We theoretically analyze the performance of free-space optical (FSO) systems using rectangular quadrature-amplitude modulation (QAM) and an avalanche photodiode (APD) receiver over atmospheric turbulence channels. Both log-normal and gamma–gamma channel models are used in the analysis for the cases of weak/moderate and strong atmospheric turbulence. The system bit error rate, when Gray code mapping is employed, is theoretically derived taking into account various link conditions and system parameters, including the APD shot noise, thermal noise, channel attenuation and geometrical loss, atmospheric turbulence strengths, and link distances. The numerical results show that using APD with a proper selection of the average gain could greatly benefit the performance of the system; as a matter of fact, in the case of optimal gain, the system using an APD receiver could provide 7 dB gain in comparison with the one with a positive-instrinsic-negative receiver. We also quantitatively discuss the impact of link conditions and system parameters on the selection of optimal APD gain.
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