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We report on a theoretical study of an all-dielectric microwave photonic receiver based on the optical whispering gallery mode resonator technology. We show that dielectric near-field concentrators of microwave radiation utilized with an all-dielectric whispering gallery mode microwave photonic receiver front-end result in achieving sensitivity levels comparable to the sensitivity of conventional metal-containing electronic receivers. On the other hand, a dielectric resonator antenna that relies upon conventional diffraction-limited high-Q microwave modes does not provide the required sensitivity. We find fundamental restrictions on the sensitivity of the receiver without specifying its design, and note that the receiver can be more generally considered as a photonic implementation of an electric (E-) field sensor with an electric field probe made of all-dielectric RF-transparent parts. The geometrical dimensions of the electric field probe can be much smaller than the wavelength of the measured electromagnetic field in the material. Our theoretical calculations show that the sensor allows detecting electric fields in a broad frequency range (100 Hz-20 GHz) with sensitivity exceeding 10 μV/[Hz1/2 m].