# Efficient CORDIC Iteration Design of LiDAR Sensors' Point-Cloud Map Reconstruction Technology +
## 4 Mobile LiDAR Sensing Circuit and Chip Design
### CORDIC Angle Calculator
#### 4.3.6 Coordinate Calculator  
After the distance transmitted by the main controller and the values of SIN and COS calculated by the angle calculator are received, the information of the X-axis, the \(Y\)-axis, and the \(Z\)-axis is outputted in the coordinate calculator. Since the input timings of the horizontal angle, vertical angle, and distance are different, the final output timings of the \(X\)-axis, \(Y\)-axis, and \(Z\)-axis can be made uniform by the delay in the coordinate conversion calculator.  
In the \(X\)-axis circuit of the coordinate conversion calculator, the COS value of the vertical angle, the SIN value of the horizontal angle, and the value of the distance are used as inputs (Figure 19). After truncation, the number of bits is 14 bits. The COS value of the vertical angle is multiplied by the value of the distance and then by the COS value of the vertical angle to obtain 42 bits. Since only the integer part of the three digits after the decimal is taken, it is necessary to divide the X axis by \(10^{7}\). However, the because divider area is large, the displacement method can be used to achieve an approximate result, as shown in Equation (14).  
\[(2^{\,0}+2^{-1}+2^{-3}+2^{-4})\,\times\,2^{-24}=1.0058\,\times\,10^{-7} \tag{14}\]  
In the \(Y\)-axis circuit of the coordinate conversion calculator, the input signal is the COS value of the vertical angle, the value of the COS value and the distance in the horizontal angle (Figure 20). After truncation, the number of bits is 14 bits. The COS value of the vertical angle is multiplied by the value of the distance and by the COS value of the vertical angle to obtain 42 bits. Since only the integer part of the three digits after the decimal is taken, it is necessary to divide the Y axis by \(10^{7}\). To reduce the divider, we use a shift instruction to achieve an approximate result, as shown in Equation (15).  
\[(2^{\,0}+2^{-1}+2^{-3}+2^{-4})\,\times\,2^{-24}=1.0058\,\times\,10^{-7} \tag{15}\]  
In the \(Z\)-axis circuit of the coordinate conversion calculator, the SIN value of the vertical angle and the value of the distance are used as inputs (Figure 21). After truncation, the number of bits is 14 bits. The COS value of the vertical angle is multiplied by the value of the distance to obtain 28 bits, and the \(Z\) axis is divided by \(10^{3}\). Approximate results can be achieved using the adder and shifting, as shown in Equation (16).  
Figure 18: Truncated bit error rate-\(S\!IN\) value.  
\[(2^{0}+2^{-6}+2^{-7}+2^{-8})\,\times\,2^{-10}=1.0032\,\times\,10^{-3} \tag{16}\]  
Figure 19: The X-axis circuit of the coordinate conversion calculator.  
Figure 20: The Y-axis circuit of the coordinate conversion calculator.  
In this section, we introduce the LiDAR decoding circuit to detail the role of each module and implement the digital hardware architecture. Here we introduce the data transmission and operation process of each module, including the horizontal angle and vertical angle calculation. For the calculation of the distance, the trigonometric function reduces the iterative conversion method to the final coordinate, uses the reduced iteration method in the operation, and allows the data to be input into the new data at the same time during processing to achieve immediate processing.