## 4 Performance Analysis
### Energy Efficiency
#### 4.2.2 Cooperative-HARQ  
Again considering the same case of _sTx_ times data packet (here _Pac_-0) transmissions from source, invoking a total of _sTx_ cooperation processes, for the successful recovery of data at the destination, the total energy consumption of the C-HARQ protocol is given by:  
\[E_{\textit{CHARQ}}=E_{\textit{CAARQ}}^{D}+E_{\textit{CHARQ}}^{S}+E_{\textit{ CHARQ}}^{\textit{CN}} \tag{13}\]  
At the destination, the total energy consumption can be expressed as:  
\[E_{\textit{CHARQ}|\textit{sTx=r}}^{\textit{D}} =rE_{\textit{Rx}}^{\textit{P}_{\textit{Rx}}-0}+(r-1)E_{\textit{ dec}}I_{\textit{DATA}}+(r-1)E_{\textit{Tx}}^{\textit{NACK}_{s}}+E_{\textit{Tx}}^{ \textit{ACK}}+rE_{\textit{Tx}}^{\textit{C}_{\textit{Rx}+}} \tag{14}\] \[+n\textit{CN}_{A}E_{\textit{Rx}}^{\textit{C}_{\textit{Mdle}}}+E _{\textit{Mdle}}^{\textit{D}}+\sum_{i=1}^{n\textit{CN}_{s}}\sum_{j=1}^{n_{ij} }n_{ij}(E_{\textit{Tx}}^{\textit{NACK}_{s-j}}+E_{\textit{Rx}}^{\textit{P}_{ \textit{Rx}-j}}+E_{\textit{dec}}I_{\textit{DATA}})\]  
\[E_{\textit{CHARQ}}^{\textit{D}}=\sum_{r=1}^{\infty}\Big{\{}E_{\textit{CHARQ} |\textit{sTx=r}}^{\textit{D}}\times\textrm{Pr}(sTx=r)\Big{\}} \tag{15}\]  
Since the basic cooperation mechanism is same for C-HARQ, the _NACK_s, _ACK_, _C_\({}_{Req}\) and _C_\({}_{\textit{Avl}}\) terms in Equation (12) are same as that in Equation (6). But, with data packets coming only from the source, the destination receives the copies only \(r\) times and every time a Viterbi decoding is attempted using the previously saved FEC packets, except the very first transmission; thus resulting in the second term in Equation (12), where, \(l_{DATA}\) is the data payload size of _Pac-0_ and \(E_{dec}\) represents the energy consumed per useful bit (data bit) in a Viterbi decoding attempt. \(N_{mx}\) is the total number of FEC packets generated by RCPC encoding and \(n_{ij}\) represents the number of times the destination had to ask the _i-th CNode_ to transmit _Pac_-j before successfully receiving and storing it. In other words, \(n_{ij}\) represents the total number of transmissions of _Pac_-j from the _i-th CNode_ during the entire process; and every FEC packet reception is accompanied by a Viterbi decoding attempt.  
The source in C-HARQ is not involved in any FEC encoding or decoding process hence the working of the source is the same as that in CARQ; the only difference is the number of _NACK_ to _CNodes_ overheard. Again, the overhearing of a _CNode_'s FEC packet has been avoided for source as well as other _CNodes_. Thus, the energy consumption at the source node is given by:  
\[\begin{split} E_{CHARQ|Tx=r}^{S}&=rE_{Tx}^{Puc-0}+( r-1)E_{Rx}^{NACK_{s}}+E_{Rx}^{ACK}+rE_{Rx}^{C_{Rx}}\\ &+nCN_{A}E_{Rx}^{C_{ad}}+E_{Idle}^{S}+\sum_{i=1}^{nCN_{A}}\sum_{j =1}^{N_{mx}}n_{ij}E_{Rx}^{NACK-j}\\ & E_{CHARQ}^{S}=\sum_{r=1}^{\infty}\left\{E_{CHARQ|Tx=r}^{S}\times \Pr(sTx=r)\right\}\end{split} \tag{16}\]  
Similarly at the cooperative nodes, the total energy consumption is given by:  
\[E_{CHARQ|Tx=r}^{CN}=\sum_{i=1}^{nCN_{A}}\left\{\begin{split} E_{Rx}^{Puc-0}+( r-1)E_{Rx}^{NACK_{s}}+E_{Rx}^{ACK}+rE_{Rx}^{C_{Rx}}+E_{Tx}^{C_{ad}}\\ +E_{Idle}^{C_{Node}+i}+\sum_{k=1}^{nCN_{A}}\sum_{j=1}^{N_{mx}}n_{ ij}E_{Rx}^{NACK-j}+\sum_{j=1}^{N_{mx}}n_{ij}E_{Tx}^{Puc-j}\\ \end{split}\right\} \tag{18}\]  
\[E_{CHARQ}^{CN}=\sum_{r=1}^{\infty}\left\{E_{CHARQ|Tx=r}^{CN}\times\Pr(sTx=r)\right\} \tag{19}\]  
A _CNode_ listens to all the _NACK_ signals but responds only to the ones meant for it. Finally, from Equations (4a) and (13), the energy efficiency of C-HARQ can be written as:  
\[\eta=\frac{E_{Tx}^{DATA}}{E_{CHARQ}}=\frac{P_{Tx}l_{DATA}T_{t}}{E_{CHARQ}^{S} +E_{CHARQ}^{D}+E_{CHARQ}^{CN}} \tag{20}\]  
Theoretical calculation of \(n_{ij}\), \(\Pr(f=p\ /\ sTx=r)\), \(\Pr(sTx=r)\) and \(T_{CO\text{-}OP}\) are beyond the scope of this paper, hence computer simulations are used instead.