# Two-Tier Cooperation Based High-Reliable and Lightweight Forwarding Strategy in Heterogeneous WBAN
## 3 Two-Tier Collaboration Based High-Reliable and Lightweight Forwarding (TTCF) Mechanism for WBAN
### Forwarding Model Based on Multi Factor Dynamic Fusion in TTCF
Assuming \(s_{j}\) is the sampling frequency of sensor \(j\) at a certain time, and because \(s_{j}\) is inversely proportional to the nodal forwarding capacity, this paper uses its reciprocal to define the importance factor of the nodal sampling frequency, as shown below. \[\delta_{j}=\frac{1/s_{j}}{\sum_{j=1}^{N}1/s_{j}} \tag{9}\]  
The residual energy of sensors is proportional to their forwarding capacity. Supposing that the initial energy of sensor \(j\) is \(E_{ini}\) and the total energy consumed in each round of data collection is \(E_{cp}\), the residual energy influence factor of sensor \(j\) is in the following:  
\[\theta_{j}=\frac{E_{ini}-E_{cp}}{E_{ini}} \tag{10}\]  
The importance of sensors in network data transmission can be expressed by the ratio of the number of packets forwarded by sensors to the number of packets forwarded by all the nodes in the network. Assume that sensor \(j\) has performed a total of \(\tau_{j}\) forwarding operations before the current time, the importance factor \(\eta_{j}\) of sensor \(j\) in the network is shown as follows:  
\[\eta_{j}=\frac{\tau_{j}}{\sum_{i=1}^{N}\tau_{j}} \tag{11}\]  
_Finally_, the forwarding decision value of each encounter sensor in the network at the current time is calculated. Leveraging the multi-factor dynamic decision method can effectively fuse nodal different attributes containing individual differences in their contributions to forwarding. This paper requires each relay node to provide a vector containing its multiple attributes in order to measure its forwarding ability. Suppose that sensor \(j\) is one of the relay nodes at some time, the forwarding capability metric \(FA_{j}\) of node \(j\) is as follows:  
\[FA_{j}=\sum_{r=1}^{a}\omega_{r}A_{r}^{j} \tag{12}\]  
In the paper, \(A_{r}^{j}\) denotes the attributes \(\delta_{j}\), \(\theta_{j}\) and \(\eta_{j}\) of node \(j\). The weight coefficient \(\omega_{r}\) meets \(1\leq\omega_{r}\leq 0\) and \(\sum_{r=1}^{a}\omega_{r}\)=1, and means the different importance of each attribute. The EW method [28] is adopted to determine the weight of the attributes, and the information entropy of the \(r\)-th attribute is obtained according to Equation (13). \[EW_{r}=-(\ln b)^{-1}\sum_{j=1}^{b}p_{rj}\ln p_{rj},r=1,2,\cdots,a \tag{13}\]  
In the equation, \(a\) represents the number of attributes of node \(j\), \(b\) is the number of encounter nodes at this time and \(p_{rj}=A_{r}^{j}\sum_{j=1}^{b}A_{r}^{j}\). Then, the weight coefficient of the \(r\)-th attribute of encounter nodes can be calculated according to the following equation. \[\omega_{r}=\frac{1-EW_{r}}{a-\sum\limits_{r=1}^{a}EW_{r}},r=1,2,\cdots,a \tag{14}\]  
Obviously, the weight value of an attribute of a node is inversely proportional to its information entropy \(EW_{r}\), and the forwarding capability of a node is directly proportional to the value of its attributes. Namely, the smaller the information entropy of an attribute, the greater its weight should be; the larger the forwarding capability metric value, the stronger the forwarding ability of the encounter node, and the easier this node is to be selected as the relay node of the forwarding path. In addition, in the short-range free space communication such as WBAN, the transmission power consumption is proportional to the transmission distance, which can be simply expressed as \(E=\chi d^{2}\). In this equation, \(\chi\) is a fixed parameter and its value in this paper is 0.0001, and \(d\) is the distance between nodes and can be calculated by using the European distance. Usually, when the distance between objects is doubled, energy consumption will be increased by four times. Thus, when relay nodes are added to a long-distance transmission, the energy consumption will be greatly reduced.