Andrey wrote:
"I want to create horizontally polarized antenna, low profile, located
above large ground plane. And I need it to be omnidirectional (sort of)
and have sufficient gain in horizontal plane.

My frequency of interest is 900 MHz. The ground plane is a roof of a
car."

A horizontal dipole above a metal car roof is a poor choice.

Polarization choice at 900 MHz does not affect signal range.

In the horizontal plane, the direct signal broadside to the dipole is
cancelled by the reflected signal from the roof unless you elevate the
dipole by 50 cm or so at 900 MHz. That`s almost 2 wavelengths. At that
height, the omnidirectionality may not be even "sort of".

Better to use a vertical which has a signal null off its tip and maximum
radiation in the horizontal plane. This can be a collinear made of
1/2-wave sections separated by 1/4-wave stub(s) for gain. As the
wavelength is only 34 centimeters, this isn`t much of a problem. It
could be made by bending a single length of stiff wire.

Best regards, Richard Harrison, KB5WZI