The average output signal-to-noise ratio(SNR),outage probability and average bit error probability of coherent optical communication system with diversity receiving are analyzed under independent Gamma-Gamma fading channel.Firstly,exact closed-form expression of average output SNR is derived based on multi-nomial theorem.Then,the probability density function(PDF) of the lower boundary of the SNR is calclated by applying the well-known inequality between arithmetic and geometric means of positive random variables(RVs).Furthermore,new upper boundaries for outage probability and the average bit error probability of heterodyne synchronous binary phase shift keying(BPSK) are derived.The problem of calculating the PDF of the SNR directly is avoided and the complexity of analysis is lower in contrast to the previous methods.The results show that the impacts of atmospheric turbulence on the performance of system are effectively overcome by diversity receiving technology.The more its branches,the better its performance.The difference of performance is larger between strong and weak turbulence conditions.Compared with the simulation results by Monte-Carlo method,the proposed union upper boundary is almost the same.