# Efficient CORDIC Iteration Design of LiDAR Sensors' Point-Cloud Map Reconstruction Technology +
## 3 Proposed Method
### Three-Dimensional (3D) Mobile LiDAR Packet Decoding  
In the process of converting the packet information into a three-dimensional point-cloud image and improving the rotation angle of the algorithm, we first need to decode the packet information scanned by LiDAR. From the decoding step, we obtain the angle, distance, reflectivity and other information of the three-dimensional space in the environment. According to the angel information, we calculate the values of SIN and COS through the proposed CORDIC iterative reduction algorithm. The X, Y, and Z values are calculated by using the three-dimensional space construction formula and then converted to construct a three-dimensional point-cloud map. In the case of a packet, the first data block will be Last Return data, and the second data block will be Strongest Return data. Selecting the Dual Return Mode will return two reflectance information at the same horizontal angle for every two blocks. Therefore, for the same horizontal angle, different data-receiving modes are selected, and the amounts of data received will be different. Selecting Dual Return Mode will double the amount of information returned by the Strongest Return and Last Return modes. Table 1 shows the packet rate for a single packet data received by the Strongest Return Mode or Last Return Mode. When the single-return method is selected, the data volume receives 754 packets and 8 Megabits per second. If we the select Strongest Return and Last Return Modes at the same time, twice the amount of data will be received. LiDAR's data packet uses the user datagram protocol (UDP) to transmit data. A packet will have a total of 1248 bytes and contain 42 bytes of header files. The 12 Data Blocks have a total of 1200 bytes and record information such as angle, distance, and reflectivity. An additional 4 bytes of timestamp record Global Positioning System (GPS) information. Finally, the 2 bytes of factory data are used to record which mode is used and the LiDAR model. A Data Block can be divided into 2 bytes of Flag, 2 bytes of horizontal angle information, and two sets of 0 to 15 channel data. One channel data is 3 bytes, which contains the information of the first 2 bytes of distance, and the reflectivity information of the last 1 byte, as shown in Figure 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mode** & **Packets/Sec** & **Mbits/Sec** \\ \hline Strongest Return Mode & 754 & 8 \\ Last Return Mode & 754 & 8 \\ Dual Return Mode & 1508 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mobile Light Detection and Ranging (LiDAR) packet rate. The LiDAR horizontal angle information is contained in the Data Block, and each Data Block contains two different horizontal angles. The first set of horizontal angles can be derived from the packet information before the first Channel 0 Data. The second set of horizontal angles, also known as drift angles, is taken before the second Channel 0 Data. To calculate the second set of drift angles, we use the first Data Block plus the horizontal angle of the second Data Block and divide by two, as shown in Equation (10). \[\text{Angular Drift }=\frac{\text{Data Block 0 }+\text{ Data Block 1}}{2} \tag{10}\]  
The vertical angle of the LiDAR is fixed. When the light is rotated, it will continuously rotate the horizontal angle by 360 degrees at 10 times per second and emit 16 rays at the same time, as shown in Figure 2. The vertical angle corresponding mode starts from Channel 0 and goes down to Channel 15, corresponding to the LiDAR vertical angles in Table 2. The laser beam from the zeroth pass is \(-15^{\circ}\), the first laser beam is \(+1^{\circ}\), the fifteenth laser beam is \(+15^{\circ}\), and each vertical laser beam is separated by 2 degrees. The decoding process is shown in Figure 3. The LiDAR sensor circuit sequentially solves the information such as the header, flag, horizontal angle, distance, and reflectivity. The data input is a