## 4 Construction of QD Experimental System and Digital Signal Processing
The multiplier, the integrate, and the dump form a correlator, which calculates the correlation values between the input signal and the local PRNs with different phases. The correlation value obtained from the Punctual code correlator is used for data recovery and phase acquisition, while the correlation values from the Early code and Late code correlators are used to track the phase of the input PRN signal using the local PRN. The polarity of the correlated values after integration is utilized to extract communication data from the input signal. The absolute \begin{table}
\begin{tabular}{c c} \hline \hline
**Experimental Apparatus** & **Parameters** \\ \hline \multirow{3}{*}{Quadrant Detector} & Model: QA4000-10-TO \\  & Responsivity: 36 A /W \\  & Active Area: 4000 \(\mu\)m \\ \hline \multirow{2}{*}{Laser} & Model: CTLP-850-002m-4-B-PD \\  & Wavelength: 850 nm \\ \hline Fiber Optic Attenators & Wavelength Range: 780 nm-980 nm \\ \hline Beam Splitter & T:R = 50\%:50\% \\ \hline ADC & Sampling rate: 65 MSPS \\ \hline FPGA & Model: EP4 CE10F17J7N \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental equipment parameters and models. value of the correlated values is input into the loop filter. The loop filter mainly consists of two states: phase acquisition and phase tracking. Phase acquisition: The local PRN generator is adjusted with half-a-chip period resolution until a certain phase deviation between the locally generated reference code and the input code is achieved. At the delayed location, correlation values that are higher than the threshold required to complete phase acquisition are detected. Phase tracking: Once phase acquisition is completed, the difference between the Early PRN correlator and the Late PRN sequence correlator is used as the error signal in the control loop to determine the phase deviation with a higher resolution. This enables the phase of the Punctual code to the input PRN signal to be tracked. As shown in Figure 6 below, when the spread-spectrum modulation PRN depth is 1023 and the received signal power is \(-40\) dBm, the correlator exhibits correlation values in two modes. During the acquisition phase, when the phases are close, there are higher correlation values. When the correlation value exceeds the threshold, the system enters the acquisition state. At this point, the despreading signal exhibits minimal jitter. The loop filter utilizes the error signal to update the oscillation frequency, which is then input into the local PRN generator. The local PRN generator generates the local PRN using a Numerically Controlled Oscillator (NCO). The updated oscillation frequency is added to the NCO's fixed-point numbers, changing the step size of the code NCO and thus modifying the code clock frequency. Eventually, the change in the local code phase is integrated to achieve phase tracking between the input signal and the local code's Punctual code phase. At this point, the digital phase-locked loop achieves the demodulation of the received beacon light communication data, while also tracking the phase of the input photoelectric signal using the local PRN. The Punctual code of the local PRN is input into four correlators in order to perform correlation operations. The results of the correlation operation are then input into the calculation of the optical spot position, achieving the calculation of the received optical spot position. Figure 5: The construction of the QD experimental system and digital signal processing. To compare the positive effect that spread-spectrum technology has on detection performance, the RMSE of the detected output positions is evaluated. Here, \(L\) represents the number of times the position of the detected optical spot is output; \(x_{i}\) represents the \(x\)-axis output position for the i-th detection; and \(x_{real}\) represents the true value of the \(x\)-axis, i.e., the actual distance moved by the displacement platform calibrated with the camera. \[\sigma_{x}=\sqrt{\frac{\sum\limits_{i=1}^{L}{(x_{i}-x_{real})^{2}}}{L}} \tag{21}\]