Linear polarized microstrip patch antenna - design help

hi there,

im pretty new to antenna design, still have a lot of theory to go through, so please be kind.

I have to design a linearly polarized microstrip patch antenna (rectangular) that is fed with 2 coaxial probe feeds.
The patch should be a square (L=W), so i can place 2 feeds orthogonally to each other.
That way i will hopefully be able to receive/separate the vertically and horizontally polarized signal "portion".
(thats why the antenna needs to be a square, as both signal "portions" (vertical and horizontal) are on the same frequency).
So far i have only modeled and simulated one coaxial feed, i would like to optimize the antenna first before adding the second orthogonal feed.
I want to design the patch on FR-4 substrate for 867 MHz.
I have done various calculations (found on the net and Balanis 3th edition) to get my patch width and length.
Also tried to calculate the inset position so i can match the feed to 50 Ohm.

I made a first design in CST and i just can not get rid of the "zero point" in the middle of the radiation pattern.
Some hints on what else i could try to improve the radiation pattern of the antenna would be great!
(radiation pattern is attached)
Is a good/the common radiation pattern even possible with a square shape (W=L)?
Most patch antennas i saw so far with the common radiation (like e.g. this: http://forums.radioreference.com/attachments/scann...) pattern are rectangular (W!=L).

The return loss is quite good, about -31dB at resonance frequency of 867 MHz.

I suspect the coaxial feed to be modeled so it does not result in a 50 Ohm impedance at the port, i used the following
parameters in order to modulate my coaxial probe in CST:

inner radius (pin): 0.5 mm
outer radius (coating): 2.5 mm
teflon: 2.1
What dimensions do you usually use for a coaxial feed to match to 50 Ohm?

Some help/hints are highly appreciated!
Thank you so much in advance!