# A Two-Stage Routing Protocol for Partitioned Underwater Wireless Sensor Networks
## 3 Methodology
### Underwater Channel Model
#### 3.3.2 Neighborhood Information Acquisition Phase
If a requesting node does not receive beacon within its Tw due to either of the above-mentioned failure scenarios, it resends beacon request by further increasing its transmission power and also sets Tw using (1). The number of attempts can be pre-determined based on the deployment pattern and the characteristics of the underwater stream carrying the sensor nodes. **Link Budget:** In order to deal with the high bit error rate of the underwater channel, the next hop selection criteria (explained in Section 3.3.3) includes link condition. Link budget is used to estimate the received power level of a signal at destination D located x meters from the source where the signal is transmitted over frequency f.  
Upon reception of a beacon, the receiver R estimates its distance from the sender S using the distance and frequency information along with other channel parameters; R estimates the achievable power level at S. It is important note that the beacon receiver R will potentially send data to the sender S in the data transmission phase. Therefore, it calculates the link budget (i.e., the estimated received power level at S) for its potential data transmission to S. The link budget information is added to the neighborhood table of R to be used during relay selection process. If the expected received power is within the acceptable limits, i.e., Eo/No, the node in question is selected for further evaluation as next hop, i.e., hop count and Residual energy evaluation (details in Section 3.3.3). Equation (13) [29] represents the link budget for the underwater wireless channel  
\[\mathrm{SNR}\ =\ \mathrm{PL-TL-N+DI_{rx}+DI_{rx}} \tag{13}\]  
where SNR, PL, TL, N, DI\({}_{\mathrm{rx}}\) and DI\({}_{\mathrm{rx}}\) represent Signal to noise ratio at destination (received power), Pressure Level at the transmitter (transmitted power), transmission loss, ambient noise, directivity index of the sender and the directivity index of the receiver, respectively. All the above quantities are stated in dB re 1 \(\upmu\)Pa. As we are assume use of omni directional antenna DI\({}_{\mathrm{tx}}\) and DI\({}_{\mathrm{rx}}\) are set to zero. Figure 5 shows a block diagram of the link budget as expressed in Equation (13). The signal power at the receiver can be converted to electrical power using  
\[\mathrm{P(mW)=10^{PdBm/10}} \tag{14}\]  
\[\mathrm{P(W)=10^{PdBm/10}/1000} \tag{15}\]  
**Required signal Level (Eo/No):** The required signal level which is a function of the desired bit error rate can be defined as the ratio of energy per bit to receiver noise level, i.e., Eo/No [29]. **Available signal Level:** The product of the link budget analysis is available SNR at the receiver. To compare with required, received power is translated to an energy-per-bit equivalent using Equation (16) [29]. \[\left(\frac{\mathrm{E_{b}}}{\mathrm{N_{o}}}\right)=\ \mathrm{P_{rcv}*\left(\frac{B} {D}\right)} \tag{16}\]  
where \(\mathrm{P_{rcv}}\), \(\mathrm{E_{b}}\), \(\mathrm{N_{o}}\), B and D represent, received power (SNR), energy required per bit of information, receiver noise in 1 Hz of bandwidth, spectral bandwidth and data rate, respectively. The link margin (LM) compares received power level with that required for the established BER (Equation (17)) [29]  
\[\mathrm{LM}\ =\left(\frac{\mathrm{E_{b}}}{\mathrm{N_{o}}}\right)_{\mathrm{ rec}}-\left(\frac{\mathrm{E_{b}}}{\mathrm{N_{o}}}\right)_{\mathrm{req}} \tag{17}\]  
Based on the above-mentioned comparison, i.e., the link margin reception is considered a success or failure. In Figure 6, we show a flowchart that illustrates the neighborhood information acquisition phase. Figure 5: Block diagram of the link budget [26]. This phase deals with hop by hop transmission of data from source node to the UW-Sink. Every node, that has a data packet to send (either of its own or received from a downstream node) searches in its neighborhood table for the nodes which have acceptable link condition (received power), minimum hop count to the UW-Sink and maximum residual energy.