# A Novel Cross-Layer Routing Protocol Based on Network Coding for Underwater Sensor Networks
## 5 Performance Evaluation
### Performance Analysis  
In this part we will analyze the performance of NCRP compared with VBF, HHVBF, DBR and VAPR, and we define the following metrics to measure the performance of SDRT. 1. Packet delivery ratio (\(PDR\)): This metric is defined as in Equation (11) \[PDR=\frac{\textit{Packets received at sink nodes}}{\textit{Packets sent by source nodes}}\] (11)
2. Average energy tax (\(AET\)): \(AET\) is defined as the average energy consumption in each node for delivering a packet successfully as in Equation (12). \[AET=\frac{\textit{Total Energy}}{\textit{Packets}_{\textit{succeed}}\times \textit{Nodes}}\] (12)  
Figure 11: Window size estimation at relay node 2 for different loop filter parameters. Figure 10: (**a**) The window size estimation for case 1; (**b**) The window size estimation for case 3. Average end-to-end delay (\(EED\)): \(EED\) is defined as the average time it takes for sending a packets from the source node to the destination successfully. According to the parameter settings in Table 1, we compare the performance with node number from 10 to 50. Firstly, the \(PDR\) performance is shown in Figure 12. From the figure we can see that it is hard for all routing protocols to find a reliable communication route from the source node to the destination node when node density is relatively low. So the \(PDRs\) almost equal zero when node number is 10. If the number of nodes is increased, the \(PDRs\) for all protocols increase in various degrees. VBF protocol only uses nodes in a straight pipe line from the source node to the destination node, so it is easily affected by node distribution. If there are no enough nodes in the pipe line, VBF cannot realize efficient data transmissions. HHVBF is an improved version of VBF, which uses multiple pipe lines for transmission and is not limited to the straight line from the source to the destination. When the optimal nodes cannot receive packets successfully, the suboptimal nodes in the transmission range can be chosen for transmission. The \(PDR\) of HHVBF can reach 80% when node density is relatively high. DBR protocol is mainly used for vertical transmission. When the number of sink nodes is small and the sink nodes are not located right above the source nodes, the performance of DBR fluctuates considerably. The above three routing protocols share the same problem: the forwarding priority cannot be distinguished clearly if the neighborhood nodes are too close to each other. So if a node cannot obtain suppression forwarding information from its neighbor, multiple nodes might participate in sending the same data packet and their next hop nodes may receive multiple copies of data packets. The sending procedure is then cancelled as duplicated packets are received and this will result in a certain probability of packet loss. VAPR uses periodic beacon messages to find a reliable route. This scheme cannot adapt to node mobility environment efficiently as it cannot update the neighborhood information in time. Meanwhile, frequent broadcasting control messages may lead to packet collisions. In addition, the length of beacon messages is usually much shorter than that of data packets, so data packets cannot transmit as far as beacon messages and the links found by beacon messages are easily broken when they are used for data packet transmissions. NCRP outperforms other protocols in \(PDR\) performance. The reasons are listed as follows: (1) We adopt error control method in our system. The nodes in the path can receive feedback from its next hop nodes and retransmissions are required if they sense a failed transmission. (2) We use secondary nodes for transmissions, which can help improve transmission efficiency in high quality channel. (3) The design of loop filter can detect the channel changes and increase the number of sending packets if the channel quality is poor. (4) NCRP can replace the inefficient nodes with good ones promptly. So the \(PDR\) performance for NCRP is improved significantly. Next we will discuss the \(EED\) performance for different protocols.