# Adaptive Suppression Method of LiDAR Background Noise Based on Threshold Detection
## 3 Adaptive Suppression Method of Background Noise
### Critical Modules Implementation  
#### 3.2.1 Noise Detection  
Rapid and accurate noise detection and quantization is a prerequisite for realizing adaptive threshold regulation. There are two common noise detection methods. One is the integral quantization of noise voltage, which has the disadvantage of low speed and is easily affected by capacitance leakage current and temperature coefficient [32]. The other is to quantify the noise by counting the pulse times of the noise discrimination threshold. This method has the advantages of simple circuit implementation and fast detection speed. Due to the non-ideal factors of the devices in the actual system, the noise pulses drift and overlap. For the noise detection in a short time, there is a deviation in quantifying the noise only by the counting output pulses of the comparator. Therefore, the noise detection method is optimized in this paper. False alarm probability can also be expressed by false alarm time [33]. False alarm probability \(\mathrm{P_{f}}\) is the ratio of the time \(\mathrm{\tau_{sum}}\) when the envelope actually exceeds the threshold and the total time \(\mathrm{T_{sum}}\) that can exceed the threshold:  
\[P_{\mathrm{f}}=\frac{\mathrm{\tau_{sum}}}{\mathrm{\tau_{sum}}}=\frac{\frac{1}{ N}\sum\limits_{k=1}^{N}\mathrm{\tau_{k}}}{\frac{1}{N}\sum\limits_{k=1}^{N}\mathrm{ \tau_{k}}}=\frac{\sum\limits_{k=1}^{N}\mathrm{\tau_{k}}}{\sum\limits_{k=1}^{N} \mathrm{T_{k}}} \tag{10}\]  
where \(\mathrm{\tau_{k}}\) is the duration of pulses exceeding the threshold, and \(\mathrm{T_{k}}\) is the interval time between adjacent noise pulses exceeding the threshold. Therefore, the threshold voltage of signal discrimination can be adjusted by measuring the changes in \(\mathrm{\tau_{sum}}\). For the noise pulse exceeding the threshold, the pulse duration is obtained by measuring the pulse width. The discrimination comparator used is a continuous-type comparator, which cannot quantify the pulse width directly. Therefore, a dynamic comparator is designed for threshold detection of noise in this paper. While detecting the noise, the duration of the detected noise pulse can be obtained. The basic structure of the dynamic comparator designed is shown in Figure 7.  
M1-M5 constitute the pre-amplifier circuit, M6-M14 constitute the latched comparator, and M12 is the reset tube. When the clock CLK is at low level, M12 is turned on to make the voltages at O and P equal, so as to avoid the unequal residual charges at O and P, thus  
Figure 6: Diagram of adaptive adjustment time. Figure 7: Schematic of dynamic comparator circuit. affecting the accuracy of the comparator. The SR latch circuit is composed of two NOR gates which are cross-connected at both ends. The noise detection threshold voltage of the noise comparator needs to be set in a reasonable range. According to Formula (10), since the receiver noise should be detected and quantified in time T\({}_{1}\) and fed back to the cascade network to completed the threshold control before laser pulse output, the total time T\({}_{\text{sum}}\) can be approximated as T\({}_{1}\), and the probability of false alarm is P\({}_{\text{f1}}\). Thus, the total time t\({}_{\text{s1}}\) of actually exceeding the noise threshold can be obtained:  
\[t_{\text{s1}}=P_{\text{f}}T_{sum}=P_{\text{f1}}T_{1}=T_{1}[\frac{1}{2}-\frac{1} {2}\text{erf}(\frac{V_{T\text{f}}}{\sqrt{2V_{n}}})] \tag{11}\]  
where V\({}_{\text{Tn}}\) is the noise detection threshold. Therefore, the relationship between the corresponding V\({}_{\text{T}}\) and the \(\overline{\text{V}}_{\text{n}}\) in time T\({}_{1}\) can be obtained.