## 4 Simulation and Comparison of FMCW Laser Target Characteristics  
### Simulation Process of Single Laser Based on 3D Particle System  
Based on the relationship between smoke concentration and visibility, it is reasonable to characterize smoke concentration through smoke visibility [21]. Under the condition of a constant smoke visibility, the concentration of smoke particles depends on the number, particle size, and spatial location of smoke particles in each localized volume of space. Variability exists in a smoke environment where the particles are uniformly distributed, and this will have different effects on the direction of the collision transmission of photons, as shown in Figure 7.  
By comparing Figure 7a with Figure 7b, Figure 7c, and Figure 7d, respectively, the variability of the smoke environment can have an uncertain impact on the probability of collision between photons and smoke particles, due to changes in the number of collisions, particle size, and relative spatial positions of the smoke particles, which is specifically expressed as a change in the number of collisions occurring based on Equation (15). In this case, the type of collision angle is difficult to determine, while the other variables are also difficult to obtain directly, which is not useful for determining a specific expression for the laser echo power signal. Since the collision angle is determined based on the interaction between three-dimensional particles, the simulation model also needs to be implemented in a three-dimensional virtual space. Unity3D is a highly integrated virtual reality platform that has a well-developed physics system and also includes a specialized particle system, in which the simulation models can be constructed [22; 23]. Therefore, based on the long-term support version of Unity, such as 2017.4.40c1, it is possible to co-simulate the laser transceiver system and the smoke particle environment based on Monte-Carlo method. Using the  
Figure 7: Effects of changes in the number of smoke particles, particle size, and spatial location on the photon transmission process: (**a**) initial situation, (**b**) changes in the number of smoke particles, (**c**) changes in the particle size, (**d**) changes in the spatial location of smoke particles. output of the laser echo signal to obtain the fuze target characteristics, this method has been applied in the field of laser fuze target characteristic simulation and achieved good simulation results in our previous works [15; 24]. Based on Equation (16), the specific form of the target echo power signal depends on the amplitude coefficient of the received power signal, which is related to the transmitting power amplitude, which is expressed in terms of the number of particles as  
\[N_{photon}(t)=\frac{P_{\mathrm{T}}S_{T}(t)}{\mu_{p}} \tag{20}\]  
where \(\mu_{p}\) is the conversion factor. The laser emission power signal is transformed into a functional form based on the number of particles emitted:  
\[S_{R}(t)=\sum_{i=1}^{N_{laser}}Amp_{i}(\theta_{ps1},\theta_{ps2},\theta_{ps}) \times\mu_{p}N_{photon}(t-\tau_{Ni}) \tag{21}\]  
The particle system simulation can output a laser echo simulation signal, with the beat signal and its spectrum, and the simulation parameters are shown in Table 1 and the process is shown in Figure 8.  
The beat frequency at a target distance of 3 m is expressed based on Equation (19) as  
\[f_{\mathrm{B}}=\frac{4B}{cT_{m}}R=\frac{4\times 150\;\mathrm{MHz}}{3\times 10^{8 }\;\mathrm{m/s}\times 0.5\;\mathrm{ms}}\times 3\;\mathrm{m}=12\;\mathrm{kHz} \tag{22}\]  
Based on smoke particle concentration \(c_{smoke}\)[21], the number of smoke particles generated can be adjusted as  
\[n_{smoke}=c_{smoke}\times\eta_{mod}=\frac{c_{type}\times\eta_{mod}}{V^{\gamma type}} \tag{23}\]  
where \(c_{type}\) and \(y_{type}\) are constants, and their values are 37.3 and 1.07, respectively. \(\eta_{mod}\) is the coefficient for rounding the number of smoke particles.