Ceramic chip PIFA ground shape

Hi! Please help me with a newb question :) Antenna manufacturers provide reference PCB size for measuring their antenna performance. Now, ideal ground planes are rather large and always rectangular.

My 2 questions are:

1. Can the size of ground plane be reduced and how much is realistic (with keeping good antenna efficiency)?
2. Does ground plane must be rectangular? Can it be like part of a circle with required minimal surface area?

Any help is greatly appreciated! :)

Nobody wants large ground planes. The reason why they are used in the reference design is because the antenna performance is much worse with small ground planes. The gain drops and the resonance frequency changes.

Monopole antennas use ground as a part of the antenna. Ground plane length is therefore related to antenna performance.
Shortest possible ground plane for a certain antenna efficiency is when antenna is placed so it can see as long ground length as possible, typical when antenna is placed in a corner of PCB.
Antenna demo-board have ideal complete ground planes and no RF absorbing components near antenna, such as battery or LCD displays. That is factors that also affect where to place antenna on a PCB for best performance.
Try to design PCB with a lossless ground plane. Reduced PCB length can also make antenna impedance matching much harder, especially for wide band antennas.
Antenna impedance in a short ground plane becomes more easily detuned due to if it is placed in free space relative hand-held.
A recommended minimum ground-plane length is lambda/4 relative actual PCB dielectric constant.
Below that length and antenna is less effective and more easily detuned. Both results in increased TX power for a certain coverage which then require increased battery size for a certain run time, which makes final product bigger and heavier.
Alternative antennas, not so much depending on ground plane are loop and dipole antennas.
If keeping antenna size as small as possible is more important then its efficiency can minimal ceramic resonators be used as antennas. Such resonators exist for example for 2.4 GHz, with size 2*4 mm.
Loop antennas type 433 MHz can be integrated in outer edge of PCB. Practical occupied antenna volume can then be made minimal.