## Abstract

In this study, the performance analysis of ${L}$-ary pulse position modulation (${L}$-PPM) and an avalanche photodiode (APD) receiver is investigated for a ground-station-to-low-Earth-orbit laser link. The performance is analyzed in the presence of spatial diversity in the transmitter side [i.e., a multiple-in single-out (MISO) scenario] under consideration of atmospheric turbulence and untracked beams where beam wandering effects occur. The modulated Málaga distribution is used to describe these two combined fading effects. At first, novel closed-form expressions of the probability density function and cumulative distribution function of Málaga distribution modulated by the beam wander effect in the case of MISO are deduced. We then derive an approximate expression for the upper bound of the average bit error rate (BER) in the case of ${L}$-PPM assuming a Gaussian model for the APD receiver in the presence of additive Gaussian thermal noise. The analytical expressions are verified by Monte Carlo simulations in the case of binary PPM, where the results are no longer upper bounds on the performance. Numerical results of the analytical upper-bound formula of the average BER are presented. For the system under consideration, the obtained results show that the effects of atmospheric turbulence and beam wandering for untracked beams can be effectively decreased by increasing the number of transmitters.

© 2022 Optical Society of America

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