I don't think it's possible to stop the cheating, technically. I also believe it has sadly, forever ruined online gaming. And it's not just FPS's that suffer from this, but that's probably the worst hit genre.
I stopped buying FPS's that don't have an incredible single player component, years ago. You can't play a FPS online without running in to cheaters. If you watch pro-gamers playing on Twitch, they run in to them all the time. It's not a "paranoia" thing, which for some people, they do like to call people who are good at the game as cheaters. Rather, it's just clear cheating with aimbots, wall hacks, etc. You can watch the "killcam" replays and see people shooting people across the map who are not visible. Snapping to their exact direction, firing and then repeating. Shooting through walls at targets not visible.
FPS was always my favorite genre. Long gone are the days in the 90's when you could join a server and expect there to not be people cheating. Some did, but it wasn't as easy as it is today where every idiot with an inferiority complex pays for a subscription and activates it with a couple clicks of the mouse.