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The transmission performance of a free-space optical (FSO) link could be severely degraded due to atmospheric turbulence, which causes the temporal and spatial fluctuation of light intensity. Both the space diversity reception technique (SDRT) and advanced modulation formats can successfully mitigate the transmission impairments of the atmospheric turbulence. The purpose of this paper is to study and compare the bit-error-rate (BER) performance of several widely used modulation formats under different atmospheric turbulence scenarios with and without SDRT. The modulation formats studied in this paper include on-off keying (OOK), differential phase-shift keying (DPSK), and differential quadrature phase-shift keying (DQPSK). We derive a series-form formula for evaluating the BER performance of the DPSK format in the Gamma-Gamma distributed channel with SDRT. We use both theoretical analysis and simulation to examine the BER performance of OOK, DPSK, and DQPSK formats with and without SDRT. It is found that, in the strongly turbulent scenario, the OOK and DPSK formats can have as large as 19.5 and 20.3 dB of SDRT gains at the BER of 10-3, respectively. Using SDRT, the modulation gains of the DPSK format over the OOK format are 3.2 dB in the strongly turbulent scenario and 4.5 dB in the weakly turbulent scenario, respectively. In addition, in the moderately and strongly turbulent scenarios, it is found that the DPSK and DQPSK formats have almost the same BER performance under the same symbol rate.