## 3 Signal Extraction Algorithms  
There are many noise reduction and signal extraction approaches reported in the literature. Signal accumulation technique [36] based on the assumption of zero mean random noise is widely used for noise reduction Coherent averaging, constant false alarm  
Figure 4: Schematic block circuit of SiPM 2-stages voltage amplifier. Figure 3: Block diagram of data acquisition part. SiPM is biased at the overvoltage of 10 volts. rate, wavelet and adaptive filters are also the most common methods. Since the signal is embedded in noise, coherent averaging has to be applied to obtain a meaningful signal [18]. When the laser power is very low, averaging should be done in multiples of 1000 depending on the distance. During the outdoor testing, the performance of our LRF, it has been observed that averaging process of up to 5000 frames is beneficial for noise reduction. At this level, the averaging process can be seen in Figure 5, where the noisy signal provides a Gaussian distribution. This situation provides flexibility in determining our signal extraction method. Since the averaging process takes a long time (1 s is required for 1000 frames), signal extraction should be started as soon as the data are acquired. The shape and pulse width of the detected pulse varies depending on the distance and attenuation rate. In addition, the detected signals are accompanied by the noises of all kind which can be classified into two different sources, optical such as background IR radiation, and electronic such as the noise of amplifiers. The SiPM itself also contributes to noise by means of dark current and excess noise. In the near-IR the excess noise of SiPMs appreciably increases even with low background noise [37]. For this reason, the use of the statistical method was preferred. The Wiener-Hopf filter is the most popular statistical-based adaptive filter [38]. Figure 6 shows the basic outline of this filter which consists of averaging process, determining Wiener-Hopf filter coefficients according to the appearance of noise signal, filtering and the decision steps. The most challenging stage in Wiener filter application is determining the desired signal. In the averaging stage, coherent pulse integration was performed over the measured data signal (shown as X\({}_{\text{Nx1}}\)) which comes as an average of 1000 data. Here, we can choose any integer number to be averaged so, e.g., if we choose 5, we obtain data which is the average of the 5000 data frame. After normalization and zeroing the negative values, the signal (shown as R\({}_{\text{Nx1}}\)) enters the Wiener-Hopf process. Using the Wiener-Hopf equation, it is possible to extract the Wiener coefficients according to our desired signal (D\({}_{\text{Nx1}}\)) properties such as their shapes and positions from the noisy signal. The designed low-pass filter with these coefficients specifically belongs to both the noisy signal and desired signal. Therefore, these coefficients (W\({}_{\text{Nx1}}\)) need to be recomputed after each measurement. The number of coefficients (M) is also of great importance in terms of computational time and effectiveness of the filtering, as well. Therefore, they need to be optimized and this is done by trial and error. Figure 5: Noise of distribution and Gaussian fitting curve. The data acquired (X\({}_{\text{Nxd}}\)) contains 4096 points and data interval corresponds to 10 ns duration. This corresponds to the maximum distance that can be measured is 6144 m. D\({}_{\text{Nxd}}\) is the filtered-out desired signal vector that contains 4096 data points. It is actually defined as all zero except the pulse representing the signal which is composed of 12 data point corresponding to 120 ns when SNR is larger than 3.5. Naturally, this gives an uncertainty in the position of the target which is 18 m. This single desired pulse is the analogy of laser pulse and approximately normalized Gaussian. The next step is to find the position of the pulse.