# Path Diversity Improved Opportunistic Routing for Underwater Sensor Networks
## 4 Simulation Result
Based on the above simulation results, we can conclude that the path correlation factor can enlarge the candidate set size to allow more nodes to participate in forwarding, and a larger candidate set size can supply the diverse path for forwarding to improve the PDR performance. **B. Compared with the previous solutions in static scenario**: Except for the source and destination nodes, other nodes are randomly deployed in the network and do not move. In the simulation, we set the depth threshold parameter as \(D_{r}=20\) m in PICS, and the depth threshold is 60 m in DBR. Various forwarding thresholds, \(P_{T}=\{20,30,40\}\), are examined in PRCS. With the increased number of candidate nodes, as shown in Figure 6d, the PDR performance of EPA, DBR, OVAR, PICS and PRCS increase, as shown in Figure 6a. Recall that DBR applies a greedy forwarding scheme with an opportunistic forwarding flavor. It will deliver packets in multiple paths to improve reliability. This makes DBR achieve a better PDR performance than EPA and OVAR, especially when the number of nodes is small (the PDR performance is better than PICS when the number of nodes is less than 200). Due to the conflict among multiple paths, the PDR performance cannot improve well with the increase in the number of nodes. Both PRCS and PICS obtain higher PDR performance than others mainly for two reasons. One is that the candidate number of PICS and  
Figure 5: Verifying the impact of candidate set size and path correlation on network performance. (**a**) Packet delivery ratio; (**b**) Average candidate number. PRCS is greater than others, as shown in Figure 6d, which is caused by the larger candidate set sizes. The other is that, with EEPA metric, the larger candidate set sizes could output an available candidates location destitution to mitigate routing void risk. Moreover, as shown in Figure 6d, PRCS employs fewer candidate nodes than PICS for forwarding, but the PDR performance of PRCS is always higher than PICS when the number of nodes is less than 300. It also benefits from the larger candidate set sizes. The increased number of candidates node and the more local topology information cause PDR performance of PICS is better higher than PRCS when the number of nodes is 350. Although the conflicts in the beacon process cause the average candidate number of OVAR to be fewer than EPA, as shown in Figure 6d, the PDR performance of OVAR is still higher than EPA for two reasons. One is OVAR adopts a larger candidate set size than EPA, and the other is the beacon process in OVAR established the path connectivity from the source node to the sink. Figure 6b measures the average end-to-end delay of the five protocols. The holding time in DBR is \(t_{dbr}(d)=\frac{2\tau}{\delta}(R-d)\), where \(\tau\) is the maximal propagation delay of one-hop, \(d\) is the depth difference between the current node and the previous forwarder. We set \(\delta=R/4\) in the simulation. In EPA, the holding time is given as \(f(d)=\alpha(R-d)\) and \(\alpha\) is the dynamic parameters in each hop, which we set as \(\alpha<0.01\) in the simulation. OVAR gets the lowest end-to-end latency because it can capture the minimum number of hops on the routing path from the source to the sink, and fewer candidate nodes also reduce the total holding time per hop. The higher end-to-end delay result in DBR is mainly caused by many redundant transmissions. PRCS and PICS achieve a lower end-to-end delay than DBR and EPA. The reason is that, when the candidate node with higher priority abandons forwarding due  
Figure 6: Compared with the previous solutions in static scenario. (**a**) Packet delivery ratio; (**b**) End-to-End delay; (**c**) Energy consumption per node and packet; (**d**) Average candidate number. to bad channel quality or the candidate node is located at a local maximum point, PRCS and PICS will choose the next forwarder that not only has higher forwarding advancement but also a lower path correlation with the previous one. It can help the forwarding escape from the routing void zone quickly.