# Self-Organizing and Scalable Routing Protocol (SOSRP) for Underwater Acoustic Sensor Networks
## 2 System Model
### Propagation Model  
Many characteristics of the underwater environment affect the acoustic communication which makes the propagation channel much more complex compared to the terrestrial communication channel. They include temperature, salinity, multipath fading, path loss, depth and Doppler effect. The acoustic signal propagation, network performance and energy dissipation are highly affected by these factors. According to these considerations, the propagation speed of sound in underwater can be expressed as:  
\[\begin{array}{ll}c=&1448.96+4.591T-5.304*0.01T^{2}+2.374*0.01T^{3}+1.340(S-35)+ \\ &1.63*0.1H+1.675*10^{-7}H-1.025*0.01T(S-35)-7.139*10^{-13}TH^{3},\end{array} \tag{2}\]  
where \(T\) is the temperature (in Celsius), \(S\) the salinity of sea water (in parts per thousands, ppt) and \(H\) is the depth (m) of sensor nodes.  
In UASNs, the signal-to-noise ratio (SNR) is a measure of transmitted signal power to noise power (in dB re 1 \(\mu\)Pa, [17]), given by passive sonar equation expressed as [18]:  
\[SNR=SL-TL-NL+DL, \tag{3}\]  
where \(SL\) is the source level (dB re 1 \(\mu\)Pa), \(TL\) the transmission losses (dB), \(NL\) the ambient noise (dB re 1 \(\mu\)Pa) and \(DL\) the directivity index (dB). Ambient noise in shallow waters is mainly caused by shipping activity or biological noise, and a suitable level adopted is 70 dB re 1 \(\mu\)Pa (50 dB re 1 \(\mu\)Pa for deep water). In relation to the source level, is defined as the intensity of sound radiated by source at the distance of 1 meter, expressed in dB re \(\mu\)Pa (as [18]) in terms of the Power Intensity (\(I_{t}\)) (W/m\({}^{2}\)) used:  
\[SL=\log 10\bigg{(}\frac{I_{t}}{0.067*10^{-18}}\bigg{)} \tag{4}\]  
Hydrophones can be assigned a typical value of 20 dB [18] for SNR, where \(DL\) is zero when considering omnidirectional modems. Therefore, using (3) \(SL\) can be written as:  
\[SL_{SH}=TL+90 \tag{5}\]  
\[SL_{DP}=TL+70, \tag{6}\]  
where \(SL_{SH}\) denotes source level in shallow waters and \(SL_{DP}\) source level for deep waters.  
Figure 1: Network Model with 99 sensor nodes (labelled 1–99) and a sink node (labelled G).  
Transmission Loss (_TL_) is dependent on the absorption coefficient (\(\alpha(f)\), dB/km) and distance. It is the collective depletion in acoustic intensity during wave propagation which significantly affects the underwater communication. Another reason for suffering transmission loss is spreading, with cylindrical shape for a depth lower than 100 meters (shallow waters) or spherical at higher depths (deep waters). In this work, nodes are deployed with random depth from zero to 200 meters so both cylindrical and spherical spreading are considered. In every case, _TL_ (dB) can be estimated using (7)-(8) [18]:  
\[TL_{CS}=10\log(r)+\alpha(f)*r*10^{-3} \tag{7}\]  
\[TL_{SS}=20\log(r)+\alpha(f)*r*10^{-3}, \tag{8}\]  
where \(r\) is the distance (in meters) between transmitter and receiver, and \(TL_{\text{CS}}\) and \(TL_{\text{SS}}\) denotes transmission loss in cylindrical and spherical spreading, respectively. The absorption coefficient \(\alpha(f)\) for frequencies ranging from 100 Hz to 10 kHz is expressed through [PERSON]'s propagation model as:  
\[\alpha(f)=1.094\bigg{(}\frac{0.1*f^{2}}{1+f^{2}}+\frac{40*f^{2}}{4100+f^{2}} \bigg{)}, \tag{9}\]  
with frequency (\(f\)) measured in kHz.