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Exact error rate performances are studied for coherent free-space optical communication systems under strong turbulence with diversity reception. Equal gain and selection diversity are considered as practical schemes to mitigate turbulence. The exact bit-error rate for binary phase-shift keying and outage probability are developed for equal gain diversity. Analytical expressions are obtained for the bit-error rate of differential phase-shift keying and asynchronous frequency-shift keying, as well as for outage probability using selection diversity. Furthermore, we provide the closed-form expressions of diversity order and coding gain with both diversity receptions. The analytical results are verified by computer simulations and are suitable for rapid error rates calculation.

Coherent wireless optical communication systems with heterodyne detection are analyzed for binary phase-shift keying (BPSK), differential PSK (DPSK), and M-ary PSK over Gamma-Gamma turbulence channels. Closed-form error rate expressions are derived using a series expansion approach. It is shown that, in the special case of K-distributed turbulence channel, the DPSK incurs a 3 dB signal-to-noise ratio (SNR) penalty compared to BPSK in the large SNR regime. The outage probability is also obtained, and a detailed outage truncation error analysis is presented and used to assess the accuracy in system performance estimation. It is shown that our series error rate expressions are simple to use and highly accurate for practical system performance estimation.