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In this study, analytical and simulation results for the bit error rate (BER) performance and fading penalty of a coherent optical binary polarisation shift keying (2PolSK) heterodyne system adopted for a free-space optical communication link modelled as the log-normal and the negative exponential atmospheric turbulence channels are presented. The conditional and unconditional BER expressions are derived, demonstrating the comprehensive similarity between the 2PolSK and the binary frequency shift keying schemes with regard to the system sensitivity. The power penalty owing to the non-ideal polarisation beam splitter is also analysed. The receiver sensitivity employing 2PolSK is compared with other modulation schemes in the presence of turbulence and the phase noise. The results show that 2PolSK offers improved signal-to-noise ratio performance compared to the binary amplitude shift keying.