# Angle of Arrival for the Beam Detection Method of Spatially Distributed Sensor Array
## 4 Experiment Results  
In order to analyze the angular measurement performance of the developed spatially distributed sensor array, we constructed an indoor angle of arrival testing platform. The experimental system uses a 1550 nm fiber laser as the light source, as shown in Figure 8a. The divergence angle of the beam is \(5^{\circ}\), and the distance to the spatially distributed sensor array is 6.5 m, with the radius of the light spot reaching the sensor array being approximately 570 mm. The ADC output data width is 16 bits. The spatially distributed sensor array is mounted on a two-dimensional gimbal with an accuracy of 0.001\({}^{\circ}\). By  
Figure 6: (**a**) Schematic diagram of the field of view division of a spatially distributed sensor array. (**b**) Multi-sensor data fusion algorithm flow chart. Figure 7: Schematic circuit diagram of digital processing. adjusting the angles of the gimbal, the orientation of the sensor can be altered, enabling the measurement of the incident angle of the beam, as shown in Figure 8b. Before the testing, the primary sources of errors in the angle of arrival detection system of the spatially distributed sensor array were analyzed, and the error calibration was implemented. Firstly, this work uses five identical photodetectors and photoelectric conversion circuit modules. However, sensor response non-uniformity and differences in circuit signal gains can affect the sensor outputs, thus reducing the measurement accuracy of the AOA. Secondly, the sensor installation error arising from the fixation of the photoelectric conversion circuit module on the 3D-printed panel, along with the error in \(\alpha\), can result in sensor position error. The spatially distributed sensor array is installed in a darkroom without light. The output voltage of each sensor is generated by dark current. The dark current noise in each sensor can be considered uniform, so the difference in circuit signal gain of each sensor circuit can be calibrated to obtain the gain correction coefficient of each sensor. The laser light source is turned on, and five sensors are placed one after another at the position of panel 1 in Figure 8b. Each sensor is irradiated by a light source with the same energy. By varying the intensity of the incident light, the actual optical response of each sensor is calibrated based on the changes in the output voltage. Taking the position of sensor 1 as a reference, by comparing the angle difference between the actual output and theoretical output of each sensor at different incident angles, the position errors of the five sensors in the azimuth and elevation directions are analyzed. The normal vector coordinate matrix of the spatially distributed sensor array after correction is expressed as:  
\[\mathbf{K^{T}}= \begin{bmatrix}\mathbf{n_{1}}\\ \mathbf{n_{2}}\\ \mathbf{n_{3}}\\ \mathbf{n_{4}}\\ \mathbf{n_{5}}\end{bmatrix} = \begin{bmatrix}1&0&0\\ \cos(\alpha+\sigma_{y2})\cos\sigma_{z2}&\sin(\alpha+\sigma_{y2})\cos\sigma_{z2 }&\sin\sigma_{z2}\\ \cos\sigma_{y3}\text{cos}(\alpha+\sigma_{z3})&\sin\sigma_{y3}\text{cos}(\alpha+ \sigma_{z3})&\sin(\alpha+\sigma_{z3})\\ \cos(\alpha+\sigma_{y4})\cos\sigma_{z4}&-\sin(\alpha+\sigma_{y4})\cos\sigma_{ z4}&\sin\sigma_{z4}\\ \cos\sigma_{y5}\text{cos}(\alpha+\sigma_{z5})&\sin\sigma_{y5}\text{cos}(\alpha+ \sigma_{z5})&-\sin(\alpha+\sigma_{z5})\end{bmatrix}  \tag{28}\]  
where \(\sigma_{y}\) is the angle error in the azimuth direction for each sensor, and \(\sigma_{z}\) is the angle error in the elevation direction. Due to the long propagation distance of light in free space and the beam diameter being much larger than the diameter of the spatial distribution sensor, the AOA detection algorithm for the spatial distribution sensor array is based on the assumption of a uniform energy distribution of the light spot. However, in this experiment, where the distance between the  
Figure 8: The experimental platform. (**a**) Laser source. (**b**) Spatially distributed sensor array and two-dimensional gimbal.