He decided to go for rectangular and has no access to (large volume) of good dielectric, so with this in mind he has limited or no options to reduce the size of the patch.
To get reasonable antenna efficiency he can only use air (or foam) as dielectric. So he can only reduce the resonant frequency (given certain size) by cutting into the rectangular patch and/or adding vertical sections to increase the capacitance to ground (of the edges of the patch).
Riyadhe: A standard patch antenna you can see as a transmission line with a half wave electrical length. Due to radiation there are losses in that line. If you know the voltage and current distribution of the standing wave pattern (similar to that of a half wave dipole), you may know that if you move the feed to one end, the impedance at resonance increases.
There is some induction in the vertical part of the probe feed, this results in a difference in the free resonant frequency of the patch and "measured" resonant frequency. If you like, you can counteract that inductance with a series capacitor. That capacitor can be a small patch at the bottom side of the FR4, or a small isolated patch in your large patch. both techniques are used in many wide band patch antenna designs with air as dielectric.
The Wilkinson divider (and if required the diplexer), you can make on a separate PCB that is at the ground plane below the radiating patch. What is the maximum thickness of the complete antenna structure?
I assume your antenna will look at the sky (so received noise is low). To get the most out of it (in combination with a good LNA), you should optimize for good radiation efficiency as the losses in the antenna are at ambient temperature and will add thermal noise.
You may try "Compact & Broadband Microstrip Antennas" (Wong) to get design ideas.
