# FL-SDUAN: A Fuzzy Logic-Based Routing Scheme for Software-Defined Underwater Acoustic Networks
## 3 Methodology
### The Path Weights between CHs  
Routing is performed based on the relay communication of CHs in FL-SDUAN. If the network status changes, the controller waits for a route request message via the control communication. When a route-request message is received, it retrieves the node state table to find the optimal path. Due to multi-hop transmission, a CH may have multiple neighboring nodes. Path weights are quantified for the distance from the CH neighbor to the controller, the node's residual energy, and the resource occupancy. The distance between the CH and the controller is determined by the strength of the signal it sends. Resource occupancy includes CPU utilization and ternary content addressed memory  
Figure 3: The FL-SDUAN routing schematic.  
Figure 2: The format of a cluster-statistics message.  
(TCAM). The CH with the lowest path weight is selected as the next hop. The path weight from CHi to CHj is counted on the controller as shown in (1).  
\[Weight(i,j)=\alpha\times Strength(j)+\beta\times(1-Residual(j))+\gamma\times Resource (j) \tag{1}\]  
where \(Strength(j)\) denotes the signal strength; \(Residual(j)\) indicates the residual energy; \(Resource(j)\) is the resource occupancy; and \(\alpha\), \(\beta\), and \(\gamma\) are weighting factors of signal strength, residual energy, and resource occupancy, respectively.  
The weights are different from the application concerns. Therefore, there are differences in the designed weighting factors. Table 1 shows the state statistics of the three CHs, including signal strength, residual energy, and resource occupancy expectation. It indicates that CH5 has the most considerable residual energy, CH7 has the most robust signal strength, and CH12 has the most significant resource occupancy. This situation exists in multi-service hydroacoustic networks. If only one weighting factor is considered, it is easy to choose the optimal CH. However, selecting CH among multiple weighting indices is a challenge.  
In general, the weighting factors are determined empirically. The subjective weight factors have a significant impact on the selection of CHs. Once a reasonable CH is not selected, the routing path is not optimal. We give three weight factors \(\alpha\), \(\beta\), and \(\gamma\), and calculate the path weights from CHi to CH5, CH7, and CH12. The weight factors are randomly set and are shown in Table 2.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**ID of CHs**} & \multicolumn{2}{c}{**Expectations**} & \multirow{2}{*}{**\begin{tabular}{c} \\ **Signal Strength** \\ \end{tabular}**} & \multirow{2}{*}{**\
\begin{tabular}{c} **Residual Energy** \\ \end{tabular}} & \multirow{2}{*}{**
\begin{tabular}{c} **Resource Occupancy** \\ \end{tabular} } \\ \hline CH5 & 0.2520 & 0.8420 & 0.2460 \\ CH7 & 0.2840 & 0.7040 & 0.2650 \\ CH12 & 0.1040 & 0.6850 & 0.2890 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Status statistics of CHs.  
Figure 4: The routing procedure of FL-SDUAN.  
The first three items indicate that the optimal node is CH5. However, the focus of each item is different. Among them, items 1 and 3 focus on resource occupation, and item 2 emphasizes signal strength. Item 4 indicates that the optimal node is CH5 or CH12. Unfortunately, the two nodes' residual energy, resource occupation, and signal strength are different. Therefore, the randomly designed weighting factors are unreasonable and cannot reflect the practical concerns.