To assess the detectability of fossil aquifers using sounding radars, we investigate the VHF attenuation characteristics of the most common sedimentary layers overlaying shallow groundwater systems in hyper-arid deserts. In particular, we quantify the dielectric and scattering losses using GPR profiles acquired over mafic dunes and sand sheets in Oman, and on the karstic limestone in Qatar, which both present radar characteristics representative of substantial portions of the upper layer of most desert environments of North Africa and the Arabian Peninsula. Understanding the amplitude and spatial variability of these losses will significantly support the ongoing development of airborne and orbital VHF sounders dedicated to large-scale groundwater mapping in hyper-arid areas . Our results suggest that VHF radars with 80-100dB effective dynamic range at the surface are capable of probing the water table in hyper-arid sedimentary environments up to 70-120 m of depth, hence covering most of the shallow aquifers located in the considered area. We observe that dielectric absorption is the main loss factor in aeolian deposits, while volume scattering, controls ~60% of the overall losses in karstic environments.