# Optimization of Acoustic Communication Links for a Swarm of AUVs: The COMET and NEMOSENS Examples
## 5 Physical Layer
### Optimization Evaluation
#### 5.4.1 BCH1 Channel  
The first selected scenario concerns the BCH1 (Brest Commercial Harbor) channel [34; 35]. This experiment was performed in France, and the transmitter was placed 800 m away from the receiver. The channel geometry data regarding this experiment is shown in Table 3.  
For running the optimization algorithm, we restricted the set of possible subcarriers value and the CP lengths. In this case, we consider \(N_{\text{sub}}=\{128,256,512\}\) subcarriers, and \(T_{\text{CP}}=\{1,5,8,10,12,15,18\}\) ms. Notice that the OFDM symbol duration (without CP) varies according to the number of subcarriers selected. So, using these information, the optimization algorithm is executed. The obtained results are depicted in Table 4. This table contains the optimized parameters for distinct overhead constraints. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Input Parameters**} \\ \hline \(f_{\text{c}}\) & Carrier frequency (in Hz) \\ \(B\) & System bandwidth (in Hz) \\ \(c\) & Sound speed (in m/s) \\ \(v\) & Relative velocity Tx/Rx (in m/s) \\ \(p_{\text{w}}\) & Water depth (in m) \\ \(p_{\text{Tx}}\) & Transmitter depth (in m) \\ \(p_{\text{Rx}}\) & Receiver depth (in m) \\ \(d_{\text{Tx,Rx}}\) & Distance Tx/Rx (in m) \\ \(\rho_{\text{max}}\) & Maximum overhead (constraint) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimization input parameters. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Output Parameters**} \\ \hline \(N_{\text{sub}}\) & number of subcarriers \\ \(T_{\text{CP}}\) & CP duration (in ms) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization output parameters. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Input Parameters**} \\ \hline \(f_{\text{c}}\) & 35 kHz \\ \(B\) & 4 kHz \\ \(c\) & 1500 m/s \\ \(v\) & 0.1 m/s \\ \(p_{\text{w}}\) & 20 m \\ \(p_{\text{Tx}}\) & 2 m \\ \(p_{\text{Rx}}\) & 5 m \\ \(d_{\text{Tx,Rx}}\) & 800 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: BCH1 channel conditions used for the optimization. In order to evaluate these optimized results, we ran other simulations with a genie-aided modem. For this comparative approach, it was transmitted 27 frames, whereas each frame had a 1 s time length. This procedure was repeated 50 times and the results are in Figure 11. This figure shows the bit-error rate (BER) obtained for all possible system configurations. An explanation for the system behavior shown in Figure 11 is as follows. Considering the same bandwidth, the usage of a larger number of subcarriers translates to a lower subcarrier spacing. When the subcarrier spacing is small, the system is more susceptible to ICI, resulting in a increase of the BER. On the other hand, the augmentation of CP length improves the system performance. The decrement on the BER value can be explained by a reduction on the IBI at the receiver side. Although, this behavior is not so explicit for \(N_{\text{sub}}=512\). In this case, the ICI dominates, masking the influence of the CP length. In this genie-aided approach, the parameters pair to be selected should also obey the overhead constraint. As each point from Figure 11 has a distinct overhead value associated, we should check the eligibility of each point. Figure 12 shows the overhead inherent to each point. In this figure it is possible to observe that a higher number of subcarriers is associated with a lower overhead. This behavior is due to the fact that the OFDM symbol duration (without CP) depends on the number of subcarriers. The larger the number of subcarriers, the longer the OFDM symbol duration. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Maximum Overhead (\(\rho_{\text{max}}\))**} \\ \cline{2-6}  & **0.1** & **0.15** & **0.2** & **0.25** & **0.3** \\ \hline \(T_{\text{CP}}\) (ms) & 5 & 10 & 8 & 10 & 12 \\ \(N_{\text{sub}}\) & 256 & 256 & 128 & 128 & 128 \\ \(T_{\text{sym}}\) & 64 & 64 & 32 & 32 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimized parameters for BCH1 channel.