HELP CST: Increase bandwidth of an aperture coupled microstrip antenna ?

Hi all members,
I have been asked by my Professor to design the following antenna and try to optimize it by increasing its BW to 4 GHz..I am getting a BW of only 2GHz.

I have experimented by varying the stub length and slot length as per reading some papers but still got nothing.. Preview below;

Can anyone please guide me on how to achieve the required 4 GHZ BW without changing the slot shape. I have found one solution of using a double stubs (paper attached) with the feed but I'm unable to find the relevant formulas for it. So plz let me know the formulas for it and some other methods as well to get the desired BW.

Awaiting replies,
Regards

Try Increasing the substrate thickness. This should increase the Bandwidth.

I cannot do that as it will cause more spurious radiation..I have to keep the dimensions same as shown in the figure...

And someone plz tell me how to calculate the dimensions of H-slot with respect to 60 GHz center frequency? The only thing that I can come up is to change the slot shape in order to improve the BW...What u guyz think...?

H-slot dimensions for 60 GHz center frequency please? Formulas?