## 2 Multi-Hop Communications through the Human Body  
Multi-hop communication is widely used in WSNs. Short distance radio transmission relay is used instead of a long distance radio transmission, so the transmission power is reduced significantly. In BSNs, the path-loss of the human body is much larger than through the air, so the multi-hop communication is no doubt an interesting research topic for _in-vivo_ BSNs. It should also be noted that the energy consumption of a transmitting node is equal to the summation of the transmission energy, which is consumed for the wireless signal transmission from the sender to the receiver, and the circuitry energy, which is consumed by the circuit of the radio and MCU of the transmitting node. Therefore, although the multi-hop communication could reduce the transmission power, the circuitry power consumption would increase due to the packet relay, which cannot be negligible. It is necessary to re-evaluate the performance of multi-hop communication through the human body. This section will examine the energy consumption performance of multi-hop communication via the human body. An important step in the development of a swallowable body sensor network is the characterization of electromagnetic wave propagation between the devices inside the human body. This paper refers to the IEEE 802.15.6 channel model [32]. The path-loss between any two nodes is both distance and frequency dependent. Equation (1) gives the statistical model of path-loss, where \(d_{0}\) is equal to 50 mm as a reference distance, n is the path-loss exponent, S is the variation due to the phenomenon of shadowing and it follows normal distribution with mean of zero and standard deviation of \(\sigma_{S}\). The 15.6 Task Group identified seven different propagation scenarios in which the sensor device may operate. For the swallowable BSN applications of this paper, only the scenarios of implant-to-implant and implant-to-body surface are involved. The corresponding parameters are expressed in Table 1. For each scenario, whether the propagation is in the deep tissue or near the body surface is classified. According to this model, the path-loss between any two sensor devices within the human body can be estimated:  
\[\mathrm{PL(d)}=\mathrm{PL(d_{0})}+10\mathrm{n}\log_{10}\left(\frac{d}{d_{0}} \right)+\mathrm{S} \tag{1}\]  
where S\(\sim\)N(0, \(\sigma_{S}\))The energy model in this section is as follows: For a transmitting node, the total energy consumption (_Pont_) is calculated as two parts: The transmission energy for signal transmission and the circuitry power as shown in Equation (2), where _Pct_ is the circuitry power consumption of the transmitter. The signal transmission power consumption (_Pt_) (in dB) is calculated as the sum of path-loss (_PL_) and the receiver sensitivity shown in Equation (3). The power consumption in receive mode (_Ponr_) is mainly composed of receive circuitry power consumption (_Pcr_) as in Equation (4):  
\[\text{Pont}=(1+\alpha)\times\text{Pt}+\text{Pct} \tag{2}\]  
\[\text{Pt}=\text{PL}+\text{Sensitivity} \tag{3}\]  
\[\text{Ponr}=\text{Pcr} \tag{4}\]  
In Equation (2), \(\alpha\) is power amplifier inefficiency factor. It is calculated as in Equation (5), where \(\beta\) is the Peak to Average Ratio (PAR) and \(\mu\) is the drain efficiency of the RF power amplifier. \(\beta\) is dependent on the modulation scheme and the associated constellation size M in Equation (6). The 4 FSK modulation scheme is used by the current commercial WCE and this paper adopts this modulation scheme. Then M is equal to 4, therefore \(\beta\) is equal to 1. For \(\mu\), different classes of amplifiers have different values of \(\mu\). This paper will analyze \(\mu\) ranging from 0.35 to 0.75, which covers most of the range for both linear and non-linear amplifiers. Then, the corresponding \(\alpha\) ranges from 0.33 to 1.86. \[\alpha=\frac{\beta}{\mu}-1 \tag{5}\]  
\[\beta=\frac{3\times\left(\sqrt{M}-1\right)}{\sqrt{M}+1} \tag{6}\]  
The circuitry power of the radio is another important parameter.