## 5 Simulation and Results Analysis
### Results Analysis  
In order to compare the detection probability of the IA-SPM with the TSPM and the ASPM, the Monte Carlo simulation is used to analyze the models. In the following experiment, we did the simulation 1000 times in each period  
In this paper, the efficiency of the IA-SPM is determined by the average number of samples. The higher the number of samples, the higher the cost of the IA-SPM, the larger the parameter \(\mu\), and the higher the linearity of the number of samples. Therefore, in order to jointly optimize the number of samples and the probability of detection, we compare the selection of parameter \(\mu\). According to the detection probability of \(\mu\) under different values, as shown below Figure 5.  
It can be seen from the figure that both the detection probabilities of IA-SPM and ASPM are influenced by the parameter \(\mu\). The detection probabilities of these two algorithms showed a monotonically increasing trend with the increase of \(\mu\). However, when the value of \(\mu\) exceeds a certain threshold, the detection probabilities of both algorithms tend to be stable. In addition, the maximum detection probability of IA-SPM algorithm is better than ASPM algorithm. Therefore, in the following experiment, we set the parameter \(\mu=3\) and the SNR was used to simulate the channel's time-varying characteristics within a certain range.  
First, we compared the improvement of the IA-SPM algorithm with respect to the TSPM algorithm. The simulation results are shown in Figure 6.  
We found that in any kind of detection algorithm the greater the SNR, the greater the detection probability; and the greater the false dismissal probability, the higher the probability of detection. At the same time, it can be clearly seen that the detection probability of the IA-SPM is superior to that of the TSPM under the same conditions.  
Figure 5: Comparison of the IA-SPM vs. the TSPM with different \(\mu\).  
Figure 6: Comparison of the IA-SPM vs. the TSPM with different false dismissal probabilities.  
Then, we compared the detection probability of the IA-SPM algorithm with the ASPM algorithm under the same SNR conditions. The simulation results are shown in Figure 7.  
As the result shows, the detection probability of the IA-SPM is better than that of the ASPM. Especially under low SNR conditions, the IA-SPM is better than the ASPM by 10-15%. With the increase of the SNR, the detection efficiency of the two algorithms tends to be consistent. This data shows that the IA-SPM is more suitable for time-varying channels.  
Finally, we set the SNR to be equal to \(-15\), \(-10\), and \(-8\) dB. Under these three conditions, we compared the differences of the false dismissal probability between the IA-SPM algorithm and the TSPM algorithm. The simulation results are shown in Figure 8.  
Through the above figures we can find that, in the same case, with the increase of the false dismissal probability, the probability of detection, and the SNR increase at the same time. So, we can see that the results of the IA-SPM are much higher than that of the TSPM.  
Figure 8: Comparison of the IA-SPM vs. the TSPM at different SNR values.  
Figure 7: The IA-SPM vs. the ASPM.