## 3 Our Contribution
### UWSN Channel Model  
To derive a robust channel model for UWSN, two different types of channel conditions and corresponding acoustic dynamism have been considered in this paper. The first refers to the one introduced due to the displacements ranging multiple wavelengths (say, large scale deviation (LSD)), and the second refers the dynamism caused due to the displacements in the magnitude of a single or a few of the wavelengths (small scale dynamism (SSD)). LSD is caused due to system dislocations, whose prediction is infeasible using traditional system geometry. Traditional transceiver localization within a predefined constant geometry and definite sound-speed characteristics can generate a constant acoustic field; the practical area might vary over the time because of the uncertainty in the system dimensions. Typically, such uncertainty is arbitrary, which gives rise to LSD that can be easily observed in the form of channel gains and the delay in transmission paths. Meanwhile, with predefined LSD, the supplementary SSD may emerge in both the path gains and end-to-end delays. Such deviations are usually considered as the result of object dislocations and scattering [50]. Nominal Conditions  
The channel dimensions in conjunction with certain specific sound-speed characteristics present the nominal response of an acoustic channel symbolising a time-invariant model, which can be examined through specific beam tracing models. The path loss suffered by a transmitted signal with frequency f traversing over the distance influences the received signal (1) [50; 51]. \[\mathrm{an}(\mathrm{l},\mathrm{f})=\mathrm{A_{0}}\mathrm{l^{k}a(f)}^{1} \tag{1}\]  
where \(\mathrm{A_{0}}\) refers to scaling factor, k presents the spreading factor and an open paren f close paren signifies the absorption coefficient, simulated using [PERSON]'s empirical model (2). \[\text{a(f)}=0.11*\frac{\ell^{2}}{1+\ell^{2}}+44\frac{\ell^{2}}{4100+\ell^{2}}+2.75 \times 10^{-4}\ell^{2}+0.003 \tag{2}\]  
In (2), f is in kHz unit. Considering multi-path communication with different paths of length \(\bar{I}_{\text{p}}\), \(\text{p}=0,\ldots,\text{P}-1\) the individual path functions as a low pass filter (LPF). The transfer function of LPF affecting received signal strength (RSSI) can be derived as (3):  
\[\overline{H}_{\text{p}}(\text{f})=\frac{\Gamma_{\text{p}}}{\sqrt{\text{A} \left(\bar{I}_{\text{p}},\text{f}\right)}} \tag{3}\]  
where \(\Gamma_{\text{p}}\) refers to the cumulative reflection coefficient (CRF) observed over the surface, which signifies the bottom-reflections generated in the direction of the pth path. For illustration, a realizable surface can be formed with reflection coefficient \(\gamma_{\text{s}}=-1\), and the individual-bottom reflection can be derived as (4):  
\[\gamma_{\text{b}}(\theta_{\text{p}})= \begin{cases}\frac{\rho_{\text{b}}\sin \theta_{\text{p}}-\rho\sqrt{\left(\frac{\kappa}{\theta_{\text{b}}}\right)^{2}- \cos^{2}\theta_{\text{p}}}}{\rho_{\text{b}}\sin\theta_{\text{p}}+\rho\sqrt{ \left(\frac{\kappa}{\theta_{\text{b}}}\right)^{2}-\cos^{2}\theta_{\text{p}}}},&\cos\theta_{\text{p}}\\ 1,&\text{otherwise}\end{cases}  \tag{4}\]  
where \(\theta_{\text{p}}\) presents \"the Grazing angle\" associated with the pth path, \(\rho\) is the fluid density (\(\rho=\)1000 kg/m\({}^{3}\)) and c signifies the speed of sound in water (c = 1500 m/s). \(\rho_{\text{b}}\) and c\({}_{\text{b}}\) represent the density and the sound speed at the bottom of the water column, respectively.