Advances in weather observation, research, and planning have led to significant progress in the development of weather radar technology. Pulse compression enables a new generation of low-cost, compact spaceborne weather radar systems. In order to suppress the range side lobes caused by pulse pressure, target detection radar usually uses methods based on amplitude modulation and mismatch filtering. However, due to its shortcomings such as main lobe expansion and power loss, it is not suitable for meteorological observations. Nonlinear Frequency Modulation (NLFM) signals can adjust the power spectral density to provide lower sidelobe output without significantly reducing the signal-to-noise ratio. In this paper, a new waveform optimization framework is designed. This framework constructs a nonlinear frequency modulation (NLFM) pulse compression waveform for meteorological particle targets through the multi-objective particle swarm optimization algorithm (MOPOS), achieving extremely low range side lobe levels and high Doppler tolerance. The very limited satellite peak power limitations and Doppler effects on the system caused by satellite platform motion can be significantly mitigated. The simulation experiment results show that the improved nonlinear FM waveform has good performance.