hi
i am sorry but i think i should say some thing about the basic of antenna for all because many time i saw this question
"Do you think that i need a ground plane?"
every one know that the magnetic charge has dipole structure so every antenna imitated this and ground is the part of antenna which u connected it the negative polarity of source
so when u applied dipole structure how u can have another ground
1-when u applied a "one side dipole "structure you dont need another ground plane
2- awr result for antenna is not reliable so i suggested you to use HFSS
but u used a simple kind of antenna for this antenna u need folded kind so and u can find some model in here https://www.edaboard.com/threads/217004/