Antenna gain is related to the antenna type, FR4 is lossy material therefore you can not expect large gain from FR4. A single patch antenna on FR4 can produce gain of 3-5dBi. Air as a substrate can give you maximum gain for a specific design since it has no dielectric loss.

To improve gain of patch antenna, (1) antenna VSWR should be near to unity (2) Substrate material must have lowest loss. (3) Density/uniformity variation in lateria direction should not be present. (4) Beam width should be lowest (as required)

You can go for patch array to increase gain

thanks Muhammad Farhan Shafique and Amipara Manilal sir...

To improve gain, effective area of the antenna should somehow be increased using techniques like parasitic patches, meandering of edges etc. Also you may use EBG superstrates. But with a lossy material like FR4 as substate, you can never get a high gain. With FR4, even 3-5 dBi seems to be too optimistic.

thanks sir.. i understand parasitic patches improves the gain. what is meandering edges ..? how it improve the gain..? and my other question is excitation of higer order mode increase the gain of the antenna,,?

Meandering edges mean enhancing the surface area through projections and/or serrations on edge. However, excitation of higher order modes should not contribute to enhancement of gain at desired frequency.

cavity backed antennas is one option for gain improvement

Air substrate increases the bandwidth of the antenna.

Gain can improve using EBG

use shorting pins to modify characteristics of the substrate and have better gain and directivity...

Usually for a patch antenna we can achieve a maximum gain of around 6dBi. You can employ EBG structures, double layer substrates, slots, meta material structures and etc.

Basically higher gain is also possible with lower permittivity. You can insert some holes on the FR-4 substrate so that effective permittivity decreases.

Have a look on this discussion:

https://www.researchgate.net/post/Improving_the_gain_of_a_patch_antenna....

As no specific geometry is provided here, some common suggestion may be

Use low loss material for realization

Use metamaterial

Use EBG structure

Use larger area (ground plane)

But practically FR4 can offer 3-6 dBi gain

To improve gain of a patch antenna recently meandering edge is a very good and useful technology, where this meandering edge increase the effective area of the antenna. Hence gain improves.

Thank You

Anik

Article An experimental study on reduction of mutual coupling betwee...

You can use metamaterial cells around your antennas or inside of the substrate.

Conference Paper Metamaterials on antenna solutions