## 3 Triangle Metric Based Multi-Layered Routing Protocol
### Link Quality Centric the Triangle Metric  
The underwater acoustic communication environment is highly constrained considering the bandwidth limitation, lower speed, and higher propagation delay. Therefore, any retransmission attempt during acoustic communication significantly increases the overall network communication systems' energy consumption and reduces the network lifetime. Toward energy-oriented reliable acoustic communication link selection, link quality estimation becomes the first-class standard directly affecting the overall lifetime of the underwater network. For the traditional wireless networking environment, measuring expected transmission count (ETX) is the preferred choice for link quality estimation [46]. Furthermore, ETX-based link quality estimation has also been utilized in underwater literature to integrate local knowledge of underwater networking environment with count-based link quality [38]. However, many transmission requirements for link quality estimation make it less feasible for an acoustic network environment. However, in this proposal, a layered underwater networking environment was considered where a multi-level pressure-based routing algorithm that estimates the link's appropriateness considered the pressure-centric layering of overall acoustic networking scenarios. Considering dynamic underwater, we want to highlight that triangle metric (TM) oriented link quality estimation is considered an underwater networking centric improvement of expected transmission count (ETX)-based link quality estimation in traditional wireless networking. The TM-based link quality estimation's vital benefits include reaping a brief assessment, reducing overheads, and a reliable estimation of acoustic links in an underwater scenario. The TM is a geometric normalization of three parameters including packet reception rate (PRR), signal-to-noise ratio (SNR), and link quality indicator (LQI). TM is a more stable and shorter overhead centric link estimation in underwater. Furthermore, it considers proper normalization between dynamic and static environments crucial for underwater networking [47]. As TM-based link estimation is a mixture of SNR, PRR, and LQI, so one can assure dependable and speedy link first-class estimation via calculating the mean SNR and LQI. The main formula of the TM can be defined as \(n\) packets, and \(m\) total packets received successfully, where \((0<m<n)\). Moreover, LQI and SNR for each successful packet\({}^{i}\) are denoted by \(SNR_{i}\)_and LQI\({}_{i}\)_. The forwarder node broadcasts ten tiny packets in a short period to its neighbors. Upon receiving, the receiving nodes calculate the mean SNR and LQI using the two equations below:  
\[\overline{SNR}=\frac{\sum_{k=1}^{m}SNR_{k}}{n} \tag{3}\]  
\[\overline{LQI}=\frac{\sum_{k=1}^{m}LQI_{k}}{n} \tag{4}\]  
The receiver node measures the distance between sensors (period of the hypotenuse) characterized through a point \(\left(\overline{SNR},\overline{LQI}\right)\) and the point \((0,0)\) by the following equation based on Equations (3) and (4):  
\[\Delta d=\sqrt{\overline{SNR}^{2}+\overline{LQI}^{2}} \tag{5}\]The next step is the sender node, which measures the hyperlink for all of its neighbors as the highest \(\Delta d\) is the efficient link. A simple architecture of the TM-based link estimation is presented mainly through a three-phase-based estimation including SNR and the LQI centric input phase, TM processing phase, and the output categorization phase (see Figure 3). The link's output categorization depends on threshold consideration for acceptable links in an underwater environment [48]. In our algorithm, every node estimates the quality of links based on the TM for its one-hop neighbors. The neighbor information table (NIT) is utilized for one-hop neighbor identification in the information acquisition phase. We want to highlight that LQI indicates the quality of the received signal computed using the energy detection (ED), the signal to noise ratio, or both.