# Reliability Improved Cooperative Communication over Wireless Sensor Networks
## 4 Main Design of RICC
### The Design of RICC  
From the above analyses, we know that the linchpin of RICC is determining the transmission power of nodes in different places in the network to increase the cooperative communication performance. In this section, this problem is studied.  
In NCCC, if the packet loss probability that the network adopts is determined, then according to Theorem 2, the energy consumption of each node in the network is calculated. First, considering the data transmission power is the minimum value that meets the reliability requirements of the application. Then, the residual energy of a node in the far-sink region is used to increase its data transmission power and thereby decrease the MFR of the transmission hop originating from it and further improve the reliability of the whole network.  
**Theorem 3**: _In NCCC, suppose the required packet loss probability is \(p_{l}\). Then, in RICC, for a certain node, say \(v_{x}\), which is \(x\) m away from the sink node, the largest transmission power \(E^{x}_{Amp}\) that it can adopt without harming the network lifetime can be calculated as:_  
\[\left\{\begin{array}{l}E^{x}_{Amp}=\frac{w^{x_{0}}_{l_{l}}-E_{k \epsilon}-\frac{p_{C_{l}}\epsilon_{t}}{\mathcal{K}_{k}}\epsilon_{t}}{\zeta^{D}_ {x,t}d_{+}\big{(}\zeta^{S}_{x,t}\ell_{+}+\zeta^{O}_{x,t}\ell_{o}\big{)}\frac{x ^{k}}{\mathcal{K}}\log^{(1-p_{l})}}\\ \epsilon_{r}=\big{(}\zeta^{D}_{x,t}\ell_{d}+\zeta^{S}_{x,t}\ell_{s}+\zeta^{O}_ {x,t}\ell_{o}\big{)}\\ \end{array}\right. \tag{29}\] \[\epsilon_{t}=\Big{(}\zeta^{D}_{x,t}\ell_{d}+\zeta^{S}_{x,t}\ell_{s}+ \zeta^{O}_{x,b}\ell_{o}\Big{)}\]  
_where \(x_{0}\) is the distance of the last hop that is from the last node to the sink._  
Proof.: According to Equations (26) and (28), for the required node failure probability and a fixed data rate, the energy consumption of node \(v_{x}\) is \(w^{x}_{p_{l}}\). In addition, from Theorem 1, we know that \(w^{x_{0}}_{p_{l}}\) is the largest energy consumption. By subtracting \(w^{x}_{p_{l}}\) from \(w^{x_{0}}_{p_{l}}\), node \(v_{x}\)'s energy left is:  
\[w^{x}_{\Delta}=w^{x_{0}}_{p_{l}}-w^{x}_{p_{l}} \tag{30}\]  
Here, \(w^{x}_{\Delta}=0\) means that node \(v_{x}\) makes full use of its residual energy, and we can directly solve for \(E^{x}_{Amp}\):  
\[\begin{array}{l}e_{T}(x_{0},p_{l})\zeta^{D}_{x_{0},l}d_{+}e_{T}(r_{b},p_{l} )\Big{(}\zeta^{S}_{x_{0},b}l_{s}+\zeta^{O}_{x_{0},b}l_{o}\Big{)}+E_{R}\times \big{(}\zeta^{D}_{x_{0},r}l_{d}+\zeta^{S}_{x_{0},r}l_{s}+\zeta^{O}_{x_{0},r}l_ {o}\big{)}\\ =e_{T}(x^{*},p_{l})\zeta^{D}_{x,l}d_{+}e_{T}(r_{b},p_{l})\Big{(}\zeta^{S}_{x,b }l_{s}+\zeta^{O}_{x,b}l_{o}\Big{)}+E_{R}\times\big{(}\zeta^{D}_{x,r}l_{d}+ \zeta^{S}_{x,r}l_{s}+\zeta^{O}_{x,r}l_{o}\big{)}\\ \Rightarrow E^{x}_{Amp}\zeta^{D}_{x,l}d_{+}E^{0}_{Amp}\Big{(}\zeta^{S}_{x,b}l_ {s}+\zeta^{O}_{x,b}l_{o}\Big{)}+E_{R}\epsilon_{r}+\frac{p_{C_{l}}}{\mathcal{ K}_{k}}\epsilon_{t}=w^{x_{0}}_{p_{l}}\\ \Rightarrow E^{x}_{Amp}\Big{[}\zeta^{D}_{x,l}d_{+}\frac{r^{k}}{d^{k}}\log^{(1-p _{l})}_{Amp}\Big{(}\zeta^{S}_{x,b}l_{s}+\zeta^{O}_{x,b}l_{o}\Big{)}\Big{]}=w^ {x_{0}}_{p_{l}}-E_{R}\epsilon_{r}-\frac{p_{C_{l}}}{\mathcal{K}_{k}}\epsilon_{t} \\ \Rightarrow E^{x}_{Amp}=\frac{w^{x_{0}}_{p_{l}}-E_{R}\epsilon_{r}-\frac{p_{C_{l }}}{\mathcal{K}_{k}}\epsilon_{t}}{\zeta^{D}_{x,b}l_{d}+\big{(}\zeta^{S}_{x,b}l _{s}+\zeta^{O}_{x,b}l_{o}\big{)}\frac{x^{k}}{\mathcal{K}}\log^{(1-p_{l})}_{ \mathcal{K}_{k}}}\end{array} \tag{31}\]  
where \(E^{c}_{Amp}\) stands for the power consumption of the amplifier within clusters and is calculated as:  
\[E^{c}_{Amp}=-\frac{Q\text{N}_{0}r^{k}}{\sigma^{2}\text{lg}(1-p_{b})} \tag{31}\]  
thus,  
\[\frac{E^{c}_{Amp}}{E^{x}_{Amp}}=\frac{r^{k}}{d^{*k}}\log^{(1-p_{l})}_{(1-p_{b})} \tag{32}\]