# Towards Efficient Wireless Body Area Network Using Two-Way Relay Cooperation
## 3 Packet Loss Probability
### Energy Efficiency  
Energy Efficiency is a measure of the useful portion of energy from overall energy consumed during transmission in a link. It is defined as a ratio of the useful fraction of the energy to overall energy consumption and given by Equation (4). The overall energy consumed by data transmission is the sum of energy cost at transmitter, receiver and radio frequency (RF) devices [29]:  
\[\eta=\frac{(1-PER)xL}{E_{DATA}+E_{ACK/NACK}}, \tag{4}\]  
where \(x=E_{TX\_dec}+E_{RX\_dec}+\frac{P_{T}}{R}\).  
\(E_{DATA}\) is the energy consumed in transmission of \(L\) bits of data, \(E_{ACK/NACK}\) is the energy consumed for transmission of acknowledgment packets, \(E_{TX\_dec}\) and \(E_{RX\_dec}\) are the energy consumed at transmitter and receiver, respectively, during the transmission of a single bit, \(P_{T}\) is the transmit power and \(R\) is the transmission rate.  
The energy expenditure on the transmission of data packets over two-way relay is summed up under the following occurrences:  
1. The direct link is in the proper working condition and the data is also overheard by the relay.
2. Both direct link and source to relay link fails, but the energy expenditure is similar as in the prior case.
3. The direct link fails, but data is successfully transmitted over relay link. It is then successfully transmitted to target node with probability \(PER_{SD}(1-PER_{SR})\).
4. The direct link fails, data is successfully transmitted over relay links \(S-R\) and \(D-R\), decoded by the relay node \(R\) and forwarded, but the broadcast link fails.  
The final expression of energy expenditure for the two-way relay and transmission of acknowledgment packet containing \(A\) bits are given in Equations (5) and (6), respectively:  
\[\begin{array}{ll}E_{TW,DATA}&=&[(E_{TX\_elec}+2E_{RX\_elec}+\frac{P_{T}}{R})(1- PER_{SD})\\ &&+(E_{TX\_elec}+2E_{RX\_elec}+\frac{P_{T}}{R})(PER_{SD}PER_{SR})\\ &&+(2E_{TX\_elec}+3E_{RX\_elec}+2\frac{P_{T}}{R})PER_{SD}(1-PER_{SR})\\ &&+(3E_{TX\_elec}+5E_{RX\_elec}+3\frac{P_{T}}{R})PER_{SD}(1-PER_{SR})(1-PER_{ DR})\\ &&PER_{RS}PER_{RD}](L+H),\\ \end{array} \tag{5}\]  
\[E_{TW,ACK/NACK}=[(E_{TX\_elec}+2E_{RX\_elec}+\frac{P_{T}}{R})(1+PER_{SD}(1-PER _{SR})](A+H). \tag{6}\]  
Firstly, the energy consumption over error-free direct link is considered. If the direct link is working properly and data is being transmitted to the other node, transmission over relay link is not needed. In the other case, the direct link experiences failure due to shadowing or deep fades and an alternate relay link is required. The second scenario of energy expenditure occurs when both the direct link and the first relay link fail. Another possibility of energy consumption for failed direct link includes the proper working of the first relay link i.e., the data is received at the relay node, after which either it is successfully transmitted to the target node or unsuccessful due to broadcast failure. In two-way relay cooperative scenario, the amount of data sent over the link is doubled as compared to the data sent over the one-way cooperative link.