# Path Diversity Improved Opportunistic Routing for Underwater Sensor Networks
## 3 Path Diversity Improved Opportunistic Routing
### Path Diversity Improved Forwarding Mechanism
Thus, the neighbor nodes which not only can provide higher progress but also have a lower path correlation with forwarding nodes already in the candidate set will be selected as the next potential forwarder. The normalized distance based path correlation can effectively avoid forwarding node concentrate in geographical. It can provide the diverse path in current forwarding hop, and offer more choice for the forwarding nodes selection at next hop. Although the random correlation coefficient cannot accurately represent the location relationship between neighbors, the PRCS method has two advantages. One is that it does not need two-hop neighbor information, and the other is that we use a broader candidates selection range. Then, the random correlation could also diversify the forwarding paths. It is computationally hard that finding a forwarding set with maximum EPA value [14]. It is similar to EEPA metric. In this paper, we propose two heuristics to search for a cluster that maximizes EEPA with different candidates selection range. In PICS, the path correlation coefficient is supported by two-hop neighbor information, making it so the candidate nodes should be in communication range of each other. The random path correlation coefficient in PRCS allows the candidates could be out of the communication range of each other. **A. Candidates Selection Algorithm for PICS**: The hidden terminal problem is that nodes in the candidate set placed beyond the communication range of each other cannot notice the transmission of any packet by other candidates, which leads to redundant transmissions and packet collisions. To avoid the hidden terminal problem, the PICS algorithm requires that all candidate nodes be a neighbor of each other. As a result, all candidate members can hear each other directly. Thus, PICS should be supported by two-hop neighbor information. The candidates selection algorithm for PICS is shown in Algorithm 1. Suppose node \(j\) is a neighbor of node \(s\), the NADV of packet forwarding from node \(s\) to \(j\) is given by \(\frac{d_{s}^{2}}{1/P_{sj}}=d_{sj}^{2}p_{sj}\). The PICS algorithm starts from the neighbor node \(j\) with the maximum NADV value, set as \(c_{0}\) (line 1). Then, find the neighbor node \(i\), \(i\in V_{c_{0}}\), with the maximum EEPA value, set as \(c_{1}\). Next, find the neighbor node \(l\), \(l\in V_{c_{s}},C_{s}=\{c_{0},c_{1}\}\) with the maximum EEPA value. Repeat the above loop until no node left within the communication range of all the node in candidate set \(\mathcal{C}_{s}\) (Lines 3-8). We define a standard plane formed by the candidate node \(c_{0}\), \(c_{1}\) and \(c_{2}\), the standard depth is defined as \(D_{z}=\sum_{i=0}^{2}(d_{s}-d_{c_{i}})/3\). When depth difference between the candidate node \(c_{i}\), \(i>2\) and its neighbor node \(j\), \(j\in V_{c_{i}}\) satisfies Equation (7)  
\[d_{c_{i}}-d_{j}\geq D_{z}+D_{r} \tag{7}\]  
where \(D_{r}\) is a depth threshold. Then, the packet forwarding carried by candidate node \(c_{i}\) is considered as an effective forwarding; otherwise, it is an ineffective forwarding and the candidate node \(c_{i}\) should be removed from the candidate set \(C_{s}\) (line 10). ```
1:Start from node \(j\) with maximum NADV, set as \(c_{t=0}\). [Node \(s\) is the current forwarder]
2:repeat
3: Find node \(i\in V_{C_{s}}\)
4: Set node \(i\) with maximum \(EEPA(V_{C_{s}})\) as next candidate node \(c_{t=t+1}\)
5:until No node satisfies \(i\in V_{C_{s}}\)
6: Remove node \(i\) from the candidate set \(V_{C_{s}}\) when it does not meet Equation (7)
```  
**Algorithm 1** Candidates Selection Algorithm-PICS