# Void Avoidance Opportunistic Routing Protocol for Underwater Wireless Sensor Networks
## 3 EEDOR Void Avoidance with Hop Count Discovery Mechanism
### Acoustic Channel Model  
Sensor nodes in wireless sensor networks are battery-powered devices. Nodes in UWSNs consume a significant amount of energy because of the underwater acoustic channel characteristics. When the sensor nodes deplete their batteries, the sensor networks eventually cannot operate correctly. In this section, we describe the path loss and ambient noise of the underwater acoustic channel as in [26; 27].  
The sonar equation, which characterizes the signal-to-noise ratio (\(SNR\)) of passive sonar, is shown in Equation (1) below, as presented in [26; 28; 29; 30]:  
The model starts with the passive sonar equation, which describes the \(SNR\) in dB:  
\[SNR=SL-TL-NL+DI \tag{1}\]  
where \(SL\) is source level, \(TL\) is transmission loss, \(NL\) is noise level and \(DI\) is directivity index. \(DI=0\) as denoted in [29].  
**Source Level (SL):** Referring to [30], we can calculate \(SL\) as:  
\[SL=170.8+10\times\log(P_{tx}) \tag{2}\]  
where \(P_{tx}\) is the total acoustic power of the source.  
**Transmission loss (TL):** Referring to [26; 31] we can calculate the \(TL\) as the sum of both spreading and absorption loss, as follows in Equation (3)  
\[TL=k\times 10\log(d)+ad\times 10^{-3} \tag{3}\]  
where \(d\) is the distance in \(km\), \(\alpha\) is the absorption coefficient, expressed in Equation (4), and \(k\) is the spreading factor (\(k=1\) is cylindrical, \(k=2\) is spherical, and \(k=1.5\) in practical spreading).  
**Absorption loss (\(\alpha\)):** We use [PERSON]'s expression since it is widely used in the publications [26; 29; 30]. According to [26], the absorption coefficient (\(\alpha\)), which depends on frequency (\(f\)), can be defined and expressed as in Equation (4)  
\[\alpha=0.11\times f^{2}/(1+f^{2})+44\times f^{2}/(4100+f)+2.75\times 10^{-4}+0.003 \tag{4}\]  
where \(f\) is the frequency in kHz.  
**Noise Level (NL):** The noise levels in the ocean have a serious influence on the acoustic channel; they can be divided into [30; 31; 32]:  
* Ambient Noise: This noise is due to seismic and biological phenomena and water movement, which includes tides, current, storms, wind, and rain.
* Man-made noise: This is unnatural noise caused by human and shipping activity such as pumps, reduction gears and power plants, especially in areas encumbered with heavy vessel traffic.  
Four sources of noises are used to model the noise level, namely: turbulence (\(N_{t}(f)\)), shipping (\(N_{s}(f)\)), wind (\(N_{w}(f)\)), and thermal (\(N_{th}(f)\)) noises. Equation (5) shows the calculation of these four factors in \(\mathrm{dB/Hz}\).  
\[\begin{array}{c}10\times\log N_{t}(f)=1-30\times\log(f)\\ 10\times\log N_{s}(f)=40+20\times(s-0.5)+26\times\log(f)-60\times\log(f+0.03) \\ 10\times\log N_{w}(f)=50+7.5\times(w)^{\frac{1}{2}}+20\times\log(f)-40\times\log (f+0.4)\\ 10\times\log N_{th}(f)=-15+20\times\log(f)\end{array} \tag{5}\]  
where \(s\) defines a shipping activity factor value ranging from 0 to 1, \(w\) gives the wind speed in \(\mathrm{m/s}\) and \(f\) is the frequency in kHz.  
Then, the overall noise is expressed in Equation (6)  
\[NL=10\times\log((N_{t}(f)+N_{s}(f)+N_{w}(f)+N_{th}(f))\times B) \tag{6}\]where \(B\) is the receiver bandwidth in Hz.  
**Bit Error Rate (BER):** We assume that the underwater acoustic micro-modem uses binary phase shift keying (BPSK) modulation [17; 19; 33]. Accordingly, the bit error rate (\(P_{e}\)) of BPSK in an underwater Rayleigh fading channel can be calculated as in [33]:  
\[P_{e}=\frac{1}{2}\times\left(1-\sqrt{\frac{10^{\frac{SNR}{10}}}{1+10^{\frac{ SNR}{10}}}}\right) \tag{7}\]  
where \(SNR\) is the signal-to-noise ratio defined by Equation (1).  
**Probability of Successful Packet Delivery:** For a packet of \(m\) bits, the probability of successful packet delivery (\(P\)) is:  
\[P=(1-P_{e})^{m} \tag{8}\]  
Figure 2(a) illustrates the impact of the channel noise level and the transmission loss on \(SNR\) for various values of wind and shipping noise. The impact of these effects on packet delivery probability is shown in Figure 2(b).