## 4 Performance Analysis
### Energy Efficiency
#### 4.2.1 Cooperative ARQ
To reduce the time overhead caused due to this repetitive _CNode_ discovery process even when not required, we present in the result section a maximum limit that can be set to the number of discovery attempts, particularly for the C-HARQ protocol, after which the destination directly goes into the cooperation, skipping the _CNode_ discovery process. Next, the energy consumption at the source node can be similarly expressed as:  
\[E^{S}_{CARQ}|_{f=p}^{TX_{n}} =rE^{DATA}_{Tx}+(r-1)E^{NACK_{s}}_{Rx}+E^{ACK}_{Rx}+\{(r-1)nCN_{A }+p\}E^{NACK_{ox}}_{Rx} \tag{8}\] \[+rE^{C_{Req}}_{Rx}+nCN_{A}E^{C_{Avl}}_{Rx}+E^{S}_{Aulle}\] \[E^{S}_{CARQ}=\sum_{r=1}^{\infty}\sum_{p=0}^{nCN_{A}}\left\{E^{S }_{CARQ}|_{f=p}^{TX_{raw}}\times\Pr(f=p|sTx=r)\right\} \tag{9}\]  
The source node not only receives _NACK\({}_{S}\)_ and _ACK_ signals meant for it but also overhears the _NACK\({}_{CN}\)_, _C\({}_{Req}\)_ and _CAvl_ signals that are exchanged between the destination and the _CNodes_; hence the energy consumption resulting from them is also included in Equation (8). The overhearing of these signals keeps the source informed about the ongoing cooperation activity. The data packet transmitted by a _CNode_ to the destination can also be overheard by the source and rest of the _CNodes_, however it has been assumed that a node can know whether a packet is meant for it or not by processing only the initial few bits (_i.e._, header part), and hence can immediately stop or continue receiving the rest of the packet. Especially for larger packets (_i.e._, data and FEC packets), decoding of the packet header can be completed much before the antenna receives the rest part of the packet, as the processing takes very less time compared to the reception time. Employing this mechanism the overhearing of a _CNode_'sdata packet (for CARQ) and FEC packet (for C-HARQ), by source and other _CNodes_, has been avoided during the computer simulations. The total energy consumption of the cooperative nodes is calculated as the sum of the energies consumed by the individual cooperative nodes, which can be expressed as:  
\[E_{\textit{CMQ}}^{\textit{CN}}\Big{|}_{f=p}^{\textit{TrTr}=}=\sum_{i=1}^{ \infty}\Bigg{\{} \begin{matrix}E_{\textit{Rx}}^{\textit{DATA}}+(r-1)E_{\textit{ Tx}}^{\textit{DATA}}+(r-1)E_{\textit{Rx}}^{\textit{NACK}_{s}}+E_{\textit{Rx}}^{ \textit{ACK}}\\ +\{(r-1)n\textit{CN}_{A}+p\}E_{\textit{Rx}}^{\textit{NACK}_{s\textit{cr}}}+rE_{ \textit{Rx}}^{\textit{c}_{\textit{Rx}+}}+E_{\textit{Tx}}^{\textit{C}_{ \textit{Lat}}}+E_{\textit{Mdle}}^{\textit{CNode-i}}\end{matrix} \Bigg{\}} \tag{10}\]  
\[E_{\textit{CMQ}}^{\textit{CN}}=\sum_{r=1}^{\infty}\sum_{p=0}^{n\textit{CN}_{ s}}\Bigg{\{}E_{\textit{CMQ}}^{\textit{CN}}\Big{|}_{f=p}^{\textit{TrTr}=} \times\textrm{Pr}(f=p\big{|}sTx=r)\Bigg{\}} \tag{11}\]  
The _CNodes_ overhear the _NACK_s and _ACK_ signals transmitted by the destination, so as to keep track of the current status of the protocol, and decide whether to retain or drop the source's overheard data packet from its packet buffer. Additionally, it can also overhear the _NACK_s signals transmitted to other _CNodes_, along with the _NACK_s signals meant for it. However, as mentioned earlier, a _CNode_ avoids the overhearing of any other _CNode_'s data packet as it already has a copy of it. Finally, we define the energy efficiency as the ratio of the useful energy consumed in transmitting the data packet to the total energy consumed in successfully delivering that packet. Hence, the energy efficiency of CARQ can be expressed as:  
\[\eta=\frac{E_{\textit{Tx}}^{\textit{DATA}}}{E_{\textit{CARQ}}}=\frac{P_{ \textit{Tx}}I_{\textit{DATA}}T_{\textit{t}}}{E_{\textit{CARQ}}^{D}+E_{ \textit{CARQ}}^{S}+E_{\textit{CARQ}}^{\textit{CN}}} \tag{12}\]