## 4 Conclusions  
In this paper, we use computer simulations to explore the feasibility of using dual-polarized microwave signals from LEO satellites to measure the raindrop size distribution. Our analysis suggests that measurements of attenuations on both horizontally and vertically polarized microwave links offer the opportunity to estimate two independent DSD parameters. As the difference between the two specific attenuations is crucial for retrieving the slope parameter and becomes less distinct as the elevation angle of the link goes higher, its retrieval needs to be performed at low elevation angles, preferably close to the minimum elevation angle of the receivers. Simulation results show that using SNR measurements from all elevation angles to retrieve the specific attenuation for horizontally polarized signals through a least-squares algorithm is feasible. Particularly for voxels with heavy rain, the retrieval error is less than 2%. It is also confirmed that the specific attenuation for vertically polarized signals can be retrieved using a few SNR measurements taken close to the minimum elevation angle. In order to achieve the precision needed for estimating the DSD parameters, the retrieval algorithm is performed on a large area that covers several voxels. It is suggested that the specific attenuation ratio of vertically to horizontally polarized signals can be used through a linear relationship to estimate the slope parameter of the DSD, and that the intercept parameter can also be retrieved using the estimated slope parameter. The retrieved values for both parameters closely agree with their true values.  
As the estimation of DSD parameters demands high accuracy in the specific attenuation measurements, the following sources of error in the system need to be further examined in future work. The first source of error comes from the definition of the voxels, which inevitably introduces a difference from the true field. This difference can be reduced by using a finer resolution grid, but it also means that the retrieval task will become more difficult. The second source of error is the unknown sky noise. The attenuation field is initially retrieved by assuming the sky noise is zero. Although the iterative process can update the sky noise and fine-tune the retrieval result, the final error is still significant. The third is the SNR estimation error, which can be reduced by designing good estimators but cannot be completely eliminated. We expect that the proposed approach can provide even better DSD estimations if these sources of error can be further mitigated.  
Conceptualization, D.D.H. and X.S.; methodology and simulation, X.S.; writing--original draft preparation, X.S.; writing--review and editing, D.D.H. and X.S.; supervision, D.D.H.; project administration, D.D.H. Both authors have read and agreed to the published version of the manuscript.  
This research was funded in part by Australian Research Council (ARC), under Grant DP190100786.  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.