# A Two-Stage Routing Protocol for Partitioned Underwater Wireless Sensor Networks
## 3 Methodology
### Underwater Channel Model
#### 3.3.2 Neighborhood Information Acquisition Phase  
The neighborhood information acquisition phase uses the ALOHA protocol for channel access. This phase can be subdivided into two steps. In step 1, the UW-Sink initiates the neighborhood information acquisition phase by transmitting a beacon with transmission power \(p\). Each sensor node that is located within the communication range of the UW-Sink receives the beacon and sets its minimum hop count to the sink node to one. After the reception of the first beacon, the receiving nodes set up a waiting time \(\mathrm{W_{t}}\) during which they wait for the arrival of beacons from other nodes. This is done to gather further neighborhood information. Acquiring information from more than one neighbor offers flexibility and reliability in case of failure of a next hop neighbor (further explained in Section 3.3.3). At the end of the \(\mathrm{W_{t}}\) of a node, the node creates a beacon containing its residual energy information and minimum hop count along with the neighborhood information received from the neighboring nodes. The minimum hop count for any receiver X is one plus the minimum hop count of the node whose minimum hop count is minimum among all the neighbors of node X. The updated beacon is retransmitted using the default transmission power. All the nodes further down the stream update their hop count based on the received beacons and repeat the above mentioned process upon  
Figure 4: Network partitioning due to connectivity holes. Figure 3: Network partitioning due to mobility. reception of beacons. Consequently, every single and multihop neighbor X of the sink node has the following information:  
1. One and two hop neighbors of node X. We refer to the set of one hop neighbors of node X as Nx and the set of two hop neighbors of node X as N2x
2. Minimum hop count of all the nodes in sets Nx and N2x
3. Residual energies of all the nodes in sets Nx and N2x
4. Distance of every node in Nx from node X and distance of every node in N2x from their corresponding node in Nx (i.e., the node in Nx that received beacon from the node in N2x). During step 1, the single and multiple hop neighbors of the UW-Sink receive beacons. Single and multihop neighbors refer to those nodes that can be accessed over single or multiple hops, while the default transmission power is being used by all the nodes. However, the partitioned nodes that are out of the default communication range of the UW-Sink and all the beacon carrying nodes will not receive beacon during step 1 of the neighborhood information acquisition phase. These partitioned nodes initiate step 2 proactively by sending beacon requests after a certain threshold time TR with increased transmission power. As all the nodes have the same initial transmission power, lack of reception of a beacon stresses the need for increased transmission power for sending requests in order to increase the chances of finding a beacon hosting node in the neighborhood. After transmission of the beacon request, the requesting node goes into wait state for time Tw which is given as  
\[\text{Tw}=2\;\text{R/C}+\alpha+\text{T}_{\text{pr}} \tag{12}\]  
where \(\text{T}_{\text{pr}}\) represents the processing delay, R is the current range, and C denotes the speed of sound under water. The second term, \(\alpha\), is used to compensate for channel asymmetry. We note that R/C measures the maximum propagation delay. Any beacon hosting node that receives a beacon request responds by transmitting beacon with transmission power equal to that of the sender of the beacon request plus an offset value that is used to compensate for the lack of symmetry in the underwater channel. This ensures that the transmitted beacon reaches the requesting node. However, there are two possible failure scenarios:  
1. A partitioned node may not find a beacon hosting node even with increased transmission power as the beacon hosting nodes may be farther away. 2. The beacon transmission in response to a request is lost due to collision or channel impairments.