# Self-Adjustment Energy Efficient Redeployment Protocol for Underwater Sensor Networks
## 6 Self-Adjustment Deployment Protocol
### Energy Efficient Deployment  
In underwater sensor networks, the energy constraint represents a critical challenge that directly impacts network performance and lifetime. This energy constraint is manifested by the limited capacity of sensors' batteries and the difficulty in replacing or recharging these batteries [13]. There are two aspects of energy consumption in the UWSN: The first is related to the sensor movement, and the second is related to the communication between sensors (energy consumed during the transmission and reception of messages). The energy consumed in the communication between nodes in our protocol is the energy consumed by the Hello message, which is a periodic message sent at the beginning of each iteration, as explained in Section 4. Hence, the number of Hello messages is fixed, and so the energy consumed by this message cannot be reduced at this level. Therefore, in this work, we focus on the energy consumed by the node displacement during the deployment. In fact, large displacement costs too much energy [32]. Our target is to reduce this energy as much as possible. Figure 4: Water currents impact on the sensor displacement. As explained above, the water currents have a speed and a direction. When the sensor moves from one position to another, these water currents based on its direction and the direction of the displacement of the sensor can help (Figure 5b) or resist (Figure 5a) to this movement. Clearly, if the displacement of the sensor is with water currents, the sensor will consume less energy to reach its destination since it is helped by the water currents. However, if the displacement of the sensor is against the water currents, the sensor will consume more energy to reach its destination. Our target in this work is to profit from these water currents to reduce the energy consumed without reducing the performance of our deployment protocol. Hence, we aim to reduce, as much as possible, the displacement of the sensor if it is against the water currents. To achieve this, we will calculate the work of the movement of the sensor from \(A\) to \(B\). Then, if the work \(w\) is positive, this means the sensor saves energy in this displacement. However, if the work is negative, this means the sensor dissipates more energy in this displacement. The node calculates the work of the new movement based on Formula (8):  
\[w=\frac{1}{2}m(V_{ss}^{2}-V_{is}^{2}) \tag{8}\]  
Based on Formula (4), we have:  
\[V_{ss}=\frac{V_{is}\text{sin}\omega}{\text{sin}(\alpha-\beta)} \tag{9}\]  
\[\omega=\pi-\gamma-(\alpha-\beta) \tag{10}\]  
\[V_{ss}=\frac{V_{is}\text{sin}(\gamma+(\alpha-\beta))}{\text{sin}(\alpha-\beta)} \tag{11}\]  
While \(\gamma\) is calculated by Formula (6). To summarize, our solution, SA-DVFA, consists of three parts:  
1. Each sensor node calculates its new position based on the 3D-DVFA algorithm. 2. Then, based on the water currents, the sensor calculates the new direction to reach its position. 3. Before moving in this direction, the sensor calculates the work of this displacement. If the work is positive, the sensor node moves immediately to its new position. If the  
Figure 5: (a) Water currents impact when the sensor displacement is in the opposed direction, (b) Water currents impact when the sensor displacement is in the same direction. work is negative, the sensor waits the next iteration hoping that the neighborhood will change. If after \(k\) times the work remains negative, the sensor moves to its new position. We can calculate the upper and lower boundaries of the work.