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As I know,
Signals travel between signal line and ground plane as electromagnetic fields. If you assume infinite ground plane, all field lines are grounded. But with finite ground plane, you limit your signal-ground path which deteriorates your signal transmission...
I hope this helps a bit, you should search in the literature some....
Infinite ground plane is a handy concept that you often encounter in simulation software. It allows significant savings in computation time due to the assumptions that it allows.
Typically, you will not see a difference between simulation results for finite ground plane or infinite ground plane if your circuit / antenna is located far (in wavelength terms) from the boundary of the substrate that you work with.
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