## 4 Numerical Results and Discussion
### Water Pool Experiments  
In order to verify the practical feasibility of the MSSS-I/Q-IM system, this subsection carried out pool experiments. The inner wall of the pool is smooth, and the size is small. Compared with the marine environment, the multipath effect is more severe, but there is no influence of environmental noise and it is almost time-invariant. Table 3 shows the parameters of the pool experiments. Through the correlation calculation of the synchronization signal, the CIRs of the channel can be estimated. In the experiment, information blocks with different parameter conditions are concatenated together to form a data packet for transmission. In addition, a synchronization signal is added before each block to estimate the CIRs. Figure 7 shows the CIRs of a data packet at different times. It can be seen from the figure that the channel has a weak variability with time and a large number of multipaths. In the experiments, due to the use of the attenuator, the amplitude of the signal can be adjusted flexibly. Figure 8 shows the waveform of the received signal for a data packet under different attenuation factors; the attenuation factors are 10, 20, and 50. Table 4 shows the BER comparison of the MSSS and MSSS-I/Q-IM systems with different parameter \(J\) under different attenuation factors. With the continuous increasing of the attenuation degree, the number of bit errors increases. This is because the signal amplitude is continuously reduced, and the interference caused by noise becomes more serious, which affects the correct demodulation. When \(J=2\), the BER of the MSSS-I/Q-IM system is slightly higher than that of the MSSS system, and when \(J=1\), the BER performance of the MSSS system is much improved. This shows that the MSSS-I/Q-IM system can adjust the BER performance by changing the number of superimposed sequences over a UWA channel and realize the trade-off between the communication rate and the BER performance. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Distance & 10 m \\ \hline Sample Rate & 100 kHz \\ \hline Carrier Frequency & 25 kHz \\ \hline Synchronization Signal & LFM Signal \\ \hline Bandwidth & 6 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of water pool experiments. Figure 7: The CIRs measured in the pool experiments. Table 5 shows the effect of the shift step size on the BER of the MSSS-I/Q-IM system. Other parameters of the system are set as \(M=1023\), \(J_{max}=5\), and \(J=2\), so the communication rates with different \(L\) are the same. It can be found that, compared with other values, the system has the best BER performance for \(L=200\). The bit errors do not appear until the attenuation factor is 50 for \(L=200\). For other values, the bit error already exists when the attenuation factor is 20. Moreover, by comparing the BER when \(L=150\) and \(L=100\), it is noted that the larger the \(L\) is, the better the BER performance is, which indicates that selecting an appropriate shift step is conducive to improving the reliability of the system. Table 6 shows the effect of the spreading factor \(M\) on the BER of the MSSS-I/Q-IM system. According to the table, it is obvious that the larger the spreading factor is, the lower the BER is. However, the duration of data transmission with \(M=511\) is shorter, and the transmission rate is nearly twice that in the case of \(M=1023\). Therefore, in practical application, the change of the spreading factor can affect the BER performance remarkably. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Attenuation Factor**} & \multirow{2}{*}{**Estimated SNR**} & \multirow{2}{*}{**MSSS**} & \multicolumn{4}{c}{**MSSS-I/Q-IM**} \\ \cline{3-6}  & & & \(\mathbf{J=3}\) & \(\mathbf{J=2}\) & \(\mathbf{J=1}\) \\ \hline
10 & \(-10.62\) & 0 & 0 & 0 & 0 \\ \hline
20 & \(-11.61\) & 0 & 0 & 0 & 0 \\ \hline
50 & \(-14.83\) & 0.0650 & 0.1610 & 0.0772 & 0.0027 \\ \hline
100 & \(-20.55\) & 0.2592 & 0.3560 & 0.3166 & 0.1347 \\ \hline \hline \end{tabular}
\end{table}