## 1 Introduction  
Free-space optical (FSO) communication has unique advantages including a large bandwidth, an unlicensed spectrum, a high data rate, rapid deployment, and low power consumption [1], leading to extensive research and experiments. The European Space Agency (ESA) launched the Inter Satellite Link Experiment (SILEX) in 1990 [2]. A two-way communication laser link between the geostationary orbit satellite (ARTEMIS) and the low-orbit satellite (SPOT-4) was established in 2002; the communication format was on-off keying (OOK) [3]. In 2003, an optical payload (laser utilizing communication equipment (LUCE)) developed in Japan was installed in the ESA ground station; two-way communication experiments were conducted with the optical terminals on the ARTEMIS satellite; the uplink OOK rate was 49.37 Mbit/s [4]. In 2005, Japan's OICETS satellite and ESA's ARTEMIS satellite successfully conducted the first two-way optical communication between satellites in orbit [5]. In 2013, the lunar laser communication demonstration (LLCCD) in the US achieved high-speed two-way laser communication between lunar orbiting satellites and the ground using the pulse position modulation (PPM) format [6; 7; 8]. In 2015, the Japan Aerospace Exploration Agency (JAXA) announced the next generation of Japan Data Relay Systems (JDRS), with optical communication using return to zero (RZ) differential phase shift keying (DPSK) and 50-Mbit/s OOK [9]. In 2016, the Shanghai Institute of Optics and Fine Mechanics conducted laser communication experiments using PPM for uplink communication [10]. In addition to large-scale experiments conducted by large institutions, researchers have conducted OOK experiments. In 1994, [PERSON] et al. theorized that an intensity-modulated coherent receiver was insensitive to laser line width [11]. In 2006, [PERSON] et al. conducted a 10-Gbit/s OOK heterodyne communication experiment, achieving a sensitivity of \(-31\) dBm [12]. In 2007, [PERSON] et al. studied the noise performance of 10-Gbit/s OOK with heterodyne reception [13]. In 2015, [PERSON] et al. analyzed an OOK receiver with a Gaussian-Schell model laser [14]. In 2015, [PERSON] et al. analyzed the bit error rate (BER) of the OOK modulation scheme with non-coherent demodulation for space uplink optical communication systems [15]. In 2019, [PERSON] et al. analyzed FSO communication using amplitude modulation (AM), OOK-RZ, and OOK-non return to zero (NRZ) [16]. In 2021, 10-Gbit/s OOK data were transmitted over 15 cm in free space to up to three receivers located in three different cards using a silicon integrated beam steering and broadcasting device [17]. The OOK system has also been validated using white or visible light [18; 19]. The literature indicates wide use of OOK in FSO systems. It is important to study the factors that affect the sensitivity of OOK receivers. Researchers have conducted many simulations on the impact of atmospheric turbulence on OOK systems, providing some solutions [20; 21; 22; 23; 24]. In addition to atmospheric turbulence, ambient light (AL) is an important factor in OOK FSO systems. In 1996, [PERSON] et al. presented the results of an experiment to measure ambient radiation [25]. In 2014, [PERSON] et al. summarized the characteristics of vacuum space environments [26]. In 2017, [PERSON] et al. introduced a simulator that could simulate actual AL noise in a space environment [27]. In 2018, [PERSON] et al. discussed the expected AL sources and levels in an FSO system [28]. In 2021, [PERSON] et al. proposed wavefront coherent compensation technology in direct sunlight in an FSO system [29]. In 2022, [PERSON] et al. summarized the basic relations of free-space avalanche photodiode (APD) receivers with an emphasis on optical low-earth orbit (LEO) downlinks and reported the dependence of the optimum multiplication factor on the AL [30]. In this AL research, theoretical derivation and experimental verification of the FSO receiver sensitivity deterioration caused by AL were not reported.