# Path Diversity Improved Opportunistic Routing for Underwater Sensor Networks
## 4 Simulation Result  
We used the underwater network simulator proposed in [33]. In the simulator, each sensor node has a single, half-duplex transducer. For acoustic communications, the channel model is in Section 3.1, and BPSK modulation is implemented in the physical layer. The transmit power is 105 dB re \(\upmu\)Pa for data transmission, and 125 dB re \(\upmu\)Pa for beacon process. Ambient noise PSD is 46 dB, SNR threshold is 20 dB and the carrier frequency \(f=25\) kHz. The packet length is 50 bits, the bit rate is 10 kbps and the acoustic speed is \(c=1500\) m/s. A CSMA-based broadcast protocol is employed in the MAC layer. When a node has data to send, it first senses the channel. If the channel is free, then the node broadcasts the packet. Otherwise, it backs off. The maximum number of backoffs is four for one data packet [11]. The network performances were evaluated by the random deployed network. The network size was \(400\) m \(\times\)\(400\) m \(\times\)\(800\) m. There was one source located at \((200,200,800)\), and three sinks located at \((100,100,10)\), \((200,200,10)\) and \((300,300,10)\). All the simulation scenarios were tested for various numbers of nodes from 100 to 350. The source node sent one packet per 10 s. For each setting, the results were averaged over 50 runs with a randomly generated topology. The total simulation time for each run was 500 s. In all simulations, we set the parameters similar to UWM1000 [11; 34]; the transmission range was 200 m, and the energy consumption on sending mode, receiving mode and idle mode was 2 W, 0.75 W and 8 mW, respectively. Note that only one sink node located at \((200,200,10)\) was used for OVAR protocol in the simulation. Five routing protocols were compared in the simulation: EPA is the EPA-based candidates selection algorithm proposed in Hydrocast [14]. DBR is the depth based protocol proposed in [13]. OVAR is proposed in [16]. PRCS and PICS are two protocols proposed in this paper. The network performances were measured in terms of packets delivery ratio, average energy consumption and end-to-end delay in the two scenarios static random network and random moving network. The packets delivery ratio means the number of packets successfully received compared to the number of packets that have been sent out in the network. Average energy consumption means the average energy consumed by one node for one packet. The average end to end delay refers to the average time taken for all packets to be transmitted across the network from source to sink. **A. Verifying the impact of candidate set size and path correlation on network performance:** The simulation study below verifies the impact of candidate set size and path correlation factor on the packet delivery ratio. Figure 5a shows the packet delivery ratio (PDR) and Figure 5b gives the average candidate number at each hop. With the same channel quality, candidate location destitution significantly affects the packets forwarding. (i) In PICS, we compare the EEPA metric with path correlation factor (\"PICS\" in Figure 5) and without path correlation factor (\"PICS-NR\" in Figure 5). With the normalized distance based path correlation factor, PICS can effectively expand the range of candidate sets, resulting in a larger candidate number to improve the PDR performance. (ii) Although PRCS obtains almost the same candidate number as the EPA when the forwarding threshold is set as \(P_{T}=40\) (the candidates number of PRCS is a litter higher than EPA when the network nodes number is less than 300), the PDR performance of PRCS is much higher than the EPA. It is because the larger candidate set size provided by PRCS improves the path diversity to deal with the routing void problem. (iii) Further, PRCS can still achieve almost the same PDR performance as the PICS without path correlation factor (PICS-NR), while its average candidate number is smaller than that one. That is also related to candidate set size.