[help] designing UWB MSA

i have material with this parameter
dielectric 2.2
thickness 1.57 mm

i want to cover band 1-15 ghz on 40x40 mm substrate
i have calculated
freq center about 7 Ghz
w of tline about 5 mm for Z in 50Ω
using basic rectangular formula i got w of patch about 15mm

any advice how to design a patch to achieve S11<-10
with variety technique i have simulated rectangular ring but bw achieved about just from 5-10ghz