## 5 Characteristics of MMW Fuze Echo Signal under Rainfall Conditions  
To present the low-frequency noise in the echo signal spectrum more intuitively and make it closer to the actual detection situation, a fixed delay time characterized by the signal propagation delay in the MMW fuze hardware system is added during the simulation process. Based on the expression of the beat signal, the simulation parameters are set as shown in Table 2.  
The time domain and frequency domain diagrams of the echo beat signal at a target distance of 9 m without rain are shown in Figure 5. In the frequency spectrum, there is only one prominent peak with a frequency of 7.60 MHz, representing the target echo signal. Therefore, the target distance is as follows:  
\[R=(T\!c/4\Delta F)\cdot 2\beta\tau_{t}-c\tau_{0}/2=9.05\ \mathrm{m} \tag{36}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Modulation bandwidth \(\Delta F\) & 150 MHz \\ Modulation period T & 2.5 μs \\ Operating frequency \(f_{c}\) & 24, 35, 60 GHz \\ Beam width \(\theta_{3 dB}\) & 120\({}^{\circ}\) \\ Fixed hardware signal delay \(\tau_{0}\) & 3 ns \\ Temperature & 25 \({}^{\circ}\)C \\ Rainfall amount & 16, 50 mm/h \\ Target scattering factor \(\alpha\) & 48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MMW fuze simulation parameters. indicating that the Monte Carlo simulation model produces accurate simulation results. The beat signal spectrum under a rainfall rate of 16 mm/h and operating frequency of 35 GHz with distances of 6, 9, and 12 m is simulated, as shown in Figure 6a-c. The beat signal spectrum under a rainfall rate of 50 mm/h and operating frequency of 35 GHz with distances of 6, 9, and 12 m is simulated, as shown in Figure 6d-f. The beat signal spectrum under a rainfall rate of 50 mm/h and operating frequency of 60 GHz with distances of 6, 9, and 12 m is simulated, as shown in Figure 6g-i. Two distinct peaks are observed in all spectra. The lower-frequency peak corresponds to the rain backscatter noise, whereas the higher-frequency peak represents the target signal. Figure 7a displays the amplitudes of the target echo signal, which decrease significantly with increasing distance. Due to the minimal attenuation of MMW signals and the concentration of scattered signals at the lower end of the spectrum, neither frequency nor rainfall significantly affects the amplitude of the target echo signal. Notably, the change in the radar cross-section area of the target due to different fuze operating frequencies are not considered in this simulation. Consequently, the amplitude of the target echo signal remains constant across different frequencies in the simulation results. The visibility of the target signal in the spectrum, as shown in Figure 6,indicates that the MMW fuze can effectively detect close-range targets with strong reflections even under rainy conditions. The rain backscatter noise corresponds to a constant frequency, and its amplitude is shown in Figure 7b. The rain backscatter noise increases with the increase in rainfall intensity and frequency. However, the amplitude of the rain backscatter noise is essentially the same under three different rainfall and operating frequency conditions. Additionally, the bottom noise on the echo signal spectrum in Figure 6 increases significantly with increasing rainfall and frequency, caused by the multiple scattering of MMW signals by raindrops in rainy environments. The signal-to-noise ratio (SNR) is defined as the ratio of the target signal amplitude to the maximum value of the bottom noise. When the target distance is 9 m, the SNR corresponding to the three combinations of rainfall and frequency are 19.9, 12.8, and 6.0 dB, respectively.