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Coherent free-space optical (FSO) communications is analyzed for long-range, high turbulence FSO systems operating under K-distributed turbulence conditions. Exact error rates are presented for M-ary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) using a closed-form moment generating function. Maximum ratio combining (MRC) reception is employed in the system with MPSK and MQAM to mitigate the turbulence effects, and asymptotic error rate analysis is presented for this MRC reception. The error rate performance degradation caused by phase compensation error is also studied, and it is found that the impact of phase compensation error on the error rate performance can be small when the standard deviation of the phase compensation error is kept below twenty degrees.