Helical antennas invented by John Kraus give a circular polarized wave. They are one of the easiest to design. Find a tube with a circumference equal to one wavelength, and wrap wire in a helix spaced a quarter wavelength.The conductor width isn't of great importance in the design. The greater the number of turns the greater the directivity or antenna gain. Receiving and transmitting antennas must be wound in the same direction, since the wave is polarized.
Another interesting fact is that they can be sliced like baloney into shorter antennas and then recombined into arrays for an antenna with greater effective aperture. The only trick is to feed them all with a line with the proper characteristic impedance.
The ground plane can be a conductor with a 3/4 wavelength diameter.
G= 10.8 + 10*log10( (C/lambda)2*N*(S/lambda) ) (Note1)
Z= 150/sqrt(C/lambda) Ohm
D= lambda /PI
HPBW= 52/( (C/lambda)*sqrt(N*(S/lambda)) ), Half power beam width.
BWFN= 115/( (C/lambda)*sqrt(N*(S/lambda)) ), Beam width first nulls.
Where C is circumference, which is normally chose to be close to one wavelength.
Note1: This taken from Kraus - "Antennas for All Applications". It is commonly believed to be too optimistic by about 3dB-4dB.
Space arrays of helical antennas on a grid of sqrt(Ae).