High gain microstrip 2.4 GHz antenna

Hello.
I want to design a high gain planar antenna at the Frequency of 2.4 GHz.
the only limiting factor of this design is that the size of the antenna is limited to 30mm*40mm.
what kind of microstrip antennas or what method of increasing gain in such an antenna do you suggest?
I will be happy to get a feeback from you.
Regards.

Using the lowest possible permittivity substrate and perhaps a gain-enhancing superstrate are probably your best options.

Here is an option:

Hi

If you are not completely restricted in the z-direction, there is the option of doing stacked patch.
If it has to be completely plannar, I only know using arrays, which will make it larger.

I think the question is: what radiation pattern is required? "High gain" sounds like directional (possibly patch), PIFA is rather omnidirection. Both have advantages, it really depends on the application.

To get the maximum possible gain from a normal patch antenna the resonant length of the patch should be about λ/2 (slightly shorter due to the extended electric fringing fields).
That means the length should be about 60mm, which is more than the required dimensions.
A smaller patch than λ/2 may have less gain in a particular direction than an inverted-F antenna.

But that's for a theoretical patch with air dielectric. With actual substrates, the size would be ok.