Problem with ground effect on gain pattern

hi
i've designed an antenna that supposed to have omni directional gain about 3 db, i tried IFA, PIFA , and any other kind of antenna,i've seen this results:
1- when the ground plane is small pattern is omni but gain is below 1 db
2- when the ground plane is big gain is about 3 db but pattern is directional
then how can i have both omni directional pattern and maximum gain of 3 db?
thanks

I guess, you are talking about planar (2-D) structures and want an omnidirectional characteristic in the XY plane? Please clarify.

A true omnidirectional charcateristic could be achieved with a circular polarized structure, but not with 3 dB gain.

first of all thanks for your consideration,
actually yes , all of antennas are planer in x-y plane and antenna should be small, polarization should be linear, what do you suggest?

If you have an antenna with a ground plane, the ground plane reflects energy and thus you get a higher direction and gain.
If you have a perfect omnidirectional antenna you have an gain of 1dBi. You get gain when your antenna focus the radiation.

you're right, actually my supervisor wanna omni-directional gain of 2 db with beamwidth of 100 degree, is that posible?