LLCD utilized the PPM [2], and works in [3; 5; 7; 28] also considered the PPM in deep space optical communication. [PERSON] et al. in [9] highlighted the use of OOK for deep space exploration. For the photodetection of PPM and OOK signals, several optical detectors are commonly deployed, including P-i-N photodiodes (PINs), avalanche photodiodes (APDs), single-photon avalanche diodes (SPADs), and superconducting nanowire single-photon detectors (SNSPDs) [29; 30; 31; 32]. APDs exhibit a compact footprint and lower power consumption compared to PINs [30], and have higher detection efficiency compared to SPADs. In addition, SPADs operate within a temperature range of 0-25 \({}^{\circ}\)C [31]. SNSPDs require cryogenic cooling below \(-268\)\({}^{\circ}\)C, resulting in prohibitively high power demands, prolonged startup times, and bulky system designs [32]. Thus, APDs are a preferred choice for deep space optical uplink communication. Webb [33] and Gaussian [34] can be used to approximate APD output. Webb distribution offers superior accuracy but is more complex [35]. In previous studies, the Gaussian distribution was widely used due to its simplicity [36; 37; 38; 39; 40; 41]. However, when the system performance evaluated by the Gaussian model is better than the actual communication performance, the actual link budget will be lower than the analytical link budget analyzed during system design, which significantly increases the probability of link outage. Motivated by the above analysis, this paper studies an APD-based deep space optical uplink communication in the presence of various channel impairments. The block diagram of our studied system is shown in Figure 2. Specifically, our contributions are as follows:  
* We study the combined effects of critical channel impairments in deep space optical uplink systems, including atmospheric and coronal turbulence, pointing errors, AOA fluctuations, link attenuation, and background noise. A closed-form analytical uplink channel model integrating these factors is derived, and its accuracy is rigorously validated through Monte Carlo simulations. * We use Webb and Gaussian distributions to approximate APD output. For both models, theoretical expressions of PPM communication SER performance are derived. A comparative analysis is performed for the [PERSON] and Gaussian models' evaluated SER performance. * We discuss various numerical results, including characteristics of channel destructive factors, [PERSON] and Gaussian modeled APD output and SER performance. While the Gaussian model exhibits inherent limitations in capturing the dynamics of avalanche noise, its operational constraints are analyzed. The results reveal non-monotonic dependencies of SER on the APD gain and FOV angle. Hence, these parameters are strategically optimized to improve the performance of our considered system. The rest of this article is organized as follows. In Section 2, we analyze various channel impairments and a closed-form expression of the uplink model is derived. Section 3 first introduces the APD output and noise model. In Section 4, theoretical expressions of PPM SER performance based on [PERSON] and [PERSON] models are derived. The simulation results are shown and discussed in Section 5. Finally, Section 6 concludes this article. Figure 1: Schematic of deep space optical uplink communication over various channel impairments.