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Abstract In this paper, with the assumption of only channel statistics information available at the receivers, a novel concept of multiplicative uniquely decomposable constellations is proposed for multi‐user single‐input multiple‐output (MU‐SIMO) FSO systems in weak atmospheric turbulence, which is modeled by spatially dependent lognormal fading channels. The design enables the fast decoding at the users' sides and meanwhile allows flexibility in assigning each user's ordering to meet different priority needs. Simulation results show that our proposed design has a significant performance improvement over the TDMA scheme at the same rates.