# Adaptive Suppression Method of LiDAR Background Noise Based on Threshold Detection
## 2 Influence of Background Noise
According to each noise formula [29], it can be obtained as the following:  
\[i_{n}^{2}=2 eBM^{2}F[R_{o}(P_{s}+P_{b})+i_{db}]+2 eBi_{ds}+\frac{4 KTB}{R_{L}}+i_ {Na}^{2} \tag{3}\]  
where e denotes the elementary charge, B is the noise bandwidth, M is the APD multiplication factor, F is the APD excess noise factor, \(\mathrm{R_{o}}\) is the APD unit multiplication factor response rate, \(\mathrm{P_{s}}\) is the received signal power, \(\mathrm{i_{db}}\) is the multiplied (bulk) of the dark current, \(\mathrm{i_{ds}}\) is the un-multiplied (surface) of the dark current, K is the Boltzmann constant, T is the temperature and \(\mathrm{R_{L}}\) is the equivalent load resistance. Based on the background radiation results in Figure 3, the noise changes in the receiver are analyzed through Formula (3), as shown in Figure 4. The simulation parameters are shown in Appendix A Table A1, and the proportion of background radiation to total noise current is shown in Appendix A Figure A1. Figure 4: Variation in total noise current. Figure 3: Simulation results of background radiation. The influence of background noise on LiDAR can be analyzed based on the SNR [30]. For the pulse detection, the SNR of the system is the ratio of the out current or voltage between the signal and the noise:  
\[SNR=\frac{R_{o}MP_{s}}{\sqrt{2\epsilon BM^{2}F[R_{o}(P_{s}+P_{b})+i_{dB}]+2 eBi_{ds }+\frac{4 KTB}{R_{L}}+i_{Na}^{2}}} \tag{4}\]  
From Equation (4), it can be seen that the increase in background radiation noise reduces the SNR, while other parameters are kept constant. The variation in the noise current makes the LiDAR more easily generate false alarms when the signal is detected over the threshold, which greatly affects the detection efficiency. In the detection, the LiDAR will misidentify the noise as a signal due to the interference of background radiation and device noise, which can be expressed by false alarm probability. Random noise probability density functions such as background radiation noise, detector noise and circuit noise all obey Gaussian distribution [31], and the statistical characteristics of noise voltage \(\mathrm{u_{n}}\) can be expressed by the Gaussian probability density function:  
Figure 3.0  
where \(\sigma_{n}\) is the root mean square (RMS) of the noise voltage. The FAR of LiDAR is the probability that the amplitude of system noise exceeds the signal detection threshold. The detection threshold voltage is set as \(\mathrm{V_{T}}\), and the RMS of noise voltage is \(\mathrm{\overline{V}_{n}}\). By integrating Equation (5), the FAR \(\mathrm{P_{f}}\) is:  
Figure 3.1  
Using the error function to simplify, it can be expressed as:  
Figure 3.2  
where \(\mathrm{R_{p}}\) is the responsiveness of APD, \(\mathrm{I_{d}}\) is the dark current of APD, \(\mathrm{G}\) is the amplification factor of the amplifier circuit, and the expression of the error function \(\mathrm{erf(x)}\) is as follows:  
Figure 3.3  
Threshold noise ratio TNR is defined as  
Figure 3.4  
Therefore, the threshold voltage or value of the noise voltage of the receiver circuit can be dynamically adjusted according to the false alarm detection in the receiver, so that the TNR remains unchanged, thus maintaining the FAR \(\mathrm{Pf}\) stable during signal detection, and achieving the purpose of suppressing the variable background noise.