(ask) effect of patch-shaped of antenna

dear all
can anyone tell me what is the relationship between patch-shaped of monopole antenna and bandwidth?
what is the best patch shaped to make an ultra wideband antenna?
thanks you

Just changing the shape of the simple patch antenna would not help too much improving the BW. You have to add some slots like in this example:

http://www.jpier.org/PIERC/pierc14/10.10050512.pdf