The Greenwood frequency (GF) is influential in performance improvement for the coherent free space optical communications (CFSOC) system with a closed-loop adaptive optics (AO) unit. We analyze the impact of tilt and high-order aberrations on the mixing efficiency (ME) and bit-error-rate (BER) under different GF. The root-mean-square value (RMS) of the ME related to the RMS of the tilt aberrations, and the GF is derived to estimate the volatility of the ME. Furthermore, a numerical simulation is applied to verify the theoretical analysis, and an experimental correction system is designed with a double-stage fast-steering-mirror and a 97-element continuous surface deformable mirror. The conclusions of this paper provide a reference for designing the AO system for the CFSOC system.