## 6 Results and Discussion
### Performance Evaluation by Computer Simulation
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Detail** \\ \hline Channel model & IEEE model CM3 \\ Path loss model & IEEE model CM3 \\ Bandwidth (\(BW\)) & 499.2 MHz \\ Central frequency (\(f_{c}\)) & 3993.6 MHz \\ Pulse shape & Gaussian mono pulse \\ Pulse duration (\(T_{p}\)) & 2.003 ns \\ Modulation & DBPSK \\ FEC & \(r_{c}=8/9\) to \(1/16\), \(K=3\) \\ Convolutional codes \\ Decoding & Soft decision \\ \multicolumn{2}{c}{Viterbi decoding} \\ ARQ protocol & Weldon’s ARQ \\ Power spectral density (\(P_{ad}\)) & \(-41.3\) dBm/MHz \\ Thermal noise density (\(N_{0}\)) & \(-174\) dBm/Hz \\ Implementation losses (\(I\)) & 3 dB \\ Receiver noise figure (\(NF\)) & 5 dB \\ Tx RF power consumption (\(P_{tx,RF}\)) & 37 \(\mu\)W \\ Tx circ. power consumption (\(P_{tx,circ}\)) & 2 mW \\ Rx power consumption (\(P_{rx}\)) & 20 mW \\ Number of pulses per bit (\(N_{cp}\)) & 2 \\ Integer number of pulse waveform positions (\(N_{nr}\)) & 32 \\ Uncoded data rate (\(R\)) & 7.8 Mbps \\ Synch. header duration (\(T_{SHR}\)) & 40.32 us \\ PHY header durations (\(T_{PHR}\)) & 82.052 us \\ Information bit length (\(L_{info}\)) & & 306 bits \\ ACK length (\(L_{ACK}\)) & & 7 bytes \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main simulation parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & **N1**\(\rightarrow\)**N2** & **N2**\(\rightarrow\)**H** \\ \hline Case 1 & Scheme 1 & Scheme 1 \\ Case 2 & Scheme 1 & Scheme 2 \\ Case 3 & Scheme 2 & Scheme 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Cases for the proposed scheme of each hop. \[T_{\text{TOT}}=T_{SHR}+T_{PHR}+\sum_{i=1}^{tr_{A\to B}}\frac{L_{ PSDU,i}}{R} \tag{21}\]  
Here, \(E_{link,~{}A\to B}\) is the energy consumption of the communication link at each hop and \(P_{succ}\) is the transmission success ratio, \(T_{TOT}\) is the total duration of packet transmission, \(T_{ACK}\) is the duration of ACK, \(L_{ PSDU,i}\) is the length of PSDU, \(N_{tx}\) is the number of transmission, \(P_{tx,RF}\) is the transmitter RF power consumption, \(P_{tx,circ}\) is the transmitter circuitry power consumption, \(P_{rx}\) is the receiver power consumption, and \(\varepsilon_{enc}\) and \(\varepsilon_{dec}\) are the encoding and decoding energies, respectively [34; 35; 36; 37]. Figures 11-13 show the performance results when the distance of the first hop \(d_{1 st}\) is changed from 10 centimeters (cm) to 3 m and the distance of the second hop \(d_{2 nd}\) is constant (\(d_{2 nd}\) = 40 cm). In this scenario, it can be said that the performance in the range in which the WBAN mainly operates (10 cm\(\sim\)1.5 m) and certain limitations of the WBAN system (1.5 m\(\sim\)2.3 m) are evaluated. PDFR means the ratio at which the two-hop relay failed beyond the maximum number of retransmissions. As can be seen, the proposed scheme satisfies the QoS requirements for data A and B as shown in Table 1, while IEEE Std. 802.15.6 and 15.4a do not. Hence, the proposed method can improve PER of Data A more, while it can improve the energy efficiency and the number of transmissions of Data B more. Conversely, Data B has better performances with respect to both standard schemes. The reason is that those standard schemes are not basically designed so that any QoSs can be satisfied. Hence, it can be considered that the performances of each mode of IEEE Std. 802.15.6 and error control schemes of IEEE Std. 802.15.4a were simply expressed. Also, that is one of problems of these standard schemes. Cases 2 and 3 show better energy efficiency and average number of transmissions than Case 1, because the coding rate of Case 2 and Case 3 is set appropriately for the channel SNR and the number of retransmissions is reduced by utilizing Scheme 2, while Case 1 uses only Scheme 1 and it requires a larger number of retransmissions. However, there is not a large difference between Cases 2 and 3 because \(d_{2 nd}\) is short and the error correcting capability of coding rate \(r_{c}\) = 8/9 at the first transmission can reduce bit errors sufficiently.