The study investigates the enhancement of quantum key rate in discrete-modulation continuous-variable quantum key distribution (DM-CV-QKD) systems over satellite-ground links through the use of optical amplifiers, and its impact on system security. Simulation analysis reveals that optical amplifiers can significantly boost the quantum key rate for short-distance communication. Although 4-ary QKD and 8-ary QKD protocols effectively improve key rate in this scenario, their relatively large degradation regions fail to cover the secure communication distance between satellites and the ground, resulting in a limited secure communication range. To break through this limitation, a novel 16-ary double-ring modulation scheme for DM-CV-QKD is introduced, which effectively reduces the degradation region and enhances the overall system reliability, thereby significantly improving both the key rate and secure communication distance. Finally, the study also analyzes the effects of factors such as turbulence strength, optical wavelength, and horizontal elevation angle on system performance. The results show that under strong turbulence conditions, the Gaussian modulation and the 16-ary double-ring modulation scheme can still effectively improve signal quality with optical amplifiers, and their enhancement region can cover the operational range of low-earth orbit satellites, demonstrating their application value and significance in complex environments.