## 5 Results and Discussion

Table 4: The simulation parameters of D-PSO algorithm. Figure 5: The average channel gain changes with the distance to the sink node in WSN. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Mark** & **Value** \\ \hline Center frequency & \(f_{0}\) & 900 MHz \\ Interval of the subcarriers & \(\Delta F\) & 15 kHz \\ Spreading code type & / & Walsh Hadamard \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The simulation parameters of MC-CDMA. Figure 6 illustrates the average BER of source sensors _versus_ total input SNR \(E/\sigma^{2}\) for the proposed WSN in an underground coal mine when the D-MSD algorithm and D-PSO algorithm are applied respectively. From Figure 6, it can be clearly observed that the average BER performance of the source sensors is improved significantly when the time-frequency coded cooperative transmission is applied both for D-MSD algorithm and D-PSO algorithm. For example, the time-frequency coded cooperative transmission outperforms none-cooperative transmission by 3 dB and 5 dB for the D-MSD algorithm and D-PSO algorithm, respectively, when the average BER is 0.25. From Figure 6, it can also be observed that the D-PSO algorithm outperforms the D-MSD algorithm by 3 dB for the time-frequency coded cooperative transmission when the average BER is 0.25. Figure 7 demonstrates the average BER of source sensors _versus_ total input SNR \(E/\sigma^{2}\) with equal and the proposed power allocation scheme when the D-MSD algorithm and D-PSO algorithm are applied to the time-frequency coded cooperative MC-CDMA WSN, respectively. From Figure 7, it can be observed that the average BER performance of source sensors is much better with the proposed power allocation scheme than that with equal power allocation scheme both for the D-MSD algorithm and D-PSO algorithm. This is because an equal power allocation scheme does not consider the channel conditions of the source sensor and its cooperative sensor. When the channel conditions from source sensor to the sink node are poor, the average BER of the source sensor will increase since the transmission power of the source sensor has not been correspondingly increased. Consequently, the overall performance of the proposed WSN will definitely be influenced. Therefore, the limited energy of wireless sensors based on MC-CDMA can be fully made use of with the proposed power allocation scheme to improve the performance of the WSN. Figure 8 depicts the average BER _versus_ total input SNR \(E/\sigma^{2}\) when the number of source sensors is 4, 8, and 16, respectively. Here, both the D-MSD algorithm and D-PSO algorithm are applied to the time-frequency coded cooperative MC-CDMA WSN. From Figure 8, it can be observed that the average BER of source sensors increases when the number of source sensors increases. This is because the MAI increases when the number of source sensors increases. For example, when the number of source sensors \(K\) varies from 4 to 16, the average BER of source sensors increases about 0.05 for  
Figure 6: Influence of different transmission manner to the average BER. \(K=8\), \(N_{c}=256\), \(E_{{}_{S_{k}}}=E_{{}_{R_{k}}}\). 38 dB with the D-MSD algorithm. However, the average BER of source sensors increases only 0.02 for D-PSO algorithm at the same conditions. Obviously, it will benefit a lot for the average BER of source sensors to apply the D-PSO algorithm to the time-frequency coded cooperative MC-CDMA WSN in underground coal mines.