# Efficient On-Off Keying Underwater Acoustic Communication for Seafloor Observation Networks
## 4 Undersea Application and Experimental Results
### Sound Rays Propagation and Placement of Communication Nodes  
The speed of sound in the ocean is a function of temperature, salinity, and pressure, all of which vary significantly in the vertical [6]. These factors cause refraction, and the sound rays always bend in the direction where the sound speed decreases. Therefore, some areas where sound rays gather are called the convergence zone, while the others where no rays pass through are called the shadow zone. The communication nodes in the shadow zone would not be able to hear the transmitted signal. Due to the positive sound speed gradient, those sound rays always bend upwards when they are emitted from a source deployed near the seafloor. This phenomenon results in a large shadow area within a few kilometers of the source. The 20 sound rays with fixed launching angles ranging from \(-10\) to \(10\) degrees are shown in Figure 8. The only different condition between Figure 8a,b is the height of the source from the seafloor. It can be concluded that, within a certain range of launching angles, the height of the source affects the range of the shadow zone and the number of the paths reflected by the seafloor. Moreover, the receiver hydrophone should be high enough from the seafloor to be in the convergence zone. In other words, the placement of the communication nodes directly affects the quality of communication. Moreover, the seafloor slope and communication distance should also be taken into account.  
In this subsection, the constraint relation among the critical heights of the source and the receiving hydrophone, the seafloor slope angle, and the communication distance is analyzed. The propagation of the sound rays is modeled under ideal conditions. In order to simplify the calculation model, the typical deep-sea Munk model is adopted and the sound speed gradient near the seafloor is set to a constant \(a\), which approximates the average sound speed gradient under the sound channel axis, and the seafloor topography is approximated as a flat floor with a certain slope angle \(\beta\). The research object is the sound ray with the largest downward launching angle, which is the lower boundary of the optimal receiving region. This sound ray is assumed to be tangent to the seafloor in order to minimize the number of the paths reflected by the seafloor. According to the theory of ray acoustics, the sound ray in the case is an arc with equal curvature:  
Figure 8: Sound ray paths from two sources with the heights of (**a**) 20 m and (**b**) 2 m away from the seafloor.  
\[\rho=\frac{\mathrm{d}\theta}{\mathrm{d}s}=a\cos\alpha_{0} \tag{11}\]  
where \(\theta\) is the direction angle of the target ray, \(s\) is the length of the sound ray, \(\alpha_{0}\) is the initial launching angle, i.e., the angle between the launching direction and the horizontal line, and \(a\) is the relative speed gradient, which is defined as  
\[a=\frac{c_{i}-c_{i-1}}{c_{i-1}(z_{i}-z_{i-1})}=9.4\times 10^{-6} \tag{12}\]  
where \(c_{i}\) is the sound speed at the depth \(z_{i}\). Modeling, as shown in Figure 9, the target sound ray with the maximum launching angle \(\alpha_{0}\) is tangent to the seafloor at point **A**, where **x** and **y** are the heights of the source and the receiving hydrophone from the seafloor, respectively. The point **B** is the projection of the receiving hydrophone on the seafloor.  
Taking the distance \(z\) between the tangent point **A** and the projection point **B** as a parameter, the relationship between \(\textbf{x},\textbf{y}\), \(L\) and \(\beta\) is obtained by analytical calculation as follows:  
\[\begin{cases}x(z,\beta)=\frac{2R}{\cos\beta}\sin^{2}\frac{1}{2}\left[\left( \arcsin\left(\frac{\left(\frac{L}{\cos\beta}-z\right)\cos\beta}{R}\right)-\sin \alpha_{0}\right)+\alpha_{0}\right]\\ y(z,\beta)=\frac{2R}{\cos\beta}\cos^{2}\frac{1}{2}\left[\left(\pi-\arcsin\left( \frac{z\cos\beta}{R}\right)-\sin\beta\right)-\beta\right]\\ z\in\left(max\left(0,\frac{L-R\sin\alpha_{0}}{\cos\beta},\frac{L}{\cos\beta} \right)\right)\end{cases} \tag{13}\]