Naturalization means scaling down the size of the device. So, antenna miniaturization means to make the size of the antenna smaller. Normally the size of the antenna is about lambda/2, with lambda is the wavelength. Instead one can use short whip antennas or loop antenna. As the operating frequency increases the antenna size becomes scaled down proportional to frequency. Microstrip antennas can be also made smaller and more compact by slotting the patches and creating defective background structures. As these methods are diverse, so, you can consult the specialized literature to downsizing the antennas while keeping the radiated power consatnt as possible.
As an example of miniaturization please refer to he paper: Article Design of a Planar MIMO Antenna for LTE-Advanced
and the paper: Article Design of a Compact Dual Band Microstrip Antenna for Ku-Band...
and the paper: Article Mutual Coupling Reduction of MIMO Antennas using Parasitic E...
Miniaturization of antenna is to reduce the dimensions of the antenna keeping the resonant frequency constant, or increasing the resonant frequency keeping the overall size of antenna constant. Use of higher dielectric constant is example of the first kind, and creating slots in patches, defected ground is example of second. The relationship among frequency, dimensions and permittivity can provide the mathematical aspect of it.
What about the relationship among frequency, dimensions and permittivity regarding miniaturization of antenna? Can you suggest me some papers regarding that?
You can find it in any book on microstrip antenna e.g. Antenna handbook by Ramesh Garg et al, Antenna by Balanis, Modern antenna design by Miligan, Antennas by JD krauss