Deep-space free-space optical (FSO) communication utilized the light wave as carriers for information transfer which has the major benefit of small size, lightweight, and low consumption compared with microwave communication loaded with the same data rate. The M-ary pulse-position modulation (M-PPM) format is a favorable choice for deep-space FSO communication by means of its high sensitivity. The preamplified thresholded M-PPM technique has been confirmed, and a corresponding demonstration has been accomplished with data rates of 1.25 Gbps and 2.00 Gbps separately. The receiving sensitivities (BER@1 x 10(-3)) of 1.25 Gbps and 2.00 Gbps 16-PPM have been detected as -57.51 dBm (11.04 photons/bit) and -55.03 dBm (12.25 photons/bit), respectively. Simultaneously, the high extinction ratio of M-PPM has been achieved, for example, the extinction ratio of 16-PPM has been detected as 39.51 and 38.27 dB for 1.25 Gbps and 2.00 Gbps, which are 17.60 and 17.44 dB higher than that of on-off keying (OOK) modulation, respectively. The results imply that our communication scheme possessed high sensitivity and eliminated the requirements of single-photon detectors (SPDs) and high-speed analog-to-digital converters (ADCs) which finds an alternative solution for deep-space FSO communication.