## 2 Multi-Hop Communications through the Human Body
The transmission and receive circuitry power consumptions of the radio have become smaller and smaller as new technologies have been developed. The commercial medical implantable RF transceiver ZL70102 has a TX/RX circuitry power of 5 mA (5 mA \(\times\) 3 V = 15 mW). [PERSON] _et al_. presented a 1.5 mA CMOS BFSK transceiver in the MICS band [33]. A 350 \(\mu\)W MSK transmitter and 400 \(\mu\)W OOK receiver for medical implant communications are proposed by [PERSON] _et al._[34]. [PERSON] _et al._, proposed a 90 \(\mu\)W MICS/ISM band transmitter [35]. In this paper, we will evaluate the Tx/Rx circuitry power from 100 \(\mu\)W to 15 mW. \begin{table}
\begin{tabular}{c|c|c|c} \hline Implant to & \multirow{2}{*}{\(PL(d_{0})(\text{dB})\)} & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(\sigma_{s}(\text{dB})\)} \\ Implant & & & \\ \hline Deep Tissue & 35.04 & 6.26 & 8.18 \\ Near Surface & 40.94 & 4.99 & 9.05 \\ \hline Implant to & \multirow{2}{*}{\(PL(d_{0})(\text{dB})\)} & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(\sigma_{s}(\text{dB})\)} \\ Body Surface & & & \\ \hline Deep Tissue & 47.14 & 4.26 & 7.85 \\ Near Surface & 49.81 & 4.22 & 6.81 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters used in path-loss estimation. To evaluate the performance of energy consumption of multi-hop communication inside the human body, five scenarios, 1-hop to 5-hop communications, within a fixed distance is simulated. The simulation refers to the IEEE 802.15.6 channel model. The energy model and application traffic are given in Table 2. -84 dBm is the sensitivity of the current commercial wireless capsule. Different circuitry powers from 10 \(\mu\)W to 15 mW are evaluated. The simulation results are shown in Figure 2. It can be seen that as the number of hops increases, the total energy consumption increases for large circuitry power, while it decreases for small circuitry power. Take 1-hop and 2-hop for example to explain the changes of the energy consumption. The total energy consumption for 1 hop, E1 hop, is expressed as in Equation (7). Pt1\({}_{\textrm{hop}}\) is the transmission power of the first node. T\({}_{\textrm{D}}\) is the time duration for data transmission. The total energy consumption is composed of two parts: signal transmission energy and circuitry energy. If one relay node is added forming a 2-hop communication, then the total energy consumption, E2 hop is expressed as in Equation (8), where Pt1\({}_{\textrm{2 hop}}\) and Pt2\({}_{\textrm{2 hop}}\) represent the transmission power of the first node and the relay node, respectively. From 1 hop to 2-hop, the transmit power reduces because the transmission distance for 2-hop becomes smaller. On the other hand, the relay node consumes energy by receiving and transmitting the data packet. E1 hop\({}-\)E2 hop is calculated as expressed in Equation (9). Whether 2-hop communication is more energy efficient than 1 hop communication depends on \((1+\alpha)\times\left(\textrm{Pt1}_{\textrm{1 hop}}-\textrm{Pt1}_{\textrm{2 hop}}-\textrm{Pt2}_{\textrm{2 hop}}\right)\) and \((\textrm{Pct}+\textrm{Pcr})\). If the former is bigger than the latter, then 2-hop communication saves energy and _vice versa_. The cases for more hops are the same. From Figure 2 it can also be seen that if the circuitry power is bigger than around 3 mW, single-hop wireless communication consumes less energy than multi-hop communication. If the circuitry power drops below 3 mW, multi-hop wireless communication saves power compared with one-hop communication.