# Reliability Improved Cooperative Communication over Wireless Sensor Networks
## 4 Main Design of RICC
### Energy Consumption of a Node  
The power consumption of transmitting circuits \(P_{Ct}\) and the power consumption of receiving circuits \(P_{Cr}\), \(P_{Ct}\) and \(P_{Cr}\) are given by:  
\[P_{Ct}=P_{DAC}+P_{mix}+P_{filt}+P_{syn} \tag{23}\]  
\[P_{Cr}=P_{LNA}+P_{mix}+P_{IFA}+P_{filt}+P_{ADC}+P_{syn} \tag{24}\]  
where \(P_{DAC}\), \(P_{ADC}\), \(P_{filt}\), \(P_{filt}\), \(P_{LNA}\), \(P_{IFA}\), \(P_{mix}\) and \(P_{syn}\) is the power consumption values for the Digital-to-Analog Converter (DAC), the Analog-to-Digital Converter (ADC), the active filters at transmitter side and receiver side, the Low Noise Amplifier (LNA), the Intermediate Frequency Amplifier (IFA), the mixer and the frequency synthesizer, respectively [9].  
According to Equation (12), the power consumption of the amplifier is:  
\[E_{Amp}=-\frac{QN_{0}d^{k}}{\sigma^{2}\lg(1-p_{l})} \tag{25}\]  
Figure 6: Status message (broadcasted) loads of nodes.  
Figure 7: Status message (received) loads of nodes.  
Therefore, the total energy consumption per bit and the required packet loss probability can be calculated as:  
\[e_{T}(d,p_{l})=E_{Amp}+\frac{P_{Ct}}{R_{b}}=-\frac{QN_{0}d^{k}}{\sigma^{2}\lg(1- p_{l})}+\frac{P_{Ct}}{R_{b}} \tag{26}\]  
where \(R_{b}\) denotes the transmission data rate. Finally, the power needed for receiving data packet per bit is:  
\[E_{R}=\frac{P_{Cr}}{R_{b}} \tag{27}\]  
**Theorem 2**.: _With the routing strategy of the NCCC system model, for a node that is \(x\) meters away from the sink node, its energy consumption in one round, denoted as \(\omega_{p_{l}}^{x}\), can be calculated as follows:_  
\[\left\{\begin{array}{ll}\omega_{p_{l}}^{x}=&e_{T}(d^{*},p_{l})\cdot\zeta_{x, t}^{D}l_{d}+e_{T}(r_{b},p_{b})\times\left(\zeta_{x,p}^{S}l_{s}+\zeta_{x,p}^{O}l_{o} \right)\\ &+E_{R}\times\left(\zeta_{x,r}^{D}l_{d}+\zeta_{x,r}^{S}l_{s}+\zeta_{x,r}^{O}l_ {o}\right)\\ d^{*}=\left\{\begin{array}{ll}x,\ for\ x<r\\ r,\ for\ x\geq r\end{array}\right.\end{array}\right. \tag{28}\]  
_where \(l_{d}\), \(l_{o}\) and \(l_{s}\) stand for the sizes of the data packet, original packet and status message, respectively. A packet consists of a payload and a packet header containing a sequence number; therefore, the size of each data packet is \(l_{d}=(l_{o}/M+l_{h})\), where \(l_{h}\) is the size of the packet header._  
**Proof.** As sending and receiving data are the critical sources of energy consumption of nodes, the latter is not considered here. The total number of bits that a node, e.g., \(v_{i}\), receives in one round depends on the data packets received from the last hop, \(\zeta_{l,r}^{D}l_{d}\); the original packets received from the source node in the same cluster, \(\zeta_{l,r}^{O}l_{o}\); and the status messages received from other nodes in the same cluster, \(\zeta_{l,r}^{S}l_{s}\). The power needed for the reception of one bit is \(E_{R}=P_{Cr}/R_{b}\). Therefore, the energy consumption of node \(v_{i}\) to receive all those data bits can be computed as \(E_{R}\times\left(\zeta_{l,r}^{D}l_{d}+\zeta_{l,r}^{S}l_{s}+\zeta_{l,r}^{O}l_ {o}\right)\). Meanwhile, in one round, the total number of bits that node \(v_{i}\) needs to transmit depends on the data packets to be transmitted to the next hop, \(\zeta_{l,l}^{D}l_{d}\); the original data packets, \(\zeta_{l,p}^{O}l_{o}\); and the status messages to be broadcasted to other nodes in the same cluster, \(\zeta_{l,p}^{S}l_{s}\). According to Equation (26), for a fixed data rate \(R_{b}\) and a required packet loss probability \(p_{l}\), the energy consumption per bit is as \(e_{T}(d^{*},p_{l})\ =\ -\frac{QN_{0}d^{+k}}{\sigma^{2}\lg(1-p_{l})}\ +\ \frac{P_{Ct}}{R_{b}}\). Therefore, the energy consumption for node \(v_{i}\) to transmit all those data bits is \(e_{T}(d^{*},p_{l})\times\zeta_{x,l}^{D}l_{d}+e_{T}(r_{b},p_{b})\times\left( \zeta_{x,b}^{S}l_{s}+\zeta_{x,b}^{O}l_{o}\right)\).