# Efficient CORDIC Iteration Design of LiDAR Sensors' Point-Cloud Map Reconstruction Technology +
## 2 Related Work  
Three-dimensional LiDAR [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] sensors mainly use pulsed laser light emitted by a laser emitter to detect the environment or measure an object. The working principle is that laser light is emitted by LiDAR and hits the object. The resulting scattering and reflection phenomena are due to the reflection of light, and LiDAR sensors receive the signal [9]. The distance information is obtained from the known speed of light. Through the reflection phenomenon of light, the smoothness and color of the surface of the object hit by the beam can be known. In general, objects have a reflectivity of 0 and 1 for light, but the reflectivity can be subdivided into 256 levels (0-255) in a LiDAR packet. In LiDAR, the reflectance can be divided into diffuse reflection and total reflection. Diffuse reflection is defined as the phenomenon wherein light is reflected out of order when light hits the surface of a rough object. When the light hits a rough black surface, the reflectance is 0 because a black surface absorbs light. When the light hits a rough white surface, the reflectance is 1 to 100. Total reflection is defined as the light being reflected directly back when the light hits a smooth surface, such as a mirror. When the light hits a reflector without any coverage, the reflectivity is 255. When the light hits a translucent covered reflector, the reflectivity is 101 to 254. In this paper, the data receiving method of the LiDAR sensor is divided into three modes. The first is the Strongest Return Mode, which is the information returned when the beam hits a near object, which is equivalent to receiving the strongest beam of infrared light. The second type is Last Return Mode; when the beam hits a far object, the information is returned. The third type is the Dual Return Mode, which means that the information includes both last return and strongest return information. After LiDAR detects the environmental information, a circuit needs to decode the collected LiDAR packet data and then decode the packet into 3D coordinates using the CORDIC algorithm [18]. The relevant literature on the CORDIC algorithm and circuit design and the explain the problems that exist in the current relevant research are described below. Traditional CORDIC algorithms use basic addition, subtraction and shifting to apply trigonometric functions and other basic arithmetic, such as multiplication and division [1]. The CORDIC algorithm was first proposed by [PERSON] in 1959 mainly for trigonometric functions [19]. In 1971, [PERSON] applied the algorithm to hyperbolic and exponential functions, to multiplication and logarithms, and other functions. In 1974, [PERSON] used the CORDIC iterative principle to perform the Fourier transform [20]. The principle of a CORDIC algorithm [21] is to use the rotation of a two-dimensional coordinate plane to complete many complicated operations. The hybrid adaptive CORDIC algorithm (HA CORDIC) [21; 22; 23; 24] is mainly used to reduce the number of iterations of traditional CORDIC rotation [1]. We assume that any point of the two-dimensional plane coordinates is the origin (X\({}_{0}\), Y\({}_{0}\)) rotated to (X, Y), and the angle of rotation is \(\theta\). We can write the rotated matrix. We decompose the angle of rotation \(\theta\) into a number of small associated angles and set these small angles as \(\alpha\) angles. If the sum of all the \(\alpha\) angles is equal to the original rotation angle \(\theta\), then in the rotated matrix the \(\theta\) angle can be replaced with the \(\alpha\) angle. [1]  
When the coordinate rotation angle is equal to some specific rotation angle, then to realize the simple displacement operation in the digital circuit design, let tan\(\alpha_{i}=\alpha_{1}2^{-i}\) and K = \(\prod_{i=0}^{n-1}\cos\alpha_{i}\). After the substitution, Formula (1) can be obtained. \[\left[ \begin{array}{c}X^{\prime}\\ Y^{\prime}\end{array} \right]=\mathrm{K}\left[ \begin{array}{cc}1&\alpha_{1}2^{ -i}\\ \sigma_{1}2^{-i}&1\end{array} \right]\left[