# Optimization Scheme for Modulation of Data Transmission Module in Endoscopic Capsule
## 4 Numerical Result  
This section presents an analysis of the performance of systems utilizing the proposed constellation scheme under various system parameters. The distribution parameters corresponding to different distances are shown as Table 5. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Modulation** & **Multipliers** & **Delay Units** & **Modulator** & **Selection** \\ \hline MIP-MDCSK & 0 & \(M\) & \(M\) & comparator, Hilbert filter & position \\ \hline MDCSK & 0 & 0 & 1 & Hilbert filter & none \\ \hline MCS-DCSK & \(N_{b}+1\) & \(N_{b}+1\) & 0 & code shift detector, Hilbert filter & Walsh code \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparisons of Receiver Computational Complexity. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & & \multicolumn{4}{c}{**SE**} \\ \hline
**Modulation** & **MIP-MDCSK** & **IP-MDCSK** & **MCS-DCSK** & **MDCSK** \\ \hline expression & \(\frac{m_{c}+1+m_{c}}{R(1+2^{m_{c}+1})B}\) & \(\frac{m_{c}+n_{c}}{R(1+2^{m_{c}})B}\) & \(\frac{n_{c}}{(2^{m_{c}+1})RB}\) & \(\frac{m_{c}}{2 RB}\) \\ numerical value & \(m_{c}=2,n_{c}=2,t=2,R=B=1\) & 0.89 & 0.8 & 0.4 & 1 \\ \(m_{c}=3,n_{c}=3,t=3,R=B=1\) & 0.71 & 0.67 & 0.33 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of spectral efficiency (SE). \begin{table}
\begin{tabular}{l l l} \hline \hline
**Depth (mm)** & **(\(\mu\), \(\sigma\))** \\ \hline
120 & (2.7, 4.9) \\ \hline
80 & (8.2, 6.6 ) \\ \hline
40 & (5.3, 8.1 ) \\ \hline
20 & (3.5, 6.2) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The distribution parameters corresponding to depth [39]. To investigate the BER performance of the system in an in-body channel environment, we examine the effects of parameters such as \(\beta\), \(M\), \(n\), and the in-body channel parameter depth. Figure 3 demonstrates the performance of the 2 IP-MDCSK system under in-body channel conditions with system parameters set as depth = 80 mm, \(M\) = 4, and \(n\) = 2. From the figure, it is evident that the overall BER performance deteriorates as \(\beta\) increases. However, when \(\beta\) = 32, the BER performance is significantly worse compared to other values. This can be attributed to the characteristics of the chaotic signal. At smaller \(\beta\) values, the system struggles to effectively exhibit the correlation properties, leading to a higher likelihood of bit errors. Figure 4 illustrates the impact of different values of M and \(n_{c}\) on the performance of the MIP-MDCSK system under varying depth conditions within an in-body environment. Overall, as M increases, the BER performance deteriorates, while an increase in \(n_{c}\) leads to improved system performance. Moreover, the influence of M on the BER performance is significantly more pronounced than that of \(n_{c}\). For instance, in Figure 4a, at a BER of \(10^{-2}\), the gap between 2 IP-4 DCSK and 4 IP-4 DCSK is 1 dB, whereas the gap between 2 IP-4 DCSK and 2 IP-BDCSK at the same BER is 2.5 dB. This clearly demonstrates that the constellation parameters have a much greater impact on the BER performance than the IP components. Regarding the effect of depth on the system, a comparison from Figure 4a,b shows that when depth = 80 mm, the overall BER performance is better than when depth = 20 mm. At a BER of \(10^{-4}\), the 2 IP-4 DCSK system shows a gain of approximately 1 dB at depth = 80 mm compared to depth = 20 mm. This suggests that a greater depth brings the system closer to the in-body channel environment, indicating that the system is better suited for in-body channel conditions. Further discussion on the impact of depth on the system is provided in Figure 5. As shown in the figure, the BER performance at depth = 80 mm is significantly better than at depth = 20 mm. At depth = 20 mm, when the \(E_{b}/N_{0}\) increases to a certain level, the system gradually experiences an error floor. The SNR value at which the error floor begins to appear shifts to a lower value as M decreases.