If Antenna impedance is Zin, antenna radiation resistance - Rrad, that Zin=Rin+j*Xin=Rrad+Rloss+j*Xin. Where: Rloss - loss resistance of antenna, Xin - reactance resistance of antenna.
Suppose that a quarter wave monopole with sufficient ground plane is connected to Vector network analyzer VNA . VNA shows return loss batter than -20 db in the desired frequency band.
What does it mean? Can i expect that the antenna will transmit power when it will be use with an amplifier (matched to 50 ohm) and 50 ohm low loss coaxial cable?
What is the importance of radiation resistance in this case?
The explanation by Marat86 has been pretty clear, I think.
A VNA S11 measurement can't discriminate real impedance Rin into Rloss and Rrad, how should it?
For a quarter wave monopole, you can assume Rloss << Rrad, so effectively all accepted power will be radiated. The importance of the radiation resistance parameter is mainly in the analysis of low efficiency antennas, e.g. electrical small ones with very low Rrad.
I would also expect Rloss < Rrad. Some resistive losses are probably introduced the matching elements like the coil. For a GSM antenna, you are mainly interested in the horizontal gain rather than total efficiency. As long as you can't find an omnidirectional antenna with higher gain, you should use it.
input impedance refers to summation loss in antenna and what we know as radiation resistance, but radiation resistance only show amount of radiation
reference : Antennas - From Theory to Practice.2008