## 3 Methodology
While to calculate the velocity of sound propagation the formula given by [PERSON] [4] is used:  
\[\mathrm{c}= 1449.2+4.6\times\mathrm{T}-0.055\times\mathrm{T}^{2}+0.00029\times \mathrm{T}^{3}+(1.34-0.01\times\mathrm{T})(\mathrm{S}-35)+0.016\times\mathrm{d} \tag{5}\]  
where T is the temperature (\({}^{\circ}\)C), S is the salinity (%\({}_{\circ\circ}\)) and d the depth (m). An accurate model of underwater noise is required in order to determine the receiver's SNR. There are three main contributors in the total underwater noise: ambient noise, self-noise and the intermittent noise. The ambient noise is the most well-defined noise. As stated by [16], the ambient noise in the ocean can be modelled by using four sources: turbulence, shipping, waves, and thermal noise, calculated by the following empirical formulas:  
\[ \begin{array}{l}10\ \log\mathrm{N}_{\mathrm{T}}(\mathrm{f})=17-30\ \ \log\ (\mathrm{f})\\ 10\ \log\ \mathrm{N}_{\mathrm{s}}(\mathrm{f})=40+20(\mathrm{s}-0.5)+26\ \log(\mathrm{f})-\ 60\ \log(\mathrm{f}+0.003)\\ 10\ \log\ \mathrm{N}_{\mathrm{W}}(\mathrm{f})=50+7.5\mathrm{w}^{1/2}+20\ \log(\mathrm{f})-\ 40\ \log(\mathrm{f}+0.4)\\ 10\ \log\ \mathrm{N}_{\mathrm{k}}(\mathrm{f})=-15+20\ \log(\mathrm{f})\end{array}  \tag{6}\]  
where s is the shipping activity factor (0 \(<\) s \(<\) 1) and W is the wind speed (m/s). The main influencer, among these four sources are the wind-driven waves that contribute in frequencies from 100 Hz to 100 kHz. The total usage of the channel capacity is very important considering that the channel must work with many challenges and that it has limited resources. So, the selection of an optimal signal transmission frequency and the available bandwidth for different ranges of communication under different acoustic channel circumstances are crucial parameters for getting the best SNR. The signal-noise ratio observed at the receiver assuming that we don't have losses caused by the multipath effect or by the Doppler Effect [8] is given by:  
\[\mathrm{SNR}(\mathrm{r},\mathrm{f},\mathrm{d},\mathrm{T},\mathrm{w},\mathrm{ s},\mathrm{P}_{\mathrm{tx}}\ )=\frac{\mathrm{SL}(\mathrm{P}_{\mathrm{tx}},\mathrm{n},\mathrm{DI})}{\mathrm{ PL}(\mathrm{r},\mathrm{f},\mathrm{d},\mathrm{T})\sum\mathrm{N}(\mathrm{f}, \mathrm{w},\mathrm{s})\times\mathrm{B}} \tag{7}\]  
where B is the receiver's bandwidth (Hz), \(\mathrm{N}(\mathrm{f},\mathrm{w},\mathrm{s})\) represents the linear sum of the four ambient noise components mentioned in Equation (6). P\({}_{\mathrm{tx}}\) is transmitter's Power. One of the most important parameters for estimating the performance of an acoustic channel is the channel capacity for many different ranges of communication that we are interested in. The maximal value of this capacity can be determined by using the Shannon-Harley formula, and can be calculated using the SNR as:  
\[\mathrm{C}(\mathrm{r},\mathrm{f},\mathrm{d},\mathrm{T},\mathrm{S},\mathrm{p} \mathrm{H},\mathrm{w},\mathrm{s},\mathrm{P}_{\mathrm{tx}})=\mathrm{B}\times \mathrm{log}_{2}(1+\mathrm{SNR}(\mathrm{r},\mathrm{f},\mathrm{d},\mathrm{T}, \mathrm{w},\mathrm{s},\mathrm{P}_{\mathrm{tx}})) \tag{8}\]  
where \(\mathrm{B}\) is the receiver's bandwidth (Hz) and \(\mathrm{C}\) is the channel capacity in (bps). The values calculated by Equation (8) are theoretical values and this way they are considerably higher than the values available for underwater operations. In general, the specifications of acoustics modems show capacities much smaller than the theoretical ones. This leads to the conclusion that the commercial modems are not designed to fit in every specific channel or in every range of communication. So, to achieve a capacity closer to the theoretical one calculated by equation Equation (8) is a challenge for the underwater acoustic communications. When the multipath effect is present approximations are made often in order to model the propagation of the acoustic signals. A good approximation is the two rays model [12,17].