## 3 Network Architecture and Underwater Acoustic Channel Modeling  
The underwater wireless sensor network (UWSN) designed in this study adopts a three-dimensional topology, forming a cross-domain architecture composed of underwater nodes, surface sink nodes, and aerial UAVs. Underwater nodes are deployed at various depths and equipped with depth sensing and power control capabilities to support layered multi-hop acoustic communication. These nodes estimate the path loss using the received signal strength and adjust their transmission power accordingly. As shown in Figure 1, the network architecture consists of source nodes, relay nodes arranged in depth-based layers, surface sink nodes, and aerial UAV nodes. Surface sink nodes act as gateways between the underwater and aerial domains, receiving acoustic signals from the underwater nodes and forwarding the data via radio. UAV nodes serve as mobile relays with flight mobility and communication capabilities. They collect data from multiple sink nodes, monitor network conditions, and transmit information to ground stations, thus supporting reliable data transmission and robust cross-domain coordination. Figure 1: Node deployment diagram. Underwater acoustic channels differ significantly from radio channels and represent one of the most challenging transmission media in communication systems. Compared with terrestrial radio channels, underwater acoustic channels feature slower propagation speeds, longer propagation delays, narrower available bandwidths, more significant Doppler effects, and more complex dynamic variations. The propagation speed of underwater acoustic signals is about 1500 m/s, which is only 1/200,000 of the speed of radio signals in air (approximately \(3\times 10^{8}\) m/s). As a result, underwater acoustic communication experiences considerable propagation delays, making multipath delays and Doppler effects several orders of magnitude greater than those in radio communications. The attenuation of underwater acoustic signal power is caused by two main factors: geometric spreading and absorption, which can be expressed as  
\[L(d,f)=L_{spr}\left(d\right)+d_{km}L_{abs}\left(f\right) \tag{1}\]  
where \(L(d,f)=10 lg(P_{rx}/P_{scr})\) is the power loss in decibels, \(L_{spr}\left(d\right)\) is the spreading loss at distance d (in meters), \(d_{km}=d\times 10^{-3}\) is the distance in kilometers, and \(L_{abs}\left(f\right)\) is the absorption loss at frequency \(f\) (kHz) per kilometer (dB/km). The spreading loss can be expressed as  
\[L_{spr}\left(d\right)=k\times 10 lg\left(d/d_{ref}\right) \tag{2}\]  
where \(k\in\left[1,2\right]\) is an exponent describing the geometric spreading shape (analogous to the path-loss exponent in terrestrial RF models). \(k=1\) corresponds to cylindrical spreading (e.g., when the water depth is much less than the horizontal range), and \(k=2\) corresponds to spherical spreading (similar to free-space path loss in terrestrial systems). For frequencies above 700 Hz, the absorption loss is commonly computed using the empirically derived Thorp formula [26] from oceanographic measurements:  
\[L_{abs}(f)=\frac{0.11\,f^{2}}{1+f^{2}}+\frac{44\,f^{2}}{4100+f^{2}}+3\times 10^ {-4}\,f^{2}+3.3\times 10^{-3} \tag{3}\]  
The Thorp formula is one of the most widely used models for estimating absorption losses in underwater environments. In underwater acoustic environments, noise is typically caused by turbulence, shipping activities, surface waves, and thermal noise. In the reference unit of 1 \(\upmu\)Pa@1m/Hz, the power spectral density of these noise sources can be expressed as  
\[\left\{ \begin{aligned} & N_{t}(f)=17-30 lg(f)\\ & N_{\omega}(f)=40+20(s-0.5)+26 lgf-60 lg(f+0.03)\\ & N_{\omega}(f)=50+7.5\sqrt{\omega}+20 lgf-40 lg(f+0.4)\\ & N_{th}(f)=-15+20 lg(f)\end{aligned} \right. \tag{4}\]  
where \(s\in\left[0,1\right]\) is the shipping activity factor (0 = low, 1 = high), and \(\omega\) is the wind speed (m/s) affecting the wave-induced noise.