I think that there is no general approach which could be applied. Of course, SAR backscatter intensity is influenced by soil moisture. But it is also influenced by roughness and shape of the surface. So according to my understanding at least two things are necessary for soil moisture mapping:
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Multi-temporal data: You can not retrieve soil moisture by a single image. Variation in SAR backscatter over a longer time (at best between rainy and dry seasons) gives you the variation which can be expected.
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Field data: There is no general mathematical relationship between SAR backscatter and soil moisture. It strongly depends on the properties of the ground, the climatic setting and the mode and resolution of the sensor. I would highly disadvise from adopting regressions from studies which claim to have found this relationship, because it is strongly limited on their geographical and temporal conditions. Only when you collect own measurements at your study sites you can correlate it to your SAR images.
There is a reason that operational soil moisture retrieval is currently limited to a resolution of 500 m or 1 km.