How to improve the realised gain of antenna?
What do you mean be IEEE gain? If i understood right theoretical or others design design have higher gain than your prototype? If so, do not believe others results too much. You must be sure you use same substrate (height, Er) and dimensions as in original work. Scaling other design not always work well.
You're apparently referring to the fact that your antenna is reflecting most of the transmiter power because is impedance is far-off from 50 ohm. Use an impedance matching network.
I checked the port impedance and it comes to around 50ohm at the resonant frequency.
You checked simulation result or measured real antenna impedance?
How do you measure gain? i mean gain you not satisfied with.
Your question is unclear to me, there are too many guesses can be made. You can add some photos or screenshot if you not sure how to formulate it.
Both measured and simulated data.
Gain is low in simulation as well as real measurement.
Impedance matching involves using Conjugate impedance.
Low loss requires low loss tangent dielectric at desired f.
Attenuationor gain is a combination of absorptive losses of dielectric (s12_ and reflective losses of mismatch (s11)
Gain is from reduction from isotropic spread or increase in directivity.
Tune for maximum return loss and use low loss dielectric. ( e.g. polyamide or teflon. )
i.e. feed point must be accurate and foil size may require tuning as dielectric constant may have a wide tolerance.
If gain is low and matching is good, you have built a 50 Ohm resistor instead of a patch antenna. Try using a low loss substrate.