# Two-Tier Cooperation Based High-Reliable and Lightweight Forwarding Strategy in Heterogeneous WBAN
## 4 Experiments Analysis and Discussion
### Comparison Model and Metrics  
To verify the reliability and energy saving of our proposed TTCF strategy, this paper will use UC-MPRP [29] and CRPBA [30] to compare and analyze it. UC-MPRP leverages a node-independent multi-path routing model to design a multi-path route between clusters, and CRPBA is a one-hop forwarding model. The two models did not consider data compression before transmission; thus, this paper firstly computes data reconstruction error to judge the performance of compressing data for our TTCF. According to the definition of the reliability in [56] and the purpose of green computing, this paper will adopt a cumulative delivery rate, residual energy and throughput to measure the reliability and energy saving of all the above models. The metrics are defined as follows. * Data Reconstruction Error  
The measurement matrix \(\Omega_{1}\) is a \(p\times q\) -order matrix generated by the Logistic chaotic system of Equation (7), and the sparsity is set to \(\delta\). The auxiliary matrix \(\Omega_{2}\) is a matrix generated by the Tent chaotic system of Equation (10). To ensure the uniqueness of sparse recovery, the maximum value of sparsity \(\delta\) is \(p/2\). The process of constructing a one-dimensional signal in the experiment is as follows:  
\[ \begin{array}{c}init=randperm(q)\\ x=zeros(q,1)\\ x(init(1:\delta))=randn(\delta,1)\end{array}  \tag{16}\]  
where \(x\) is a one-dimensional signal, \(q\) is the signal length. In this paper, the signal length is set to 240, that is, \(x\in R^{240}\), the maximum sparsity is set to 60, and the positions of non-zero elements are randomly generated. If \(x\) is the original signal and the reconstructed signal is \(x^{\prime}\), the reconstruction error is calculated as shown in Equation (17). \[\frac{\|x-x^{\prime}\|}{\|x\|} \tag{17}\]  
This paper considers that the reconstruction is successful when the reconstruction error of the experiment is less than \(10^{-6}\). * Cumulative Delivery Rate  
\[C_{dr}=\frac{PK_{received}}{PK_{sent}} \tag{18}\]  
where \(PK_{received}\) represents the number of packets successfully received by sink node, and \(PK_{sent}\) is the number of packets sent by all the human body sensor nodes. * Residual Energy  
It includes data compression energy consumption and transmission energy consumption. Assuming that \(Q\)-dimension transmission data on the \(i\)-th sensor is compressed into the \(P\)- dimension by using the STPCS evolution model, the data compression energy consumption per unit time on sensor \(i\) is as follows:\[E_{stp}=\left(2Q\times\sqrt{PQ}+PQ\right)\times E_{sc} \tag{19}\]  
where \(E_{sc}\) denotes the energy consumed to compress one bit of data, and its value is 0.05 J/bit. The energy consumption of data transmission per unit time is shown in Equation (20). \[E_{tr}=J_{e}\times d_{v-i}\times t_{tr-i} \tag{20}\]  
where \(J_{e}\) represents the energy consumption of data transmitted by sensors, and its value is 1 J/KB; \(d_{v-I}\) and \(t_{tr-i}\), respectively, representing the data rate (shown in Nomenclature part) and the transmission duration of the \(i\)-th relay sensor on the transmission path, so the calculation method of sensor energy consumption is shown in Formula (21). \[E_{total}=E_{stp}+E_{tr} \tag{21}\]  
Obviously, sensor residual energy is the difference between its original energy and energy consumption \(E_{total}\), and the residual energy of the networking is the sum of the residual energy of all sensors. * Throughput  
\[Tr=\frac{1}{T_{received}-T_{sent}}\sum_{\kappa=1}^{K}R_{bytes}(\kappa) \tag{22}\]  
where \(K\) is the number of packets transmitted to the sink node successfully on sensor \(i\), \(R_{bytes}(\kappa)\) represents the number of bytes when the \(\kappa\)-th packet successfully reaches sink node, \(T_{received}\) represents the time when the sink node starts receiving packets on sensor \(i\) and \(T_{sent}\) denotes the time when the sink node ends receiving packets on sensor \(i\).