## 4 Proposed CLCQ Protocol
### Selection of Next Hop
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Symbols** \\ \hline Constant reward & \(g_{0}\) \\ Channel quality sensitivity & \(\varphi_{q}\) \\ Channel-quality-related reward & \(c(q)\) \\ Delay and congestion sensitivity & \(\varphi_{t}\) \\ Delay-and-congestion-related reward & \(c(t)\) \\ Residual energy sensitivity & \(\varphi_{c1}\) \\ Residual energy reward & \(b(n_{i}),b(n_{j})\) \\ Energy distribution sensitivity & \(\varphi_{c2}\) \\ Energy distribution reward & \(d(n_{i}),d(n_{j})\) \\ Residual energy of node \(n_{i}\) & \(E_{res}(n_{i})\) \\ The initial energy of node \(n_{i}\) & \(E_{init}(n_{i})\) \\ Average residual energy of \(n_{i}\) neighbor nodes & \(\overline{E}(n_{i})\) \\ Current buffer length & \(Buff_{now}\) \\ Maximum buffer length & \(Buff_{max}\) \\ A handshake time & \(t_{MAC}\) \\ Proportionality factor & \(\alpha_{1},\alpha_{2}\) \\ BER from \(n_{i}\) to \(n_{j}\) & \(BER_{ij}\) \\ Average BER to its neighbor nodes & \(\overline{BER}\) \\ Maximum number of retransmissions & \(N_{\max}\) \\ Discount factor & \(\gamma\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The list of symbols. \[t_{total}\ =\ \alpha_{1}\times\left(\left[\frac{Buff_{now}}{Buff_{\max}}\right]+1 \right)\times t_{MAC}+\alpha_{2}\times t_{MAC} \tag{23}\]  
where \(t_{MAC}\) is the total delay of data transmission in the Slotted FAMA protocol, and \(\alpha_{1}\)\(\in\)[0, 1] and \(\alpha_{2}\)\(\in\)[0, 1] are two delay coefficients, respectively. The candidate node with a larger buffer length is less likely to be selected as the next hop node. **Channel-quality-related reward**: The channel quality and connection reliability between network nodes are factors that cannot be ignored in the system networking. Here, the BER is used to measure the reliability of the communication link. We propose an improved reward related to channel quality as follows:  
\[c(q)\ =\ \sigma^{BER_{ij}}-1 \tag{24}\]  
where \(\sigma\) is a predetermined base, and, in order to ensure that the range of \(c(q)\) is \([0,1)\), \(\sigma\) is set to 2. A greater BER results in a greater channel-quality-related cost, which makes it less likely that the node will be chosen as the next hop. If the number of retransmissions of the data packet reaches the maximum limit and the next hop has not received the data packet, the data packet forwarding process is unsuccessful. The reward function for forwarding failure is presented by the following:  
\[R_{F_{ij}}^{a_{ij}}\ =\ -g_{0}-\varphi_{q}\times c^{\prime}(q)-\varphi_{t} \times c^{\prime}(t)-\varphi_{e1}\times b(n_{i})+\varphi_{e2}\times d(n_{i}) \tag{25}\]  
\[c^{\prime}(q)\ =\ \sigma^{\overline{BER}}-1 \tag{26}\]  
\[c^{\prime}(t)\ =\ 1-\frac{1}{t_{total}^{\prime}+1} \tag{27}\]  
\[t_{total}^{\prime}\ =\ \alpha_{1}\times\left(\left[\frac{Buff_{now}}{Buff_{ \max}}\right]+1\right)\times t_{MAC}+\alpha_{2}\times t_{MAC}\times N_{\max} \tag{28}\]  
According to [15], \(N_{\max}\) is the maximum number of retransmissions, and \(c^{\prime}(t)\) is the delay-and-congestion-related overhead of transmission failure. \(\overline{BER}\) is the average bit error rate from node \(n_{i}\) to all neighbor nodes, and \(c^{\prime}(q)\) is the channel-quality-related reward of transmission failure. The dynamic nature of the underwater acoustic channel makes it challenging to ascertain the likelihood of successful data packet transmission. Consequently, this paper employs the bit error rate of point-to-point communication to delineate the channel state.