# A Cross-Layer Optimized Opportunistic Routing Scheme for Loss-and-Delay Sensitive WSNs
## 5 The Design of the COOR Scheme
### Transmission Power Optimization
Meanwhile, it is also used to inform the sending node of the final receiving result of the current packet in this hop transmission. In a single transmission, each candidate node sends an ACK message in order of priority, and if a candidate node with a priority greater than the current node confirms that its recipient succeeds,the current node deletes the same packet immediately. This means that a single-hop transmission is finished, and the current node does not need to send an ACK message. Therefore the total number of ACK messages sent by the node \(n_{l}\) in a round is given as:  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]2  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]3  
\(\square\)  
For traditional routing methods, typically, all nodes not only have the same emission distance but also have the same transmit power. According to Equations (2) and (4), the success rate of single transmission \(p_{l}\) is equal everywhere in the network. Given these circumstances, a special case of Theorem 3 can be deduced:  
**Theorem 3**. : _Considering that the success rate of a single transmission in the traditional routing method is p. The numbers of all kinds of packets sent or received by the node \(n_{l}\) in a round of transmission are as follows:_  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]4  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]5  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]6  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]7  
_where \(p_{N}=1-(1-p)^{N}\) indicates the reliability of one-hop transmission._  
**Proof. ** Recursively expand the Equation (19):  
\[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]8 \[s=\frac{1}{2}(l+d_{x})^{2}d_{\theta}-\frac{1}{2}l^{2}d_{\theta}\]9 \[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]0  
\[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]1  
Putting tighter with Equation (21):  
\[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]2  
\[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]3  
\(\square\)  
Therefore, the data volume of the nodes using traditional routing method at different distances from the sink in a round of sending can be calculated. From Figures 6 and 11, the influence of transmission distance and size of candidate set on packet load is generated. The shorter the transmission distance and the more candidate nodes make the wireless network transmission more reliable. As the data loss rate becomes smaller, the amount of data on the network also becomes larger. \[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]4 (**a**) Data volume of node under \(N=3\), \(r=60\); (**b**) Data volume of node under \(N=3\), \(r=70\). Combined with Equations (6)-(10), the energy consumption of nodes at different distances from sink can be calculated. The results are shown in Figures 7 and 12. Due to different network parameters, the level of energy consumption of single round may be different, so it is not intuitive enough to use the subtraction value to measure the residual energy. In this paper, the energy residual degree \(\lambda_{l}\) is adopted to measure the residual energy of the node \(n_{l}\). **Definition 1. **_The energy residual degree \(\lambda_{l}\) of the node \(n_{l}\) is defined as the ratio of the energy saved by the node \(n_{l}\) compared to the maximum energy consumption to the energy consumed by the node itself in single sending round. Generally, the value of \(\lambda_{l}\) is computed as:_  
\[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]5  
\[S_{l,k}=\rho s=\rho ld_{\theta}d_{x}\]6 (**a**) Energy consumption of node under \(N=3\), \(r=60\); (**b**) Energy consumption of node under \(N=3\), \(r=70\). It can be seen from the Figure 13 that the residual energy of the network edge nodes will increase dramatically, but the energy consumption of the nodes in the near sink region is relatively small.