## 1 Introduction  
Various applications using unmanned aerial vehicles (UAVs) increasingly require large capacity and high-speed data transmission for inter-UAVs or between UAVs and ground control stations (GCS). The use of the millimeter wave band by fifth-generation mobile communication have increased, and the rapid depletion of the existing radio frequency spectrum have intensified. This phenomenon drives the development of ultra-broadband free space optical (FSO) communication, FSO-based application services, and an FSO-based network [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. FSO communication features several advantages including no spectrum licensing, low-power consumption, electromagnetic interference immunity, enhanced channel security, and long-distance high-speed transmission [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. Because FSO communication requires a line of sight (LOS) between FSO terminals, the pointing, acquisition, and tracking (PAT) system is essential for FSO communication [15]. To maintain uninterrupted LOS, various methods were proposed using a quadrant photodiode (QPD), modulated retro-reflector (MRR), fast steering mirror (FSM), and hybrid of QPD and FSM [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39]. MRR-based PAT systems, represented by retroreflector free space optics, were mounted on UAVs for 560 m FSO communication, but they exhibited a limited performance in terms of transmission speed (Mbps) and simplex communication [16; 17; 18]. UAVs carrying a reflector only without TRx are lightweight but they cannot perform full-duplex communications. Full-duplex communication, which is essential for FSO network scalability and Gbps communication diversification, requires TRx's on both the FSO terminals [9; 10; 11; 12; 13; 14]. The FSM-based PAT system increases the control complexity and requires additional integrated modules for precision control [19; 20; 21]. Hybrid methods exhibit a good and stable performance. Nonetheless they present disadvantages, such as increased structural complexity, production costs, increased size and weight, and the need for an additional beacon beam subsystem with additional light sources [22; 23; 24; 25; 26; 27; 28]. The realization of a precise PAT system, which enables Gbps full-duplex transmission and maintains LOS, is more challenging in dynamic UAV environments. The high resolution and fast response speed of the QPD-based PAT system emerged as an interesting solution [29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39]. In addition, based on the incident beam size and incident beam position on the QPD, tracking efficiency was increased without additional components (i.e., FSM, deformable mirror, etc.).  
Previously reported FSO communication systems employing an adaptive beamforming function [40] demonstrated an improved tracking efficiency between FSO terminals within a limited size, weight, and power (SWaP) value for UAV mounting.  
In this study, a QPD-based PAT system without an additional beacon beam subsystem is proposed for FSO communications based on a common optical path. Furthermore, observability and controllability were confirmed by obtaining linearized control points from the QPD output according to the incident beam size on the QPD. Moreover, PAT was performed by controlling the pan and tilt unit (PTU). Therefore, precise LOS maintenance without additional beacon light sources and full-duplex Gbps high-rate data communication were simultaneously performed via a common optical path. We simulated and experimentally analyzed the QPD output and tracking efficiency depending on the incident beam size on QPD, based on a compact FSO PAT system.