## 5 Results and Discussion  
In this section, the average BER performance of the wireless sensor nodes for the time-frequency coded cooperative MC-CDMA WSN in uplinks is evaluated by Monte Carlo simulation, which is carried out via Matlab simulation on an IBM server with Linux environment at the Wireless Sensor Networks Laboratory of Beijing Jiaotong University. As shown in Figure 1, assume that the sink node in the considered WSN is located at coordinates (2.5, 1.5, 0) and the coordinates of a wireless sensor node are (2.5, \(-1.5\), \(z\)), \(0<z\leq 600\). It is also assumed that the number of source sensors is equal to the spreading gain, _i.e._, \(K=G\). Meanwhile, the channel state information (CSI) between the transmitting and receiving sensors is available. The simulation parameters of the mine tunnel, time-frequency coding of wireless sensor node, MC-CDMA modulation and D-PSO algorithm are shown in Tables 1-4, respectively. Since the channel gain is different for different subcarrier of MC-CDMA, it is more reasonable and simple to apply total input signal noise ratio (SNR) namely \(E/\sigma^{2}\) to describe the BER performance [25,33]. \begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Mark** & **Value** \\ \hline Permittivity of vertical wall & \(\varepsilon_{v}\) & 5 \\ Permittivity of horizontal wall & \(\varepsilon_{h}\) & 5 \\ Permittivity of the air & \(\varepsilon_{a}\) & 1 \\ Conductivity of vertical wall & \(\sigma_{v}\) & 0.01 \\ Conductivity of horizontal wall & \(\sigma_{h}\) & 0.01 \\ Conductivity of the air & \(\sigma_{a}\) & 0 \\ Width of the mine tunnel & 2 \(a\) & 10 m \\ Height of the mine tunnel & 2 \(b\) & 6 m \\ Coverage length of WSN & \(L\) & 1200 m \\ Antenna gain of transmitting sensor & \(G_{t}\) & 3 dB \\ Antenna gain of receiving sensor & \(G_{r}\) & 18 dB \\ Permittivity of vacuum space & \(\varepsilon_{0}\) & \(8.854\times 10^{-12}\) \\ Permeability of the wall and air & \(\mu_{0}\) & \(1.256\times 10^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The simulation parameters of the mine tunnel. \begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Mark** & **Value** \\ \hline Length of information bit stream & \(F=N_{\omega}/G^{*}R-n\) & 29 \\ Length of channel coding frame & \(M=N_{\omega}/G^{*}R\) & 32 \\ Length of CRC check bits (FCS) & \(n\) & 3 \\ Rate of convolutional coding & \(R\) & 1/2 \\ Modulation type & / & K \\ \hline \end{tabular}
\end{table} 
Table 2: The simulation parameters of time-frequency coding. The average channel gain between the wireless sensor node and the sink node of MC-CDMA that varies with the distance is shown in Figure 5a. It can be seen that the average channel gain presents a damped curve overall with some fluctuations. In some areas of the considered WSN, the channel gain is relatively higher, such as when sensors are less than 100 m away from the sink node. However, the channel gain is relatively lower in some area, such as when sensors are more than 500 m away from the sink node. Assume that the channel gain threshold \(\eta\) is \(-13\) dB. Consequently, the alternative cooperative sensors are distributed in the area where the channel gain is above the threshold of \(-13\) dB. Figure 5b describes the transmission pattern of sensors according to the threshold \(\eta\), where \"0\" represents none-cooperative transmission because of better channel conditions; \"1\" represents cooperative transmission because of the poor channel conditions. Assume that \(K\) source sensors are randomly distributed between 250 m-400 m and \(J\) alternative cooperative sensors are randomly distributed between 250 m-400 m and 20 m-180 m, \(J\!>\!K\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Mark** & **Value** \\ \hline Learning factor & \(c_{1}\) & 2 \\ Learning factor & \(c_{2}\) & 2 \\ Inertia weight coefficient & \(w\) & 0.99 \\ Total number of particles & \(N_{p}\) & 20 \\ Iteration time & \(Max\_dt\) & 30 \\ Maximum velocity & \(V_{max}\) & 2 \\ \hline \hline \end{tabular}
\end{table}