## 3 Our Contribution
### UWSN Channel Model
To avoid any destructive reflection, c\({}_{\text{b}}\) is often kept less than c. With the transfer function for the individual propagation path, the cumulative transfer function (CTF) of the multipath channel is derived as (5):  
\[\overline{H}(\text{f})=\sum_{\text{p}}\overline{H}_{\text{p}}(\text{f})\text {e}^{-|2\pi\text{f}\overline{\tau}_{\text{p}}} \tag{5}\]  
To achieve a simple channel model, we approximated the function \(\overline{H}_{\text{p}}(\text{f})\) and, with reference to the reference path \(\text{p}=0\), the function is approximated as (6):  
\[\overline{H}_{\text{p}}(\text{f})=\frac{\Gamma_{\text{p}}}{\sqrt{\left(\frac {\bar{I}_{\text{p}}}{I_{\text{o}}}\right)^{\text{k}}\text{a}(\text{f})^{\bar {I}_{\text{p}}-\bar{I}_{\text{o}}}}}\overline{H}_{\text{o}}(\text{f}) \tag{6}\]  
The frequency-reliance distinguishing pth path from the reference path is combined to form a(f)\({}^{\bar{I}_{\text{p}}-\bar{I}_{\text{o}}}\). Approximating a(f)\({}^{\bar{I}_{\text{p}}-\bar{I}_{\text{o}}}\), assuming it as a constant, designing all the paths using equi-shaped impulse response with distinct gain parameter is feasible. For acoustic communication, the absorption factor a(f) possesses near 1 value, and for a wide range of acoustic frequencies, might validate approximation in the form of (7):  
\[\text{a(f)}^{-(\bar{I}_{\text{p}}-\bar{I}_{\text{o}})/2}\approx\text{a}_{0}^{ -(\bar{I}_{\text{p}}-\bar{I}_{\text{o}})/2} \tag{7}\]  
where a\({}_{0}\) refers to the absorption parameter for the frequency range \([\text{f}_{0},\text{f}_{0}+\text{B}]\). Using (7), the CTF is derived as (8):  
\[\overline{H}_{\text{p}}(\text{f})\approx\overline{h}_{\text{p}}\overline{H}_ {\text{o}}(\text{f}) \tag{8}\]  
where the corresponding path gain is given in (9):  
\[\overline{h}_{\text{p}}=\frac{\Gamma_{\text{p}}}{\sqrt{\left(\frac{\bar{I}_{ \text{p}}}{I_{\text{o}}}\right)^{\text{k}}\text{a}_{0}\bar{I}_{\text{p}}- \bar{I}_{\text{o}}}} \tag{9}\]In the above expression, the parameter \(a_{0}\) can be considered as the absorption parameter at a certain frequency within the operating bandwidth range. The frequency can be located anywhere, for example, at the centre frequency or the edge frequency (lower or upper edge). In case frequency exists at the lower edge of the frequency range, it leads to maximum path gain, while frequency at the upper edge may result in minimum path gain. As already stated, \(a(f)\) remains constant across the acoustic communication bandwidth, and the frequency can be selected in any way. It signifies that the design of a channel model is feasible by decoupling the effect of path filtering and multipath in such a manner that the individual path provides a gain \(\overline{h}_{p}\) and delay \(\overline{T}_{p}\), while maintaining the static filtering effect across all propagation paths and being characterized in terms of the function \(\overline{H}_{o}(f)\). Thus, the cumulative CTF can be derived as (10):  
\[\overline{H}(f)=\overline{H}_{o}(f)\underset{p}{\sum}\overline{h}_{p}e^{-|2\pi rf }\overline{T}_{p} \tag{10}\]  
Large-Scale Deviations (LSD) Caused Due to Location Dynamism  
In an acoustic environment, there are many parameters that significantly influence the geometry and make it uncertain. Some of these parameters are the transceiver movement, variation in the surface height, bottom shape, etc., which make exact system geometry uncertain. Such dislocation introduces variation in the path length \(\left(\text{i.e., }l_{p}=\overline{l}_{p}+\Delta l_{p}\right)\). It should be noted that the variation in the path length is often random. Usually, delay \(T_{p}\) is estimated for the lengths \(l_{p}\). The parameter \(h_{p}\) representing path gain is estimated using \(l_{p}\) (9).