Hello,
cause dimension are not short related to wavelength, you would need EM simulation to calculate the loop antenna (I wouldn't call it a coil) halfway accurate. The next point is , that at 1 GHz the "coil" also has considerably radiated power. Thus the equipment must either be operated at an ISM frequency (if power is within respective limits) or have a closed metallic shield.
It seems meaningful to have one "winding" only, trying to match 50 ohms impedance and use an UHF amplifier (after calculating the power requirement).
Regards,
Frank