## 4 Simulation and Comparison of FMCW Laser Target Characteristics
### Echo Characteristic Simulation Results Under Smoke Particle Characteristic Variation  
Particle collision probability is affected by the number, particle size, and location of smoke particles, which directly results in a change of the particle collision scattering type. The amplitude of the smoke echo component and the target echo component of the laser echo signal will also be changed. Therefore, it is necessary to analyze the effect of variation in smoke particle characteristics on the echo characteristics of laser targets. Under the condition of a single laser emission, the simulation results of the amplitude-frequency characteristics based on the beat signal spectra are shown in Figures 10, 11 and 12, respectively, based on the parameters in Table 1. The analysis is described as follows:  
Figure 9: Setup and process of laser prototype test and virtual particle system simulation: (**a**) Smoke particle count reduction, (**b**) smoke particle size enlargement, (**c**) smoke particle position downshift. 0, and the average value of the maximum peak frequency was 5 kHz and 12 kHz, respectively. Peak frequency migration and fluctuations occurred in the spectrum of the beat signal, as shown in the solid line area. In addition, frequency migration and fluctuations were affected by changes in visibility and only occurred in low-visibility smoke environments, even including the appearance of false alarms, such as the dotted line area in Figure 10a. For the high-visibility case, fluctuations in the amplitude of the maximum spectral peak occurred compared to the initial condition, as shown in Figure 10b. 2. From Figure 11, the particle size difference increased the possibility of photon collision with smoke particles within the scene. At the same time, the laser penetration through the smoke was limited, and the laser echo characteristics were affected. The percentage of the maximum peak frequency of the beat signal spectrum changes were 89% and 100%, and the average value of the maximum peak frequency was 3 kHz and 8 kHz, respectively. Peak frequency migration and fluctuations occurred in the spectrum of the beat signal, which could lead to missed alarms in high visibility, as shown in the solid line area. 3. From Figure 12, the height differences affected the initial collision of photons with smoke particles within the scene. The ability of the laser to penetrate through the smoke was affected in an indeterminate way. Significant changes in the type of photon collision transmission occurred and the laser echo characteristics were more affected. In this case, the percentage changes in the maximum peak frequency of the beat signal spectrum were all 100%, and the average value of the maximum peak frequency was 8 kHz. Peak frequency migration and fluctuations occurred in the beat signal spectrum, as well as missed alarms in high visibility, as shown in the solid line area in Figure 12. Moreover, the lower the visibility, the larger the effect of the smoke particle position on the frequency migration and fluctuation. In summary, the main effect of the beat signal spectrum peak fluctuation was the false and missed alarms caused by the difference in amplitude, which was analyzed here by comparing the initial amplitude with the average spectral amplitude under the action of each particle characteristic. The results of the amplitude comparison and average amplitude at each frequency are shown in Figure 13.  
From Figure 13, the positional difference had the largest effect on the peak amplitude of the laser echo signal under low-visibility conditions. The average growth rate in amplitude  
Figure 13: Comparison of average results of beat signal spectral amplitudes in the case of amplitude variability. was about 75.4%. The number and particle size characteristics were about 16.2% and 20.6%, respectively. It is important to pay attention to the effects of changes in the number and location of smoke particles on the echo characteristics.