# A Novel Cooperative Opportunistic Routing Scheme for Underwater Sensor Networks
## 3 Opportunistic Void-Avoidance Routing Protocol
### System Model  
In contrast to the terrestrial networks in which the network topology is simplified into a 2D one, an underwater sensor network has a 3D network topology. In our underwater acoustic sensor network model, a single sink is considered on the water surface, which is equipped with an acoustic modem for underwater communication and a radio modem for out of water communication with the monitoring centre [27; 28]. Anchored nodes are located at the bottom of the ocean in the predetermined locations to collect the information and deliver it to the sink by using the relay nodes, which are located at different levels in between [22; 27; 28]. Relay nodes and anchored nodes use acoustic signals to transmit the packets. Packets can be forwarded at longer distances by using the higher intensity of acoustic pressure. Moreover, the velocity of an acoustic signal depends on the varying pressures and temperatures [21].  
We assume that each node knows its current depth (_i.e._, vertical distance from each node to the water surface) by using an embedded depth sensor [26]. Moreover, nodes can obtain their hop count distance to the sink with the aid of distributed beaconing [8]. Nodes randomly move in the horizontal direction because of the water current, and their small vertical movements are negligible. The batteries are the energy suppliers of the underwater sensor nodes. Nodes are homogeneous in terms of energy consumption and transmission range. The Thorp model is used for designing the underwater acoustic propagation and adjusting the transmission power [22; 28]. Moreover, we consider a lossy channel inwhich path loss and bit error depend on the traversed distance and signal frequency. The path loss or attenuation over distance \(d\) with the signal frequency \(f\) is defined as follows [13]:  
\[A(d,f)=A_{0}d^{k}\alpha(f)^{d} \tag{1}\]  
where \(A_{0}\) represents a unit-normalizing constant and \(k\) is the geometric spreading factor, which is set to 1.5 for practical scenarios. Furthermore, the absorption coefficient \(\alpha(f)\) is defined by the Thorp formula. The ratio of the signal power, which contains meaningful data, to the unwanted signal power (_i.e._, noise) is defined as the signal-to-noise ratio (SNR). By considering the attenuation formula, the signal-to-noise ratio over distance \(d\) with the signal frequency \(f\) can be expressed as follows [13]:  
\[SNR(d,f)=\frac{P\mathbb{R}(f)}{A(d,f)PN(f)} \tag{2}\]  
where \(P\mathbb{R}(f)\) and \(PN(f)\) indicate the transmission power of the forwarding node with frequency \(f\) and the underwater environment noise, respectively. In order to decode the received signal without error, \(SNR\) at the receiver should be higher than a detection threshold. The ambient noise in the underwater environment includes four main components of turbulence \(P\mathbb{N}_{t}(f)\), shipping \(P\mathbb{N}_{s}(f)\), waves \(P\mathbb{N}_{w}(f)\) and thermal energy \(P\mathbb{N}_{th}(f)\), which can be expressed as [22]:  
\[PN(f)=PN_{t}(f)+PN_{s}(f)+PN_{w}(f)+PN_{th}(f) \tag{3}\]  
These noises are dominant in the different frequency regions, which can affect the communication channel throughput.