# AI-Driven Adaptive Communications for Energy-Efficient Underwater Acoustic Sensor Networks
## 4 Channel Model  
In this work, we adopt a widely used statistical model for underwater acoustic (UWA) channel characterization [15] (All the parameters used for UWA channel characterization are reported in detail at the following link: [[https://millitsa.coe.neu.edu/projects.html](https://millitsa.coe.neu.edu/projects.html)]([https://millitsa.coe.neu.edu/projects.html](https://millitsa.coe.neu.edu/projects.html)) (accessed on 8 June 2025)) that captures both physical acoustic propagation effects and random variations, ensuring that our experiments reproduce realistic conditions. Two main types of channel variations are addressed:  
* _Large-Scale Variations_ due to the displacement of system components over many wavelengths, leading to slow, large-scale changes;
* _Small-Scale Variations_ over short distances (a few wavelengths) and leading to fast fluctuations in the channel response.  
In order to model large-scale variations coming from the displacement of the transmitter, the receiver, or due to the presence of reflective surfaces which cause changes in path delay and gain, the transfer function \(H(f)\) can be written as  
\[H(f)=\bar{H}_{0}(f)\sum_{p}h_{p}e^{-j2\pi f\tau_{p}} \tag{1}\]  
where \(\tau_{p}\) and \(h_{p}\) are the path delay and gain, respectively, where if the path length variation (location uncertainty) can be modeled as Gaussian, the path gain will be log-normally distributed. Also, the term \(\bar{H}_{0}(f)\) accounts for the effects of path filtering, which is considered the same for all the paths.  
Concerning small-scale variations, these are caused by scattering due to surface roughness, obstacles along the propagation path, and Doppler effects. The above phenomena  
Figure 1: Scenario overview of underwater acoustic sensor network for monitoring.  
cause rapid, short-term fluctuations in the received signal. Each propagation path is decomposed into \"micropaths\" with random delays and gains. In particular, the transfer function can be rewritten as  
\[H(f)=\bar{H}_{0}(f)\sum_{p}\sum_{i}h_{p,i}e^{-j2\pi f\tau_{p,i}} \tag{2}\]  
where \(h_{p,i}\) is the intra-path gain and \(\tau_{p,i}\) is the corresponding delay. Accordingly, a small-scale fading coefficient \(\epsilon_{p}(f,t)\) can be considered, where  
\[\epsilon_{p}(f,t)=\frac{1}{h_{p}}\sum_{i\leq 0}h_{p,i}e^{-j2\pi f/\delta\tau_{p,i}} \tag{3}\]  
and thus,  
\[H(f)=\bar{H}_{0}(f)\sum_{p}h_{p}e_{p}(f,t)e^{-j2\pi f\tau_{p}} \tag{4}\]  
where \(\tau_{p,i}=\tau_{p}+\delta\tau_{p,i}\).  
Since the scattering points are separated by distances in the order of the typical \(\lambda\) values in relation to the low frequency traditionally used in acoustic underwater communication systems, the intra-path gains will be similar, but the phases will not. Thus, this will cause significant variations in \(\epsilon_{p}(f,t)\).  
The small-scale variations can be modeled as a complex Gaussian random process when a sufficiently high number of micropaths are present and the path amplitudes will exhibit a Ricean distribution.  
Motion of the transmitter, receiver, and reflective surface results in Doppler shifts and spreads, which impact small-scale phenomena and can be modeled via the function \(\tilde{\epsilon}_{p}(f,t)\):  
\[\tilde{\epsilon}_{p}(f,t)=\epsilon_{p}(f,t)e^{j2\pi a_{p}(t)ft} \tag{5}\]  
with \(a_{p}(t)=\frac{v_{p}(t)}{c}\), taking into account the three types of elements that influence the Doppler, i.e., unintentional transmitter/receiver motion (drifting), intentional transmitter/receiver motion (vehicular motion), and effect of waves at the surface, with \(v_{p}(t)\) being the velocity term and \(\tau_{p}(t)=\tau_{p}-a_{p}\cdot t\).