UHF antenna with circular polarization

I want to design a UHF antenna for a RFID doorway reader with circular polarization of at least 30 deg. My approach was printing a yagi-uda antenna on a PCB with a coaxial port. However, it had less directivity. So an array of two yagi antennae were used and in order to get circular polarization another array was fixed in 90 deg orthogonal to the previous array. Now the pencil beam is too narrow. I need someone who can give some assistance with this. I use CST Microstripes for the design. A pic is attached as well.:addSymbol('%C2%B0',%20'vB_Editor_001')" target="_blank" rel="nofollow">

As you only try to model your antennas, please consider that models may not be good as your antennas will not operate in a free space.
Any surrounding objects, mainly conductors, will strongly affect antenna parameters.
I would recommend to do simple experiments. For your RFID communication, why not try simply a pair of half-wave dipoles linked with a 90-deg.long twin-lead, to generate a circ-pol response?
If this works, you can add to each dipole a reflector and one or two directors, and try again.
Yagi antennas generally require a clean surrounding space, to phase the incoming wavefronts so that their co-phase sum appears on the primary dipole. Such situation is not available in a RFID system installation. Modeling is only a lost time.