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Optical preamplification introduces non-Gaussian electrical domain noises (beat noises) to digital pulse position modulation (DPPM) free-space optical (FSO) communication systems impaired by atmospheric turbulence, which do not appear for a simple PIN photodiode-based FSO receivers and thus necessitate a more sophisticated approach to bit error rate (BER) modelling. To explore this BER performance analyses, notably the Gaussian approximation, Chernoff bound and modified Chernoff bound (MCB), for such a system are presented and the MCB is seen to be an appropriate technique to use. Furthermore, the effectiveness of spatial diversity techniques, specifically aperture averaging, in mitigating the turbulence effect is investigated. The gamma-gamma distribution model is used to characterise the whole range of turbulence conditions. The results reveal the superiority of DPPM with improved receiver sensitivity (at a binary data rate 2.5-Gb/s and at typical FSO BER of 10-9) of about 7-9-dB [for coding level of 5 and optical link length (for turbulent interaction) of 1500-m] more than an equivalent optically preamplified on-off keying non-return-to-zero approach, depending on the level of turbulence.