWSNs using physical distance and residual energy (ERP\({}^{2}\)R) [51]. R-ERP\({}^{2}\)R aims to improve the reliability between nodes by selecting the next forwarding nodes based on link quality. Thus, it utilizes a reliable metric named Expected Transmission Count (ETX) [52], along with physical distance and residual energy. To this end, sensor nodes share residual energy between neighbors, and compute ETX and physical distance. Then, each node broadcasts this information to its neighbors. At the end of this step, each node will have information about its neighbors in terms of physical distance, ETX, and residual energy. Next, the sender node selects forwarding nodes that are closer to the sink node (in terms of physical distance) with high residual energy and good link quality. The node with minimum cost is the best node to forward the data packets, i.e., the cost is calculated based on ETX and residual energy using this equation: \(Cost\left(i,j\right)=\left(1-\frac{RE(j)}{RE\max}\right)+\left(1-\frac{ETX (i,j)}{ETX\max}\right)\). R-ERP\({}^{2}\)R has some advantages. It does not require localization information for identifying the node's position. Moreover, the multi-sink structure has been used in this protocol, which helps improve the performance of the protocol.