## 6 Results and Discussion  
### Performance Evaluation by Computer Simulation  
In this section, the proposed and standard schemes with two-hop extension are evaluated based on communication distance by computer simulations. The computer simulator was built by us with MATLAB. The main simulation parameters are listed in Table 3 and refer to our previous work [20; 21; 22]. Table 4 shows the preset parameters of Weldon's ARQ protocol at the \(i\)th transmission for Scheme 1 [20; 21; 22]. The computer simulation assumes that there is no error in SHR and PHR. That is, only the characteristics of PSDU are evaluated. In computer simulations of the compared schemes, Data A was transmitted using the default mode with (63, 51) BCH code in IEEE Std. 802.15.6 and the error control scheme utilizing the (63, 55) Reed-Solomon code in IEEE Std. 802.15.4a with ordinary ARQ, whereas Data B was transmitted using the high QoS mode with (126, 63) shortened BCH code and type-II hybrid ARQ, and then the error control scheme utilizing the concatenated code consisting of the (63, 55) Reed-Solomon code and the convolutional code whose constraint length is three and coding rate is 1/2 in IEEE Std. 802.15.4a with ordinary ARQ [17; 19]. In these computer simulations, the IEEE model CM 3 is applied as a channel model, which is targeted for wearable WBAN and includes multi-path fading [33]. Then, a hospital room case in the IEEE model CM3 is utilized as a path loss model [33]. The path loss is expressed as follows:  
\[PL(d)=a\times log_{10}d+b+N \tag{15}\]  
Here, \(a\) and \(b\) are linear fitting coefficients, \(d\) is the communication distance (millimeter, mm) between a transmitter and a receiver, and \(N\) is a normally distributed variable with zero mean and standard deviation \(\sigma_{N}\). Details about these parameters can be found in the literature [33]. Using \(PL(d)\), the signal to noise ratio (SNR) at a receiver can be expressed as follows:  
Figure 9: Bit error probability in each coding rate. \[(\text{SNR})_{dB}=P_{r}-P_{n} \tag{16}\] \[P_{r}=P_{t}-PL(d)\] (17) \[P_{n}=N_{thermal}+\left(NF\right)_{dB}+I_{dB} \tag{18}\]  
where \(P_{t}\) is transmission power and \(N_{thermal}\) is thermal noise. The average path loss is shown in Figure 10. It is assumed that the channel condition does not change until the two-hop relay is completed or the two-hop relay fails beyond the maximum number of retransmissions. In addition, each case of the proposed scheme in each hop is summarized in Table 5.  
Then, energy efficiency \(\eta\) is derived from our previous work [22] as follows:  
\[\eta\equiv\frac{P_{succ}L_{info}}{E_{link,N1\to N2}+E_{link,N2\to H}} \tag{19}\] \[E_{link,~{}A\to B}=(T_{\text{TOT}}+N_{tx}T_{ACK})(P_{tx,RF}+P_{tx,circ}+P_ {rx})+N_{tx}(\varepsilon_{enc}+\varepsilon_{dec}) \tag{20}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \(i\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** \\ \hline Data A & 1 & 4 & 4 & 5 & 5 & 6 & 6 & 7 & 7 & 8 & 8 \\ Data B & 1 & 1 & 2 & 3 & 4 & - & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Preset number of data copies in Weldon’s ARQ \(n_{i}\).