# Efficient Health Data Transmission Method in a Wireless Body Area Network for Rural Elderly
## 3 Wireless Body Area Network Model  
Sensors are responsible for sensing physiological parameters related to important portions of the human body and send the collected information to the sink directly or through a forwarding node. Compared with ordinary sensor nodes with limited energy, in order to better aggregate the data and process algorithms, the energy of the sink is considered to be almost unlimited. Let the WBAN consists of \(N\) sensor nodes and a sink. It is represented by a directed graph \(G=(V,E)\). \(E\) is the set of all links. Edge \(e_{ij}\in E\) exists if, and only if, node \(v_{i}\) and \(v_{j}\) can communicate directly. The sensors and sink will not move in a short time after deployment. The initial energy of all sensors is the same. The parameters are shown in Table 1.  
A common WBAN is shown in Figure 1. A health-monitoring network for the elderly with \(n=5\) is shown in Figure 1. The sink is placed at the waist and collects all sensed data. The other five sensors are placed on the heart, stomach, left knee, right knee and armpit. \begin{table}
\begin{tabular}{l l} \hline
**Parameters** & **Definition** \\ \hline \(N\) & Number of sensors \\  & Directed graph composed of wireless nodes. \\ \(G=(V,E)\) & \(V=[v_{1},v_{2},\dots,v_{N}]\) represents the set of sensors, and \(v_{i}\) represents the sensor node \(i\), \(1\leq i\leq N\). \\  & \(E\) is the set of network links \\ \(Er=\{Er_{1},Er_{2},\dots,Er_{N}\}\) & Represents the residual energy set \\ \(Er_{i}\) represents the residual energy of node \(v_{i}\) \\ \(d_{ij}\) & Represents the distance between nodes \(v_{i}\) and \(v_{j}\) \\ \(E_{T}\) & Total energy consumption \\ \(E_{TX}\) & Transmission energy consumption \\ \(E_{RX}\) & Receiving energy consumption \\ \(c_{ij}\) & Path loss coefficient \\ \(p_{ij}^{t}\) & Connection probability of link \(e_{ij}\) in time \(t\) \\ \(w_{ij}^{t}\) & Link quality evaluation index of link \(e_{ij}\) in time \(t\) \\  & Connectivity between \(v_{i}\) and \(v_{j}\) \\ \(L_{ij}\) & If the distance between any node and \(v_{i}\) is less than its sensing range \\  & \(R\), \(L_{ij}=1\), otherwise, \(L_{ij}=0\) \\ \(T_{window}\) & Measurement window through which the average connection quality \\ \(a^{t}\) & Attenuation factor of the impact of link quality at time \(t\) \\ \(E0\) & Initial energy \\ \(LCS_{i}\) & Link stability metrics \\ \(Ca_{i}\) & Candidate set of node \(v_{i}\) \\ \(de_{iCa}\) & Expected transmission time of one anycast transmission between \(v_{i}\) \\  & and the candidate set \(Ca_{i}\) \\ \(\varphi\) & Data priority \\ \hline \end{tabular}
\end{table} 
Table 1: Basic symbols. The importance of different physiological data collected in a WBAN varies. As shown in Table 2, we classified the sensing data into three groups: emergency data, important data, and periodic data. Among them, emergency data are related to life safety and are usually beyond the normal threshold. They need to be transmitted to the sink in a fast and reliable way, with the highest priority. Important data such as EGG have the second priority, while periodic data such as body temperature have the lowest priority. (1) Energy consumption model  
In a WBAN, each node consumes energy in data sensing, transmission, and processing. Among these processes, data transmission consumes the most energy; in this case, energy consumption mainly includes sending consumption and receiving consumption. The sending consumption \(E_{TX}\) includes the energy consumption \(E_{TXelx}\) produced by the transmitter and the energy consumption \(E_{amp}d_{ij}^{c_{ij}}\) produced by the amplifier. The receiving energy consumption \(E_{RX}\) is recorded as the energy consumption \(E_{RXelx}\) generated by the receiver.