# Efficient Health Data Transmission Method in a Wireless Body Area Network for Rural Elderly
## 3 Wireless Body Area Network Model
Assuming that the sensor transmits \(k\)-bit data in a communication process, the total energy consumption \(E_{T}\), total sending energy consumption \(E_{TX}\) and total receiving energy consumption \(E_{RX}\) can be calculated by the following Equations:  
\[E_{T}=E_{TX}+E_{RX} \tag{1}\]  
\[E_{TX}=k\times(E_{TXelc}+E_{amp}d_{ij}^{c_{ij}}) \tag{2}\]  
\[E_{RX}=kE_{RXelc} \tag{3}\]  
Since the network on the human body is quasi-dynamic, the signal will not only be affected by the change of human posture, but also be disturbed by various electromagnetic waves in the environment, so the path loss coefficient \(c_{ij}\) is usually larger than in other situations. (2) Prediction of the link connectivity probability  
Probabilistic routing predicts the probability of link connectivity according to the transmission history and connection history. After the \(t\)-th interval, \(p_{ij}^{t}\) can be dynamically updated as follows:  
\[p_{ij}^{t}= \begin{cases}p_{ij}^{t-1}+(1-p_{ij}^{t-1})\times\omega,&if\;e_{ij}= 1\\ p_{ij}^{t-1}\times\omega,&if\;e_{ij}=0\end{cases}  \tag{4}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Priority** & **Data Type** \\ \hline
0 & Emergency data, the data exceed the normal threshold \\
1 & Important data \\
2 & Periodic data \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data priority. Figure 1: Schematic diagram of the health-monitoring network for the elderly. If the link is connected, \({p_{ij}}^{t}\) increases at a rate determined by the constant \(w\) (\(0\leq w\leq 1\)). If the links are frequently connected in history, \({p_{ij}}^{t}\) will gradually reach its maximum value of \(1\). If the link is rarely connected in history, \({p_{ij}}^{t}\) gradually becomes 0. Therefore, for a given \(w,{p_{ij}}^{t}\) can approximately reflect the connected state of link \(e_{ij}\) at time \(t\). Ideally, \(w\) should be variable. For a good link in the past (maintaining a stable connection for a long time), \({p_{ij}}^{t}\) should grow very fast and decrease very slowly; for a bad link in the past, \({p_{ij}}^{t}\) should grow very slowly and decrease very quickly. This means that \(w\) should be able to capture the long-term history information of the link. Equation (5) defines the historical connection quality of link \(e_{ij}\) at time \(t\)[21]:  
\[w_{ij}^{t}=\sum\limits_{r=t-T_{window}}^{t}\frac{L_{ij}^{r}}{T_{window}} \tag{5}\]  
If the link is connected within time \(r\), then \({L_{ij}}^{r}\) is 1; otherwise, it is 0. We used a sliding time window to record the link state. \(T_{window}\) represents a measurement window through which the average connection quality can be obtained. The parameter \({w_{ij}}^{t}\) represents the quality of the link connection during the last \(T_{window}\). The link stability is calculated by the link state within the \(T_{window}\) before the current time \(t\). The better the link quality, the larger is \({w_{ij}}^{t}\). The worse the link quality, the smaller is \({w_{ij}}^{t}\). Studies have shown that \(T_{window}\) is reasonable between 7 s and 14 s [18; 21]. In Equation (5), the historical connection quality is obtained by calculating the average value, but this method does not consider the variation trend of the error. The link evaluation index is designed as follows:  
\[w_{ij}^{t}=0.5\times\sum\limits_{r=t-T_{window}}^{t}\frac{\alpha^{t-r}L_{ij}^ {r}}{T_{window}}+0.5\times(1-\sum\limits_{r=t-T_{window}+1}^{t}\frac{\alpha^ {t-r}(L_{ij}^{r}-L_{ij}^{r-1})}{T_{window}-1}) \tag{6}\]  
Equation (6) includes the weighted average of the overall link quality during the observation period and the weighted average of the change in link quality. \(\alpha\) indicates that the longer the time from the current time, the smaller the impact of link quality on the final evaluation. (3) Evaluation of link stability  
Most of the rural elderly are still engaged in agricultural production as laborers. In a WBAN, the transmission channel changes with the actions performed.