## 6 Results and Discussion  
### Analysis of the Simulation Results  
The input signal waveform is shown in Figure 7. The input signal uses a random digital signal \(\text{g1}=\text{a}=[\text{zeros}(1,20)\text{ }1\text{ zeros}(1,29)]\), inverting a to obtain the signal g2. These two signals are then sampled at 2500. Finally, FSK modulation is performed to obtain two carriers. The input signal is obtained by summing the two carriers. In addition, because of the delay of each intrinsic signal, it is necessary to complement the zero before and after the signal when the signals are superimposed, so that the length of each intrinsic signal is the same. The relevant parameters of the intrinsic path model are shown in Table 2.  
The attenuation and delay of each intrinsic path are shown in Table 3; a negative sign in a value indicates a phase change of 180\({}^{\circ}\). Figure 8 shows the output signal of the channel, which can be seen as a signal with severe interference and a significant time delay. Because the output waveform is a superposition of output waveforms from different eigenpaths, the features of every sub-waveform are eventually displayed on the total output waveform. In addition, Gaussian narrowband noise is present in each eigenpath signal, so the amplitude of the output waveform is modulated, and its envelope is random narrowband noise. This is the reason the waveform of the total output signal will show a random undulation phenomenon. The speed of sound propagation in seawater is about 1500 m/s, but sound waves are affected by a variety of  
Figure 6: The algorithm flow chart. factors, such as sea depth, salinity, temperature, etc. The variation in the speed of sound, which in turn leads to the generation of the propagation time delay, is expressed as follows:  
\[\text{C}=1449+4.6\text{T}-0.055\text{T}^{2}+0.0003\text{T}^{3}+(1.34-0.010\text{ T})(\text{S}-35)+0.017\text{Z} \tag{23}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Channel Parameter** & **Parameter Value** \\ \hline Sea depth/km & 0.1 \\ \hline Emitter depth/km & 0.05 \\ \hline Receiver depth/km & 0.06 \\ \hline Transmission distance/km & 2 \\ \hline Surface reflection coefficient & 0.5 \\ \hline Bottom reflection coefficient & 0.9 \\ \hline Number of intrinsic paths & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The relevant parameters of the intrinsic path model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Intrinsic Path** & **Attenuation** & **Delay(s)** \\ \hline
1 & 0.48326 & 0 \\ \hline
2 & \(-0.43472\) & 0.00131 \\ \hline
3 & \(-0.24155\) & 0.00087 \\ \hline
4 & 0.21715 & 0.00394 \\ \hline
5 & 0.21708 & 0.004  
C is the speed of sound (m/s), T is the temperature (\({}^{\circ}\)C), S is the salinity, and Z is the depth (m). In the simulation process of the proposed algorithm, there are three users participating in the collaborative detection algorithm, there were 1000 Monte Carlo simulation cycles, the false alarm probability pf is 1 \(\times\) 10\({}^{-5}\), and the missed detection probability pm is 0.01. The numbers of sample points are N = 4000, and N1 = 1000. Figures 9-11 show the experimental comparison between the proposed algorithm and the various traditional algorithms in this paper to verify the effectiveness of the proposed algorithm from different aspects. Three different simulation comparison experiments were conducted separately. First, the proposed algorithm was compared with two algorithms with the same number of users but a different number of thresholds. Second, it was compared with two traditional collaborative energy detection algorithms. Finally, because the parameter k in the k-verdict criterion in the collaborative detection algorithm is adjustable, a simulation comparison was performed for the case of a different number of users participating in the verdict. Figure 8: The output signal of the channel. Figure 9: Simulation comparison chart.