## 2 System Model and Connection Setup
### Interference Statistics Acquisition Stage  
As previously stated, and without loss of generality, let us refer to \(u_{1}\) and \(u_{2}\) as the transmitting and receiving nodes, respectively, placed at the left and right side of the time diagram in Figure 1 (however, transmitting and receiving roles can be interchanged). The first stage of CS is the acquisition of interference (represented by the vertical blocks in Figure 1). This stage must be used by both the nodes interested in setting up the communication, and it deals with the acquisition of interference statistics that can require a long time, and even multiple frames. It is worth noting that, depending on the (possibly) different propagation conditions, the result of interference acquisition is different at the transmit and receive sides. During interference statistics acquisition, lasting \(T_{a,\text{CS}}\) seconds, no transmission is acted on by the nodes that remain in listening mode. Hence, the continuous-time received signal is:  
\[r_{a,\text{CS}}^{(u_{i})}(t)=z^{(u_{i})}(t)=w^{(u_{i})}(t)+\chi^{(u_{i})}(t),\ \ i=1,2 \tag{1}\]  
where \(w^{(u_{i})}(t)\) is the zero mean \(\mathcal{N}_{0}\)-variance Additive White Gaussian noise at node \(u_{i}\) and \(\chi^{(u_{i})}(t)\) is the possibly present interference due to acoustic sources (e.g., mammals and/or ship engines) plus the ambient noise described in [40]. Moreover, the term \(\chi^{(u_{i})}(t)\) in Equation (1) can be detailed as follows:  
\[\chi^{(u_{i})}(t)=\sum_{n=1}^{N_{l}}\psi_{n}(t)*h_{n,u_{i}}(t) \tag{2}\]  
with \(\psi_{n}(t)\) being the \(n\)-th interfering source (in a number of \(N_{l}\)), \(*\) the convolution operator and \(h_{n,u_{i}}(t)\) the impulse response describing the channel from the \(n\)-th interference source to the node \(u_{i}\). It is important to underline that both \(\chi_{n}(t)\) and \(h_{n,u_{i}}(t)\) change, frame by frame, due to sea stream changes, the Doppler effect and multipath changes. This is the reason for performing long acquisition during the connection setup. Furthermore, it is important to emphasize that, at regime, the time-varying nature of interference may be considered limited within multiple frames, thus meaning that statistical features do not change among some consecutive frames, let us say in a number of \(Q_{a}\). At first sight, such an assumption may appear unreasonable. In fact, while for periodic and quasi-periodic interferences (e.g., engine of a ship) it is simple to prove that statistics do not change within a certain number of frames, a really different scenario is met when dealing, for instance, with mammal sounds. However, in this regard, the analysis reported in [41] proves that sound capture lasting in the order of hundreds of milliseconds allows a reliable collection of the statistical features of several interference sources, including also the sporadic ones (e.g., mammals). \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Definition** \\ \hline \(T_{f}\) & Transmission frame length \\ \(T_{s}\) & Slot time of a frame, equating the OFDM symbol length (including CP) \\ \(T_{c}\) & Sampling time \\ \(T_{x}\) & OFDM symbol length (without CP) \\ \(T_{CP}\) & OFDM CP length \\ \(T_{a,\text{CS}}\) & Interference acquisition time during CS \\ \(T_{a,\text{EC}}\) & Interference acquisition time during EC \\ \(T_{e,\text{CS}}\) & Channel acquisition time during CS \\ \(T_{e,\text{EC}}\) & Channel acquisition time during EC \\ \(T_{d}\) & Frame portion of time dedicated to data transmission during EC \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of variables related to time intervals.