# Angle of Arrival for the Beam Detection Method of Spatially Distributed Sensor Array
## 1 Introduction  
In recent years, low-earth-orbit satellite (LEO) constellations have been developing rapidly. Through inter-satellite laser links, satellites can achieve high-speed data exchange, significantly enhancing global coverage and low-latency communication performance [1, 2, 3, 4]. However, current LEO satellite laser communication terminals mainly operate in a point-to-point configuration, requiring multiple communication terminals for inter-satellite connectivity. This approach significantly increases the satellite's size, weight, and power (SWaP), as well as system complexity. To address this problem, a laser terminal using a low-switching wide field of view (FOV) transceiver is proposed to achieve one-to-many communication [5, 6, 7, 8]. Through distributed multi-transmitting units, these optical terminals facilitate flexible transmission across multiple beams and angles. Furthermore, the laser communication terminal must possess wide field of view detection capabilities to obtain the approximate position information of target satellites for the requirements of multi-target positioning and tracking, which is used for the multi-beam coarse alignment. With the integrated precise tracking module, the terminal can achieve rapid switching between one-to-many links, ensuring efficient and reliable inter-satellite communication. The popular approach for angle of arrival (AOA) wide field of view detection involves utilizing a lens system to focus the incident light onto a sensor array or CCD. The position of the beam is calculated by the change of the centroid of the light spot. In 2017, [PERSON] et al. used a 4 \(\times\) 4 silicon photomultiplier (SiPM) array with a 20\({}^{\circ}\) FOV [9]. In 2022, [PERSON] et al. proposed a detection system that consisted of a fisheye lens and a CCD with a resolution of 640 pixels \(\times\) 512 pixels. The system's measurement FOV was 120\({}^{\circ}\)\(\times\) 96\({}^{\circ}\), and the angle error was 0.5\({}^{\circ}\)[10]. The lens-based AOA detection has limitations such as a restricted field of view, optical distortions, and large SWaP consumption, which decrease its applicability in multi-satellite laser communication applications [11; 12]. Another approach is to detect the AOA using the signal strength of the sensor array at different spatial angles. It has no lens system and consists of multiple photodiode sensors, which ha the advantages of a wide field of view and low-SWaP. In 2017, [PERSON] et al. designed a hemispherical 5 \(\times\) 5 photodetector array and evaluated it using Monte Carlo simulations, showing an estimation error within 5\({}^{\circ}\) for elevation and azimuth [13]. In 2018, [PERSON] et al. proposed a system that used five sensors distributed on the side panels of a truncated pyramid to detect the AOA. Within a 120\({}^{\circ}\) field of view, the estimated errors of elevation and azimuth angles were mostly less than 6\({}^{\circ}\)[14]. In 2020, [PERSON] et al. proposed an omnidirectional optical communication/navigation device based on a truncated icosahedron with a measurement field of view of 4\(\pi\) and an RMS of 0.076\({}^{\circ}\)[15; 16]. In 2024, [PERSON] et al. designed a deployable optical receiving aperture consisting of five sensors and tested it for six angles. The maximum angle error exceeded 5\({}^{\circ}\), and no two-dimensional test was performed [17; 18]. These research institutions have clarified the AOA detection principle of spatially distributed sensor arrays, developed prototypes, and conducted verification experiments, but the impact and optimization design of key parameters of such arrays, data processing methods, and error analysis are not in-depth enough. There is also a lack of systematic design methods for spatially distributed sensor arrays. In this paper, we first present the principle of AOA detection using the spatially distributed sensor array.