## 1 Introduction  
To provide network services everywhere, non-terrestrial networks have emerged as next-generation wireless back-haul systems. FSO communication has been actively studied for its application to non-terrestrial networks due to its great advantages of wide bandwidth, low power consumption, high security, etc. [1; 2; 3]. Unmanned aerial vehicle (UAV) based FSO systems suffer from atmospheric and misalignment induced fading. To overcome this atmospheric fading and connect areas hundreds of kilometers apart, high-altitude platform (HAP) UAVs are employed to establish FSO based back-haul networks. Although a horizontal FSO link can overcome the impact of atmospheric turbulence, a vertical FSO link still suffers from the atmospheric fading issue. These fading issues make the received power insufficient to establish seamless communication systems [4; 5]. Therefore, improving the power margin is significant in order to achieve seamless and high data rate communication for FSO based non-terrestrial networks. A well-known technique to mitigate channel fading issues is to utilize diversity channels. Time diversity and wavelength diversity are challenging to implement as they require long symbol duration and wide wavelength spacing [6; 7]. However, a simple distant arrangement of a few meters can accomplish the required spatial diversity; and having a larger distance than the coherence length can easily achieve independent channels [8]. Many research groups have worked on spatial diversity based FSO systems. The effect of atmospheric turbulence on the MIMO based FSO communications was modeled by the Malaga distribution [9]. The outage probability of the multi-input single-output (MISO) and the MIMO FSO systems was analyzed with the atmospheric fading and the pointing error in the log-normally distributed channel [10; 11]. The closed-form expression and performance analysis for the MIMO system were researched over the Gamma-Gamma distributed channels with a generalized pointing error in [12; 13]. Moreover, the performance of spatial diversity based FSO systems was analyzed with the effect of non-zero boresightpointing errors [14; 15]. The channel modeling with UAVs' movements in the presence of atmospheric turbulence and pointing error was presented [16; 17]. Although the impacts of various atmospheric channel models and pointing errors were analyzed for the MIMO FSO transmissions, these researches assumed that the pointing jitter is the only source of the pointing error. Thus, the pointing errors considered in these researches were consistent, regardless of the increasing number of channels. However, the pointing error could be increased due to multiple beam transmissions in the misalignment detection process of PAT systems, so the pointing loss is increased to reduce the diversity gain. Therefore, even if the diversity performance is derived in the presence of atmospheric turbulence and pointing error, the achievable diversity gain could be worse than expected. The increased pointing error cannot be neglected to achieve the desired diversity gain using the spatial diversity technique. Our previous work [18] investigated a statistical misalignment model for the increased alignment error for multiple transmitters and a single receiver. We also analyzed how it is affected by atmospheric turbulence and the arrangement of the transmitters. However, when multiple receivers are employed, the increased pointing error can be reduced by averaging the detected misalignment. Furthermore, for the bi-directional communication characteristic of FSO based wireless back-haul networks, the pointing error behavior and the transmission performance of the uplink can differ from the downlink due to the reversed number of transmitters and receivers in the MIMO system. Thus, the transceiver configuration becomes significant for implementing power-efficient FSO transmissions.